tensor-optix 1.14.3

Autonomous training loop for any sequential learning model — PPO, DQN, SAC, TD3, Rainbow DQN, Recurrent PPO for TensorFlow, PyTorch, and JAX/Flax; distributed async actor-learner (IMPALA + V-trace)

tensor-optix

Autonomous training loop for any sequential learning model - built-in PPO, DQN, SAC, TD3, Rainbow DQN, and Recurrent PPO for TensorFlow, PyTorch, and JAX/Flax.

---

About

tensor-optix is a framework-agnostic autonomous training loop. It owns evaluation, checkpointing, hyperparameter tuning, policy evolution, and ensemble management for any model that can act and learn from sequential data - reinforcement learning agents, online forecasters, trading systems, robotics controllers, or any custom architecture that fits the six-method BaseAgent interface.

The framework has zero assumptions about your model, algorithm, or framework. No RL-specific logic exists in the core loop - it works equally well with PPO, a custom evolutionary strategy, a supervised sequence model, or anything else. For RL specifically, it ships with production-ready implementations of PPO, DQN, SAC, TD3, Rainbow DQN, and Recurrent PPO for TensorFlow and PyTorch, plus a JAX/Flax PPO adapter, so you can start training without writing a single algorithm line.

The system never stops at a fixed episode count. It detects convergence through exponential backoff, spawns policy variants when it plateaus, and uses both training and validation signals to drive every decision - not training alone.

New in 1.13.0:

• Dale's Law — biologically-faithful excitatory/inhibitory neuron types. Set cell_type="excitatory" or "inhibitory" on any neuron; NeuronGraph.enforce_dale() clamps outgoing weights to the correct sign after every optimizer step. GraphAgent calls this automatically.
• BrainNetwork — modular brain regions: multiple named NeuronGraph subgraphs connected by sparse, learnable inter-region pathways with configurable delays. Each region can carry its own TopologyController. Forward pass runs regions in topological order. brain.add_pathway("sensory", "executive", n_connections=8, delay=1).
• HebbianHook — local Hebbian learning running alongside PPO. Accumulates h_pre × h_post co-activation products across a full episode, then applies Δw = η·mean(h_pre·h_post) − λ·w to every edge. Works on NeuronGraph directly or all regions of a BrainNetwork via HebbianHook.from_brain(brain). Respects Dale's Law automatically.
• NeuromodulatorSignal — global parameter modulation driven by RegimeDetector. Translates "trending" / "ranging" / "volatile" regimes into biologically-analogous changes: dopamine (consolidate on improvement), norepinephrine (explore on volatility), acetylcholine (expand topology on plateau). Modulates HebbianHook.hebbian_lr, GraphAgent entropy coefficient, and TopologyController grow/prune thresholds simultaneously.

New in 1.12.0:

• neuroevo - free-form topology evolution: NeuronGraph, GraphAgent, TopologyController. Grow, prune, split, and merge neurons at runtime with function-preserving operations. Variable-delay recurrent edges. Hooks into the existing loop via LoopCallback on COOLING state. pip install tensor-optix[neuroevo]

New in 1.9.0:

• Distributed async actor-learner (IMPALA + V-trace) - N actors run in parallel POSIX shared-memory processes, learner applies V-trace off-policy correction, 4× sample throughput on CPU
• JAX/Flax PPO adapter - FlaxPPOAgent and FlaxAgent base class; XLA-compiled updates, optax optimisers, pickle-safe weight serialisation; convergence-parity with TorchPPOAgent
• Live terminal dashboard - RichDashboardCallback renders a real-time Rich panel (score sparkline, hyperparams, loop state) with zero extra dependencies

Core philosophy: We own the loop. You own the model.

---

Real-World Use Cases

tensor-optix was designed for production environments where training can't be babysat. Here are the patterns it solves well.

Algorithmic Trading

A trading agent faces non-stationary markets: a strategy that works in a trending regime collapses in a ranging one. tensor-optix handles this via live streaming, train/val split across time, and automatic rollback when out-of-sample performance degrades.

from tensor_optix import RLOptimizer, BatchPipeline, PolicyManager
from tensor_optix import LivePipeline

# Train on rolling window, validate on the next period (never seen during training)
train_pipeline = LivePipeline(data_source=MarketFeed(), agent=agent,
                               episode_boundary_fn=LivePipeline.every_n_seconds(300))
val_pipeline   = LivePipeline(data_source=MarketFeed(offset="1d"), agent=agent,
                               episode_boundary_fn=LivePipeline.every_n_seconds(300))

opt = RLOptimizer(
    agent=agent,
    pipeline=train_pipeline,
    val_pipeline=val_pipeline,        # all checkpoint + rollback decisions use val score
    rollback_on_degradation=True,     # restore best weights the moment val drops
    checkpoint_score_fn=lambda a: backtest(a, held_out_period),  # external scoring
)

pm = PolicyManager(registry, max_spawns=4)
cb = pm.as_callback(agent, agent_factory=make_agent)
cb.set_stop_fn(opt.stop)
opt.add_callback(cb)
opt.run()
# When market regime shifts, DORMANT fires → MetaController spawns a variant
# with perturbed hyperparams → ensemble diversifies across regime hypotheses

What tensor-optix provides here: val-driven checkpointing prevents saving a model that overfits recent price action; rollback catches regime breaks before they compound; policy spawning creates ensemble variants that collectively cover multiple regimes.

---

Robotics & Continuous Control

Locomotion tasks (BipedalWalker, MuJoCo Ant, custom robot) collapse mid-training when the critic diverges. A fixed training loop has no recovery path. tensor-optix detects the collapse and rolls back automatically.

from tensor_optix.algorithms.torch_sac import TorchSACAgent
from tensor_optix.algorithms.torch_td3 import TorchTD3Agent

# SAC for stochastic envs, TD3 for dense-reward deterministic locomotion
agent = TorchSACAgent(actor=actor, critic1=c1, critic2=c2, action_dim=action_dim,
                      actor_optimizer=..., critic_optimizer=..., alpha_optimizer=...,
                      hyperparams=hp, device="auto")

opt = RLOptimizer(
    agent=agent,
    pipeline=pipeline,
    rollback_on_degradation=True,
    dormant_threshold=8,              # recover fast  -  off-policy collapse is sharp
    min_episodes_before_dormant=30,   # let Q-function stabilise before evaluating plateau
    checkpoint_score_fn=lambda a: eval_deterministic(a, env_id, n_eps=5, seed=42),
)
pm = PolicyManager(registry, max_spawns=3)
cb = pm.as_callback(agent, agent_factory=make_agent)
cb.set_stop_fn(opt.stop)
opt.run()

What tensor-optix provides here: collapse detection + rollback replaces the "restart and hope" workflow; adaptive SPSA tunes tau and gamma online as the Q-function matures; external checkpoint_score_fn avoids saving mid-collapse snapshots.

---

Game AI & Atari

Discrete action games benefit from sample-efficient algorithms. Rainbow DQN with all six improvements is one line. The async actor-learner scales throughput linearly with CPU cores.

from tensor_optix.algorithms.torch_rainbow_dqn import TorchRainbowDQNAgent, RainbowQNetwork
from tensor_optix.distributed import AsyncActorLearner

# Option A: Rainbow DQN  -  best sample efficiency for discrete action games
q_net = RainbowQNetwork(obs_dim=obs_dim, n_actions=n_actions,
                         hidden_size=256, n_atoms=51, v_min=-10.0, v_max=10.0)
agent = TorchRainbowDQNAgent(q_network=q_net, n_actions=n_actions,
                              optimizer=torch.optim.Adam(q_net.parameters(), lr=6.25e-5),
                              hyperparams=hp, n_atoms=51, v_min=-10.0, v_max=10.0)

# Option B: IMPALA async actor-learner  -  4× throughput, same convergence
learner = AsyncActorLearner(
    actor=actor, critic=critic, optimizer=optimizer,
    env_factory=lambda: gym.make("ALE/Pong-v5"),
    n_actors=8, trajectory_len=64, seed=0,
)
stats = learner.run(max_steps=10_000_000)
print(f"{stats['steps_per_second']:.0f} steps/s")

What tensor-optix provides here: Rainbow handles the exploration/exploitation problem across sparse-reward levels; the async learner saturates CPU cores without any infrastructure code; convergence detection stops training once the agent has solved the game rather than running a fixed 10M step budget.

---

Industrial & HVAC Control

Control systems have slow, expensive simulators and no tolerance for parameter drift. SPSA adapts hyperparams online in just two episodes per update - no grid search needed.

class HVACAgent(BaseAgent):
    """Custom control agent  -  tensor-optix owns the loop, you own the policy."""
    def act(self, obs): ...
    def learn(self, episode_data): ...
    def get_hyperparams(self): ...
    def set_hyperparams(self, hp): ...
    def save_weights(self, path): ...
    def load_weights(self, path): ...

opt = RLOptimizer(
    agent=HVACAgent(),
    pipeline=BatchPipeline(env=HVACSimulator(), agent=agent, window_size=96),  # 96 = 8h @ 5min steps
    optimizer=SPSAOptimizer(param_bounds={
        "setpoint_gain":  (0.1, 2.0),
        "integral_coef":  (0.01, 0.5),
        "comfort_weight": (0.5, 5.0),
    }),
    checkpoint_score_fn=lambda a: simulate_week(a, seed=0),  # week-long holdout eval
    verbose=True,
)
opt.run()

What tensor-optix provides here: SPSA tunes control parameters with only 2 simulator rollouts per gradient estimate - far cheaper than grid search over a slow HVAC sim; checkpoint scoring on a full held-out week prevents saving a policy that game-theorises the training schedule.

---

Partially Observable Environments

Environments where the agent can't see the full state (POMDPs, multi-step signal processing, robotics with proprioception only) need memory. Recurrent PPO carries LSTM hidden state across steps automatically.

from tensor_optix.algorithms.torch_recurrent_ppo import TorchRecurrentPPOAgent

agent = TorchRecurrentPPOAgent(
    obs_dim=obs_dim,
    n_actions=n_actions,
    hidden_size=128,       # LSTM hidden dimension
    hyperparams=hp,
    device="auto",
)

# act() and learn() carry hidden state internally  -  same interface as all other agents
pipeline = BatchPipeline(env=gym.make("PartiallyObservableMaze-v0"),
                          agent=agent, window_size=512)
opt = RLOptimizer(agent=agent, pipeline=pipeline)
opt.run()

What tensor-optix provides here: hidden state is stored per step in the rollout buffer and reset at episode boundaries automatically - no BPTT truncation bookkeeping; the same RLOptimizer loop, callbacks, and PolicyManager work unchanged with recurrent agents.

---

Requirements: Python >= 3.11, Gymnasium >= 1.0, NumPy >= 1.24. The core loop, PolicyManager, and all ensemble/evolution logic are framework-free. Install the ML framework extra(s) that match your platform - do not rely on the bare pip install tensor-optix to pull in a framework.

---

Installation by platform

Linux / WSL2 - NVIDIA GPU (CUDA)

# TensorFlow with CUDA
pip install tensor-optix[tensorflow-gpu,cuda]

# PyTorch with CUDA 12.8
pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu128
pip install tensor-optix[torch]

# Both frameworks + CUDA tools
pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu128
pip install tensor-optix[tensorflow-gpu,torch,cuda]

Linux / WSL2 - CPU only

# TensorFlow (CPU)
pip install tensor-optix[tensorflow]

# PyTorch (CPU)
pip install tensor-optix[torch]

# Both frameworks
pip install tensor-optix[tensorflow,torch]

Windows - NVIDIA GPU (CUDA)

Note: tensorflow[and-cuda] is not supported on native Windows. Use the CPU TensorFlow build or run under WSL2 for GPU TensorFlow support.

# PyTorch with CUDA 12.8 (cmd / PowerShell)
pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu128
pip install tensor-optix[torch]

# TensorFlow CPU on Windows
pip install tensor-optix[tensorflow]

Windows - CPU only

pip install tensor-optix[tensorflow,torch]

JAX / Flax (any platform)

pip install tensor-optix[jax]

Environment extras (Atari, MuJoCo, Box2D)

pip install tensor-optix[atari]
pip install tensor-optix[mujoco]
pip install tensor-optix[box2d]   # also requires: apt install swig  /  brew install swig

Everything (CPU builds, all environments)

pip install tensor-optix[all]

---

Benchmarks

Results

All runs: 3 seeds, same architecture, same starting hyperparameters.
Baseline = fixed step budget, no auto-tuning. tensor-optix = autonomous loop with AdaptiveOptimizer.

CartPole-v1 - DQN (discrete)

Metric	Baseline	tensor-optix	Δ
Final eval score	241.9	499.3	+106%
Solved (≥ 475)	2 / 3	3 / 3

Acrobot-v1 - PPO (discrete)

Metric	Baseline	tensor-optix	Δ
Steps to threshold	47.8k ±9.7k	34.1k ±9.7k	−29%
Final eval score	−78.3 ±5.9	−74.8 ±0.9	+4%
Score variance	±5.9	±0.9	−85%
Solved (≥ −100)	3 / 3	3 / 3

The variance reduction on Acrobot (±5.9 → ±0.9) reflects the rollback and adaptive optimizer stabilising training across seeds that vanilla PPO handles inconsistently.

Run it yourself

# Quick  -  CartPole + Acrobot, 1 seed each
uv run python benchmarks/benchmark.py --envs cartpole acrobot --seeds 0

# Full  -  all 5 environments, 3 seeds
uv run python benchmarks/benchmark.py

Additional flags:

--optix-only       skip baseline, run tensor-optix only
--no-plot          skip matplotlib chart
--verbose          print per-episode output
--seeds 0 1 2      override seeds

---

Quick Start

TensorFlow PPO

import tensorflow as tf
import gymnasium as gym
from tensor_optix import RLOptimizer, TFPPOAgent, BatchPipeline, HyperparamSet

actor = tf.keras.Sequential([
    tf.keras.layers.Input(shape=(4,)),
    tf.keras.layers.Dense(64, activation="tanh"),
    tf.keras.layers.Dense(64, activation="tanh"),
    tf.keras.layers.Dense(2),                    # logits, one per action
])
critic = tf.keras.Sequential([
    tf.keras.layers.Input(shape=(4,)),
    tf.keras.layers.Dense(64, activation="tanh"),
    tf.keras.layers.Dense(64, activation="tanh"),
    tf.keras.layers.Dense(1),                    # scalar value estimate
])

agent = TFPPOAgent(
    actor=actor,
    critic=critic,
    optimizer=tf.keras.optimizers.Adam(3e-4),
    hyperparams=HyperparamSet(params={
        "learning_rate": 3e-4,
        "clip_ratio":    0.2,
        "entropy_coef":  0.01,
        "vf_coef":       0.5,
        "gamma":         0.99,
        "gae_lambda":    0.95,
        "n_epochs":      10,
        "minibatch_size": 64,
    }, episode_id=0),
)

env      = gym.make("CartPole-v1")
pipeline = BatchPipeline(env=env, agent=agent, window_size=2048)

opt = RLOptimizer(agent=agent, pipeline=pipeline)
opt.run()  # runs until convergence, auto-tunes hyperparams, saves best checkpoint

PyTorch PPO

import torch
import torch.nn as nn
import gymnasium as gym
from tensor_optix import RLOptimizer, BatchPipeline, HyperparamSet
from tensor_optix.algorithms.torch_ppo import TorchPPOAgent

obs_dim, n_actions = 4, 2

actor  = nn.Sequential(nn.Linear(obs_dim, 64), nn.Tanh(), nn.Linear(64, n_actions))
critic = nn.Sequential(nn.Linear(obs_dim, 64), nn.Tanh(), nn.Linear(64, 1))

agent = TorchPPOAgent(
    actor=actor,
    critic=critic,
    optimizer=torch.optim.Adam(
        list(actor.parameters()) + list(critic.parameters()), lr=3e-4
    ),
    hyperparams=HyperparamSet(params={
        "learning_rate": 3e-4, "clip_ratio": 0.2, "entropy_coef": 0.01,
        "gamma": 0.99, "gae_lambda": 0.95, "n_epochs": 10, "minibatch_size": 64,
    }, episode_id=0),
)

pipeline = BatchPipeline(env=gym.make("CartPole-v1"), agent=agent, window_size=2048)
opt = RLOptimizer(agent=agent, pipeline=pipeline)
opt.run()

---

Built-in Algorithms

PPO - Proximal Policy Optimization

Discrete action spaces. Actor + critic are separate models.

from tensor_optix.algorithms.tf_ppo import TFPPOAgent        # TensorFlow
from tensor_optix.algorithms.torch_ppo import TorchPPOAgent  # PyTorch (auto-detects CUDA)

What it implements:

• GAE-λ advantage estimation with episode-boundary handling
• Clipped surrogate objective: L = min(r·A, clip(r, 1−ε, 1+ε)·A)
• Value function loss (MSE) with configurable coefficient
• Entropy bonus for exploration regularization
• n epochs of shuffled minibatch gradient descent per rollout
• Global gradient norm clipping

Hyperparams exposed to the tuner:

Key	Default	Tune range	Notes
learning_rate	3e-4	1e-4 – 3e-3	Log-scale; most sensitive param - use log_float in TrialOrchestrator
clip_ratio	0.2	0.1 – 0.3	Higher = larger policy steps; >0.3 destabilises training
entropy_coef	0.01	0.0 – 0.05	Keep ≥ 0.001 to prevent premature entropy collapse
vf_coef	0.5	0.25 – 1.0	Weight of value loss relative to policy loss
gamma	0.99	0.95 – 0.999	Lower for short-horizon or dense-reward tasks
gae_lambda	0.95	0.9 – 1.0	0 = pure TD bootstrap, 1 = full Monte Carlo return
n_epochs	10	3 – 15	More epochs = better sample use; too many = rollout overfitting
minibatch_size	64	32 – 256	Larger = less gradient noise, better GPU utilisation
max_grad_norm	0.5	0.3 – 1.0	Raise if gradients are consistently hitting the clip

---

PPO Continuous - Gaussian Policy (Continuous Actions)

Continuous action spaces. Squashed Gaussian actor with learned log-std.

from tensor_optix.algorithms.tf_ppo_continuous import TFGaussianPPOAgent        # TensorFlow
from tensor_optix.algorithms.torch_ppo_continuous import TorchGaussianPPOAgent  # PyTorch

What it adds over discrete PPO:

• Gaussian policy head outputs [mean || log_std] - action_dim * 2 outputs
• Actions sampled as a = tanh(mean + std * ε), squashed to (−1, 1)
• Log-prob corrected for tanh squashing (numerically stable)
• action_dim required at construction

import torch.nn as nn
from tensor_optix.algorithms.torch_ppo_continuous import TorchGaussianPPOAgent

obs_dim, act_dim = 8, 2   # e.g. LunarLanderContinuous-v3

actor  = nn.Sequential(nn.Linear(obs_dim, 64), nn.Tanh(), nn.Linear(64, act_dim * 2))
critic = nn.Sequential(nn.Linear(obs_dim, 64), nn.Tanh(), nn.Linear(64, 1))

agent = TorchGaussianPPOAgent(
    actor=actor, critic=critic,
    optimizer=torch.optim.Adam(
        list(actor.parameters()) + list(critic.parameters()), lr=3e-4
    ),
    action_dim=act_dim,
    hyperparams=HyperparamSet(params={
        "learning_rate": 3e-4, "clip_ratio": 0.2, "entropy_coef": 0.01,
        "gamma": 0.99, "gae_lambda": 0.95, "n_epochs": 10, "minibatch_size": 64,
    }, episode_id=0),
)

---

DQN - Deep Q-Network

Discrete action spaces. Single Q-network; target network updated periodically.

from tensor_optix.algorithms.tf_dqn import TFDQNAgent        # TensorFlow
from tensor_optix.algorithms.torch_dqn import TorchDQNAgent  # PyTorch (auto-detects CUDA)

What it implements:

• Experience replay buffer (circular)
• Target network with hard periodic updates
• Epsilon-greedy exploration with multiplicative decay
• TD loss: MSE(Q(s,a), r + γ max Q_target(s',·))

q_net = tf.keras.Sequential([
    tf.keras.layers.Input(shape=(obs_dim,)),
    tf.keras.layers.Dense(64, activation="relu"),
    tf.keras.layers.Dense(n_actions),    # Q-values for all actions
])

agent = TFDQNAgent(
    q_network=q_net,
    n_actions=n_actions,
    optimizer=tf.keras.optimizers.Adam(3e-4),
    hyperparams=HyperparamSet(params={
        "learning_rate": 3e-4, "gamma": 0.99,
        "epsilon": 1.0, "epsilon_min": 0.05, "epsilon_decay": 0.995,
        "batch_size": 64, "target_update_freq": 100,
        "replay_capacity": 100_000,
        "per_alpha": 0.0,        # 0 = uniform replay; 1 = full prioritized
        "per_beta":  0.4,        # IS correction exponent
        "n_step":    1,          # multi-step TD return length
    }, episode_id=0),
)

---

SAC - Soft Actor-Critic

Continuous action spaces. Squashed Gaussian actor, twin critics, auto-entropy tuning.

from tensor_optix.algorithms.tf_sac import TFSACAgent        # TensorFlow
from tensor_optix.algorithms.torch_sac import TorchSACAgent  # PyTorch (auto-detects CUDA)

What it implements:

• Reparameterized squashed Gaussian: a = tanh(μ + σε), actions ∈ (−1, 1)
• Clipped double-Q (twin critics) to reduce overestimation bias
• Soft Polyak target network updates: θ_tgt ← τθ + (1−τ)θ_tgt
• Auto-entropy temperature: learnable log_α, target entropy = −dim(A)
• Off-policy experience replay

action_dim = 6   # e.g. MuJoCo Ant

actor   = tf.keras.Sequential([        # obs → [mean || log_std], shape [batch, 2*action_dim]
    tf.keras.layers.Input(shape=(obs_dim,)),
    tf.keras.layers.Dense(256, activation="relu"),
    tf.keras.layers.Dense(action_dim * 2),
])
critic1 = tf.keras.Sequential([        # [obs || action] → Q-value
    tf.keras.layers.Input(shape=(obs_dim + action_dim,)),
    tf.keras.layers.Dense(256, activation="relu"),
    tf.keras.layers.Dense(1),
])
critic2 = tf.keras.Sequential([...])   # independent weights (twin-Q)

agent = TFSACAgent(
    actor=actor, critic1=critic1, critic2=critic2,
    action_dim=action_dim,
    actor_optimizer=tf.keras.optimizers.Adam(3e-4),
    critic_optimizer=tf.keras.optimizers.Adam(3e-4),
    alpha_optimizer=tf.keras.optimizers.Adam(3e-4),
    hyperparams=HyperparamSet(params={
        "learning_rate": 3e-4, "gamma": 0.99,
        "tau": 0.005, "batch_size": 256,
        "replay_capacity": 1_000_000,
    }, episode_id=0),
)

---

TD3 - Twin Delayed Deep Deterministic Policy Gradient

Continuous action spaces. Deterministic actor, twin critics, target policy smoothing, delayed actor updates.

from tensor_optix.algorithms.torch_td3 import TorchTD3Agent  # PyTorch

What it adds over SAC:

• Deterministic policy (no entropy term) - lower variance, better on dense-reward locomotion
• Target policy smoothing: adds clipped Gaussian noise to target actions to prevent value over-fitting to narrow peaks
• Delayed actor updates: critic updated every step, actor updated every policy_delay steps (default 2)
• Twin-Q minimization over both critics (same as SAC)

import torch.nn as nn
from tensor_optix.algorithms.torch_td3 import TorchTD3Agent

obs_dim, act_dim = 24, 4   # e.g. BipedalWalker-v3

actor   = nn.Sequential(nn.Linear(obs_dim, 256), nn.ReLU(), nn.Linear(256, act_dim), nn.Tanh())
critic1 = nn.Sequential(nn.Linear(obs_dim + act_dim, 256), nn.ReLU(), nn.Linear(256, 1))
critic2 = nn.Sequential(nn.Linear(obs_dim + act_dim, 256), nn.ReLU(), nn.Linear(256, 1))

agent = TorchTD3Agent(
    actor=actor, critic1=critic1, critic2=critic2,
    action_dim=act_dim,
    actor_optimizer=torch.optim.Adam(actor.parameters(), lr=3e-4),
    critic_optimizer=torch.optim.Adam(
        list(critic1.parameters()) + list(critic2.parameters()), lr=3e-4
    ),
    hyperparams=HyperparamSet(params={
        "learning_rate": 3e-4, "gamma": 0.99, "tau": 0.005,
        "batch_size": 256, "policy_delay": 2,
        "target_noise": 0.2, "noise_clip": 0.5,
        "expl_noise": 0.1, "replay_capacity": 1_000_000,
    }, episode_id=0),
)

---

Rainbow DQN

Discrete action spaces. Combines six DQN improvements: Double Q, Dueling networks, Prioritized Experience Replay, n-step returns, Noisy Networks, and Distributional RL.

from tensor_optix.algorithms.torch_rainbow_dqn import TorchRainbowDQNAgent, RainbowQNetwork

What it implements (all six Rainbow components):

• Double Q - target actions from online net, values from target net (reduces overestimation)
• Dueling - separate value and advantage streams; advantage-mean subtraction prevents identifiability issues
• PER - SumTree prioritized replay with IS-weight correction; priority exponent α, correction exponent β
• n-step - multi-step bootstrap targets; trades variance for bias, dramatically speeds up sparse-reward environments
• Noisy Nets - factorized Gaussian noise on linear layers replaces ε-greedy; exploration driven by learned uncertainty
• Categorical / C51 - distributional Q as a 51-atom categorical distribution; KL loss instead of MSE

obs_dim, n_actions = 8, 4

q_net = RainbowQNetwork(obs_dim=obs_dim, n_actions=n_actions,
                         hidden_size=256, n_atoms=51,
                         v_min=-10.0, v_max=10.0)

agent = TorchRainbowDQNAgent(
    q_network=q_net, n_actions=n_actions,
    optimizer=torch.optim.Adam(q_net.parameters(), lr=6.25e-5),
    hyperparams=HyperparamSet(params={
        "learning_rate": 6.25e-5, "gamma": 0.99,
        "n_step": 3,            # multi-step return length
        "per_alpha": 0.5,       # PER priority exponent
        "per_beta": 0.4,        # IS-weight correction exponent
        "batch_size": 32,
        "target_update_freq": 1000,
        "replay_capacity": 100_000,
    }, episode_id=0),
    n_atoms=51, v_min=-10.0, v_max=10.0,
)

---

Recurrent PPO - LSTM Actor-Critic

Discrete action spaces. Hidden state carried across episode steps; handles partial observability and sequence-structured tasks.

from tensor_optix.algorithms.torch_recurrent_ppo import TorchRecurrentPPOAgent

What it adds over standard PPO:

• LSTMActorCritic module - shared LSTM trunk, separate actor/critic heads
• Hidden state (h, c) carried across episode steps and reset at episode boundaries
• Rollout buffer stores per-step hidden states - no BPTT truncation artifacts
• Same clipped surrogate objective as PPO; hidden state dimension configurable

from tensor_optix.algorithms.torch_recurrent_ppo import TorchRecurrentPPOAgent

obs_dim, n_actions, hidden_size = 4, 2, 64

agent = TorchRecurrentPPOAgent(
    obs_dim=obs_dim,
    n_actions=n_actions,
    hidden_size=hidden_size,
    hyperparams=HyperparamSet(params={
        "learning_rate": 3e-4, "clip_ratio": 0.2, "entropy_coef": 0.01,
        "vf_coef": 0.5, "gamma": 0.99, "gae_lambda": 0.95,
        "n_epochs": 4, "minibatch_size": 64,
    }, episode_id=0),
    device="auto",
)
# act() carries hidden state internally  -  same BaseAgent interface
action = agent.act(obs)

---

JAX / Flax Adapter

Discrete action spaces. FlaxAgent base and FlaxPPOAgent implement the same BaseAgent interface as all PyTorch/TF algorithms using Flax NNX + optax.

# pip install tensor-optix[jax]
from tensor_optix.adapters.jax.flax_agent    import FlaxAgent
from tensor_optix.adapters.jax.flax_evaluator import FlaxEvaluator
from tensor_optix.algorithms.flax_ppo         import FlaxPPOAgent

Key properties:

• nnx.value_and_grad differentiates through the combined actor+critic in one pass - no separate backward calls per head
• nnx.Optimizer(model, optax.adam(lr), wrt=nnx.Param) - only trainable Param variables are updated
• Weights serialised as a plain nested dict via nnx.to_pure_dict(nnx.state(model)) and restored with nnx.replace_by_pure_dict + nnx.update - pickle-safe, version-stable
• Convergence-parity with TorchPPOAgent on CartPole-v1 (within 10%, verified by test suite)

import gymnasium as gym
from tensor_optix import HyperparamSet
from tensor_optix.algorithms.flax_ppo import FlaxPPOAgent

env = gym.make("CartPole-v1")
obs_dim  = env.observation_space.shape[0]   # 4
n_actions = env.action_space.n              # 2

agent = FlaxPPOAgent(
    obs_dim=obs_dim,
    n_actions=n_actions,
    hyperparams=HyperparamSet(params={
        "learning_rate": 3e-4, "clip_ratio": 0.2, "entropy_coef": 0.01,
        "vf_coef": 0.5, "gamma": 0.99, "gae_lambda": 0.95,
        "n_epochs": 10, "minibatch_size": 64,
    }, episode_id=0),
    hidden_size=64,
    seed=0,
)

# Drop-in with any existing tensor-optix loop:
from tensor_optix import BatchPipeline, RLOptimizer
from tensor_optix.adapters.jax.flax_evaluator import FlaxEvaluator

pipeline = BatchPipeline(env=env, agent=agent, window_size=2048)
opt = RLOptimizer(agent=agent, pipeline=pipeline, evaluator=FlaxEvaluator())
opt.run()

---

Distributed Training - Async Actor-Learner (IMPALA + V-trace)

IMPALA-style asynchronous actor-learner for PyTorch discrete policies. N actor processes collect trajectories in parallel using POSIX shared memory - learner weight updates are instantly visible to all actors with zero serialization overhead.

# pip install tensor-optix[torch]
from tensor_optix.distributed import AsyncActorLearner, compute_vtrace_targets

Architecture:

flowchart LR
    SM["Shared Memory\nactor weights\ncritic weights\n(share_memory=True)"]

    subgraph Actors["Actor Processes (×N)"]
        A0[Actor 0]
        A1[Actor 1]
        AN[Actor N]
    end

    subgraph Learner["Learner (main process)"]
        VT[V-trace targets]
        GU[gradient update]
        OS[optimizer.step]
    end

    SM -->|lock-free reads| Actors
    A0 -->|trajectory| VT
    A1 -->|trajectory| VT
    AN -->|trajectory| VT
    VT --> GU --> OS -->|write new weights| SM

Off-policy correction (V-trace):

ρ̄_t = min(ρ̄, π_θ(a_t|s_t) / π_μ(a_t|s_t))   ← clipped IS weight
v_t  = V(s_t) + δ_t + γ c̄_t (v_{t+1} − V(s_{t+1}))

Actors may lag behind the current learner policy (μ ≠ θ). V-trace corrects for this staleness so the learner can safely train on trajectories from any actor generation.

Throughput: 4 actors achieve ≥ 2× single-actor sample throughput in tests on CartPole-v1.

import torch.nn as nn
import gymnasium as gym
from tensor_optix.distributed import AsyncActorLearner

obs_dim, n_actions = 4, 2

actor  = nn.Sequential(nn.Linear(obs_dim, 64), nn.Tanh(), nn.Linear(64, n_actions))
critic = nn.Sequential(nn.Linear(obs_dim, 64), nn.Tanh(), nn.Linear(64, 1))
optimizer = torch.optim.Adam(
    list(actor.parameters()) + list(critic.parameters()), lr=3e-4
)

learner = AsyncActorLearner(
    actor=actor,
    critic=critic,
    optimizer=optimizer,
    env_factory=lambda: gym.make("CartPole-v1"),
    n_actors=4,
    trajectory_len=64,
    gamma=0.99,
    rho_bar=1.0,   # V-trace IS clip ρ̄
    c_bar=1.0,     # V-trace trace clip c̄
    entropy_coef=0.01,
    seed=0,
)

stats = learner.run(max_steps=500_000)
# stats: {total_steps, total_updates, steps_per_second, elapsed}
print(f"Throughput: {stats['steps_per_second']:.0f} steps/s")

Platform note: uses mp.get_context("fork") - designed for Linux. On macOS or Windows (spawn start method), pass picklable factory callables.

---

Live Terminal Dashboard

RichDashboardCallback renders a live terminal panel during training using the Rich library.

# pip install rich   (optional dependency)
from tensor_optix.callbacks import RichDashboardCallback

opt = RLOptimizer(
    agent=agent,
    pipeline=pipeline,
    callbacks=[RichDashboardCallback(refresh_rate=2)],
)
opt.run()

The dashboard shows:

• Real-time score sparkline (last 20 eval points)
• Current loop state (ACTIVE / COOLING / DORMANT)
• Live hyperparameter values
• Smoothed score, best score, episode count
• Estimated convergence progress

No extra configuration required - pass it as a callback and it wires itself to the LoopCallback hooks automatically.

---

Parallel Environments - VectorBatchPipeline

Run N environments simultaneously. Increases sample throughput N× over a single BatchPipeline.

import gymnasium as gym
from tensor_optix.pipeline.vector_pipeline import VectorBatchPipeline

env_fns  = [lambda: gym.make("CartPole-v1")] * 8
pipeline = VectorBatchPipeline(env_fns=env_fns, window_size=256)

# Async (subprocess-based) for CPU-bound envs:
pipeline = VectorBatchPipeline(env_fns=env_fns, window_size=256, async_envs=True)

---

Observation & Reward Normalization

from tensor_optix.core.normalizers import ObsNormalizer, RewardNormalizer

obs_norm    = ObsNormalizer(obs_shape=(obs_dim,), clip=10.0)

# Update stats from a collected rollout, then normalize in act():
obs_norm.update(obs_batch)
normed_obs = obs_norm.normalize(raw_obs)

RewardNormalizer is most useful with on-policy agents. Pass it directly to the agent - it handles the step/reset cycle at episode boundaries internally, so you don't have to track done flags manually:

from tensor_optix.core.normalizers import RewardNormalizer

reward_norm = RewardNormalizer(gamma=0.99, clip=10.0)

agent = TFPPOAgent(
    actor=actor, critic=critic, optimizer=optimizer, hyperparams=hp,
    reward_normalizer=reward_norm,   # resets at done, normalizes before GAE
)

The agent calls step(r) and reset() for each reward in the window during learn(), then normalizes the full batch before GAE. This is a correctness requirement for multi-episode windows - forgetting to reset the running return across episode boundaries biases the return variance estimate.

---

Extend Any Algorithm

All algorithms implement BaseAgent. Subclass to add domain-specific logic without reimplementing PPO:

class TradingPPO(TFPPOAgent):
    """Adds action distribution logging to standard PPO."""

    def learn(self, episode_data):
        diag = super().learn(episode_data)           # full PPO update
        obs  = tf.cast(episode_data.observations[:256], tf.float32)
        probs = tf.nn.softmax(self._actor(obs, training=False))
        probs_mean = tf.reduce_mean(probs, axis=0).numpy()
        diag["p_flat"]  = float(probs_mean[0])
        diag["p_long"]  = float(probs_mean[1])
        diag["p_short"] = float(probs_mean[2])
        return diag

---

The Loop Interface

The core loop calls exactly six methods on any agent. Nothing else is assumed.

class BaseAgent(ABC):
    def act(self, observation) -> any: ...         # any action type
    def learn(self, episode_data) -> dict: ...     # any algorithm
    def get_hyperparams(self) -> HyperparamSet: ...
    def set_hyperparams(self, hp: HyperparamSet): ...
    def save_weights(self, path: str): ...
    def load_weights(self, path: str): ...

Any model - RL algorithms, evolutionary strategies, supervised sequence models, online forecasters - plugs in by implementing these six methods. No specific framework, action space, or learning paradigm is assumed.

---

How the Autonomous Loop Works

Every episode flows through four components in sequence. Understanding this pipeline is the key to configuring tensor-optix effectively.

flowchart TD
    A([Episode N]) --> B[agent.learn + evaluator.score]
    B --> C{BackoffScheduler}

    C -->|improvement detected| D[ACTIVE\ninterval resets to 1]
    C -->|no improvement| E[COOLING\ninterval ×= backoff_factor]
    E -->|consecutive plateau\n≥ dormant_threshold| F[DORMANT]

    D -->|next episode| A
    E -->|next episode| A

    F --> G{MetaController}
    G -->|val improving| H[SPAWN]
    G -->|gap high & worsening| I[PRUNE]
    G -->|budget exhausted| J[STOP]
    G -->|otherwise| K[NO_OP  -  resume training]
    K -->|next episode| A

    H --> L[PolicyManager]
    L --> L1[1. rollback if degraded]
    L1 --> L2[2. clone best checkpoint]
    L2 --> L3[3. perturb hyperparams σ]
    L3 --> L4[4. add variant to ensemble]
    L4 --> L5[5. prune if over size limit]
    L5 -->|budget remaining| A
    L5 -->|budget exhausted| J

    J --> M([best weights restored\ntraining complete])

Key insight: BackoffScheduler only fires DORMANT events - it has no opinion on what to do next. MetaController makes that decision based on generalization signals. PolicyManager executes it. This separation means you can swap or bypass any layer without touching the others.

---

How It Works

Adaptive Eval Scheduling

One of tensor-optix's core strengths is that it decides when to evaluate - not you, and not a fixed schedule.

The BackoffScheduler dynamically controls eval frequency based on learning progress:

  [loop] ep=   1  raw=  -67.2  smoothed= -150.6  state=ACTIVE  interval=1
  [loop] ep=   2  raw= -191.9  smoothed= -129.5  state=ACTIVE  interval=1
  [loop] ep=   4  raw= -106.8  smoothed= -100.5  state=ACTIVE  interval=2
  [loop] ep=   6  raw= -258.8  smoothed= -178.6  state=ACTIVE  interval=2
  [loop] ep=   8  raw=   65.7  smoothed=  -96.6  state=ACTIVE  interval=4
  [loop] ep=  16  raw=  208.1  smoothed=  136.9  state=ACTIVE  interval=8
  [loop] ep=  17  raw=  194.8  smoothed=  201.5  state=ACTIVE  interval=1  ← improvement detected, reset

• No improvement → interval doubles (2, 4, 8...) - more training time between evals, budget spent on learning
• Improvement detected → interval snaps back to 1 - dense eval to track the breakthrough
• DORMANT → loop stops, best weights restored automatically

Vanilla frameworks evaluate on a fixed schedule regardless of progress. tensor-optix spends the budget where it matters.

Enable verbose output to see this in action:

opt = RLOptimizer(agent=agent, pipeline=pipeline, verbose=True)

The Loop States

ACTIVE   → learning detected, evaluates frequently
COOLING  → no recent improvement, exponential backoff on eval frequency
DORMANT  → plateau confirmed  -  training is done, loop stops cleanly

DORMANT = trained. Not a fixed episode count - the system backs off evaluation geometrically until improvement stops, then declares convergence and restores the best known weights.

Backoff Schedule

interval₀ = base_interval
intervalₙ = min(intervalₙ₋₁ × backoff_factor, max_interval_episodes)

Plateau detected when:  consecutive_no_improvement ≥ plateau_threshold
DORMANT declared when:  consecutive_no_improvement ≥ dormant_threshold

Every improvement resets the counter. The system accelerates evaluation when learning is happening, backs off when it isn't.

Hyperparameter Optimization - Two Layers

tensor-optix provides two complementary levels of hyperparameter optimization. They are designed to compose: run TrialOrchestrator first to find a good starting configuration, then hand those params to RLOptimizer for the final full-budget run with SPSA online adaptation.

Layer 1 - Online Adaptation (SPSA, within a single run)

The default optimizer is SPSAOptimizer (Simultaneous Perturbation Stochastic Approximation). It adapts hyperparameters during a training run, episode by episode, responding to non-stationarity in real time.

Episode 1 (probe+):  sample Δ ∈ {−1, +1}ᴺ  (Rademacher vector)
                     apply θ⁺ = θ + c·Δ,  record score f⁺

Episode 2 (probe−):  apply θ⁻ = θ − c·Δ,  record score f⁻

Gradient estimate:   ĝᵢ = (f⁺ − f⁻) / (2·c·Δᵢ)   ← unbiased for all i simultaneously

Update:              x_new = clip(x + α·ĝ, 0, 1)   ← in normalized [0,1] param space
                     θ_new = denormalize(x_new)

All probing is done in a normalized [0, 1] parameter space - a fixed perturbation scale applies equally to a learning rate of 3e-4 and a clip ratio of 0.2 without manual tuning.

Probe-aware degradation gating: during probe episodes, score drops are self-inflicted perturbations, not genuine policy collapses. The loop skips degradation checks while the optimizer is probing.

BackoffOptimizer is also available for single-parameter cycling via two-phase finite difference:

from tensor_optix.optimizers.backoff_optimizer import BackoffOptimizer

opt = RLOptimizer(
    agent=agent,
    pipeline=pipeline,
    optimizer=BackoffOptimizer(param_bounds={
        "learning_rate": (1e-5, 1e-2),
        "clip_ratio":    (0.05, 0.4),
    }),
)

Layer 2 - Trial-Level Search (TrialOrchestrator, across independent runs)

TrialOrchestrator runs N fully independent RLOptimizer trials, each with a different hyperparameter configuration, and uses Optuna TPE (Tree-structured Parzen Estimator) to select configurations. It is mathematically the same algorithm used by Stable-Baselines3, CleanRL, and RLlib for RL HPO sweeps.

When to use it: before committing to a long training run. Give each trial 10–20% of your final budget - enough to rank configurations, not enough for full training.

from tensor_optix import TrialOrchestrator, RLOptimizer
# pip install optuna   (optional dependency)

def make_agent(params: dict) -> BaseAgent:
    net = tf.keras.Sequential([...])
    return TFPPOAgent(
        actor=net, critic=critic_net,
        optimizer=tf.keras.optimizers.Adam(params["learning_rate"]),
        hyperparams=HyperparamSet(params=params, episode_id=0),
    )

def make_pipeline() -> BasePipeline:
    return BatchPipeline(env_id="LunarLander-v3", n_steps=2048)

orchestrator = TrialOrchestrator(
    agent_factory=make_agent,
    pipeline_factory=make_pipeline,
    param_space={
        "learning_rate": ("log_float", 1e-4, 3e-3),   # log-uniform (good for lr)
        "clip_ratio":    ("float",     0.1,  0.3),
        "entropy_coef":  ("float",     0.001, 0.05),  # 0.001 floor prevents entropy collapse
        "gamma":         ("float",     0.95, 0.999),
    },
    n_trials=20,          # number of independent runs
    trial_steps=50_000,   # step budget per trial
)
best_params, best_score = orchestrator.run()

# Final full-budget run with the best configuration found
agent = make_agent(best_params)
optimizer = RLOptimizer(agent=agent, pipeline=make_pipeline(), max_episodes=500)
optimizer.run()

Parameter space spec:

Spec	Description
("float", lo, hi)	Uniform float in [lo, hi]
("log_float", lo, hi)	Log-uniform float - use for learning rate, α
("int", lo, hi)	Uniform integer
("log_int", lo, hi)	Log-uniform integer - use for batch size, buffer size
("categorical", v1, v2, ...)	One of the listed values

How TPE works:

TPE fits two kernel density estimates - p(x | good) over the top-k% of trials and p(x | bad) over the rest. The next configuration is chosen by maximising the acquisition ratio p(x | good) / p(x | bad). This is equivalent to Bayesian optimisation with a non-parametric surrogate, without the O(n³) cost of Gaussian Process inference.

MedianPruner: after a short warmup, any trial whose score falls below the median of all trials at the same episode is terminated early. This cuts wall time by stopping clearly bad configurations without committing to a fixed bracket schedule.

Each trial gets an isolated checkpoint directory - no cross-trial interference. The underlying Optuna study is accessible via orchestrator.study for inspection, plotting, and storage to SQLite for distributed sweeps.

Adaptive Improvement Margin

A gain of +0.001 on a signal with ±5 noise is not a real improvement. The loop computes an adaptive floor before crediting any score as a new best:

effective_margin = max(user_margin, noise_k × std(recent_scores))

noise_k = 2.0 by default. Gains below 2σ of recent score noise do not reset backoff, preventing noise-level fluctuations from blocking convergence detection.

---

The Science: Train + Val Together

Without validation, every decision - checkpoint saves, rollbacks, spawn triggers - is made on training data alone. That is overfitting disguised as improvement.

Validation Pipeline

opt = RLOptimizer(
    agent=agent,
    pipeline=train_pipeline,
    val_pipeline=val_pipeline,   # held-out  -  agent acts, never learns
)

On every eval window, the loop runs one val episode (act() only, no learn()), then calls evaluator.combine(train_metrics, val_metrics):

primary_score        = val_score          ← drives ALL checkpoint and rollback decisions
generalization_gap   = train_score − val  ← surfaced in every EvalMetrics

Every adaptation decision - rollback, spawn, noise scale, MetaController - is driven by out-of-sample performance, not training performance.

External Checkpoint Scoring

The training window mean is a noisy signal - it diverges from the true policy quality that matters at deployment. Pass checkpoint_score_fn to decouple checkpoint saving from training noise:

def external_eval(agent) -> float:
    # deterministic, fixed seed  -  measures true policy quality
    return eval_policy(agent, env_id="LunarLander-v3", seed=42, n_episodes=5)

opt = RLOptimizer(
    agent=agent,
    pipeline=pipeline,
    checkpoint_score_fn=external_eval,
)

The best checkpoint is selected by the external score. The training signal still drives convergence detection - only checkpoint saving uses the external eval.

Three-Signal Adaptive Noise

When spawning a policy variant, the mutation intensity is computed from three signals:

Signal 1 - Val slope (improvement rate)

t = clip(slope(val_scores) / max_slope, 0, 1)

t → 1 when val is improving strongly. t → 0 on plateau.

Signal 2 - Generalization gap

gap_penalty = clip(mean(train − val) / |mean(val)|, 0, 1)

Large gap means the model fits training data but not held-out data - explore different solutions.

Signal 3 - Train/val correlation (Pearson)

corr_penalty = clip(1 − Pearson(train_scores, val_scores), 0, 1)

corr → 1 means train and val move together (healthy). corr → 0 means train is moving but val isn't - a signal to explore.

Combined formula:

effective_t = t × (1 − 0.5 × gap_penalty) × (1 − 0.5 × corr_penalty)
noise_scale = max_scale − effective_t × (max_scale − min_scale)

Without a val pipeline, spawn noise adapts to the training improvement ratio:

σ = base_noise / (1 + improvement_ratio)

Exploit when improving, explore when stuck.

---

Policy Evolution

Automatic Rollback

When run() returns, the agent always holds the best known weights - whether stopped by convergence, budget, or manual stop(). This is unconditional and requires no configuration.

For mid-training rollback on degradation:

opt = RLOptimizer(agent=agent, pipeline=pipeline, rollback_on_degradation=True)

Spawn Budget - When Is Training Done?

from tensor_optix import PolicyManager

pm = PolicyManager(registry, max_spawns=3)
cb = pm.as_callback(agent)
cb.set_stop_fn(opt.stop)

opt.run()  # returns cleanly when budget is exhausted

When budget is exhausted, a training report is printed automatically:

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
  Training Complete
  Reason           : Spawn budget exhausted
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
  Best score       : 0.8732
  Val score        : 0.8612
  Generalization   : 0.0120  (train − val)
  Spawns used      : 3 / 3
  Pruned agents    : 1
  Ensemble size    : 3
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Autonomous Spawning

def make_agent():
    return TFPPOAgent(actor=build_actor(), critic=build_critic(),
                      optimizer=tf.keras.optimizers.Adam(3e-4),
                      hyperparams=initial_hp)

pm = PolicyManager(registry, max_spawns=5, max_ensemble_size=4)
cb = pm.as_callback(agent, agent_factory=make_agent)
cb.set_stop_fn(opt.stop)

On DORMANT: rebalance ensemble weights → rollback if degraded → clone best checkpoint → perturb hyperparams → add to ensemble → prune if over limit → stop when budget exhausted.

MetaController - Autonomous Decisions

from tensor_optix import MetaController

cb = pm.as_callback(
    agent,
    agent_factory=make_agent,
    meta_controller=MetaController(
        gap_threshold=0.3,
        gap_slope_threshold=0.02,
        improvement_threshold=0.05,
    ),
)

MetaController decides SPAWN / PRUNE / STOP / NO_OP on each DORMANT event based on generalization gap level, gap slope (overfitting progression), and val improvement rate.

Ensemble

from tensor_optix import PolicyManager, EnsembleAgent

pm = PolicyManager(registry)
pm.add_agent(agent_a, weight=1.0)
pm.add_agent(agent_b, weight=1.0)

ensemble = EnsembleAgent(pm, primary_agent=agent_a)
# Actions: a = Σ(wᵢ × aᵢ) / Σ(wᵢ)

opt = RLOptimizer(
    agent=ensemble,
    pipeline=BatchPipeline(env=env, agent=ensemble, window_size=2048),
    callbacks=[pm.as_callback(agent_a)],
)

---

Custom Evaluator

from tensor_optix import BaseEvaluator, EpisodeData, EvalMetrics
import numpy as np

class SharpeEvaluator(BaseEvaluator):
    def score(self, episode_data: EpisodeData, train_diagnostics: dict) -> EvalMetrics:
        rewards = np.array(episode_data.rewards)
        sharpe  = rewards.mean() / (rewards.std() + 1e-8)
        return EvalMetrics(
            primary_score=float(sharpe),
            metrics={"sharpe": float(sharpe), "mean_reward": float(rewards.mean())},
            episode_id=episode_data.episode_id,
        )

opt = RLOptimizer(agent=agent, pipeline=pipeline, evaluator=SharpeEvaluator())

---

Live Pipeline

from tensor_optix import LivePipeline

pipeline = LivePipeline(
    data_source=MarketFeed(),
    agent=agent,
    episode_boundary_fn=LivePipeline.every_n_seconds(300),
)

---

Callbacks

Built-in callbacks

from tensor_optix.callbacks import WandbCallback, TensorBoardCallback, RichDashboardCallback

# Weights & Biases  -  logs every on_episode_end and on_improvement event
opt = RLOptimizer(agent=agent, pipeline=pipeline,
                  callbacks=[WandbCallback(project="my-project")])

# TensorBoard  -  writes to ./runs/ by default
opt = RLOptimizer(agent=agent, pipeline=pipeline,
                  callbacks=[TensorBoardCallback(log_dir="./runs/cartpole")])

# Live terminal dashboard (requires `pip install rich`)
opt = RLOptimizer(agent=agent, pipeline=pipeline,
                  callbacks=[RichDashboardCallback(refresh_rate=2)])

Custom callbacks

from tensor_optix import LoopCallback

class MyLogger(LoopCallback):
    def on_improvement(self, snapshot):
        print(f"New best: {snapshot.eval_metrics.primary_score:.4f}")

    def on_dormant(self, window_id):
        print(f"Converged at window {window_id}")

opt = RLOptimizer(agent=agent, pipeline=pipeline, callbacks=[MyLogger()])

Available hooks: on_loop_start, on_loop_stop, on_episode_end, on_improvement, on_plateau, on_dormant, on_degradation, on_hyperparam_update.

---

Full Configuration

opt = RLOptimizer(
    agent=agent,
    pipeline=pipeline,

    # ── Pipelines & components ────────────────────────────────────────────
    val_pipeline=val_pipeline,              # held-out pipeline; agent acts only, never learns
    evaluator=None,                         # default: TFEvaluator (or TorchEvaluator for PyTorch)
    optimizer=None,                         # default: SPSAOptimizer (all params in 2 episodes)

    # ── Checkpointing ─────────────────────────────────────────────────────
    checkpoint_dir="./checkpoints",         # where snapshots are saved
    max_snapshots=10,                       # keep only the N best snapshots on disk
    checkpoint_score_fn=None,               # callable(agent) → float; when set, checkpoint
                                            # selection uses this external eval instead of the
                                            # noisy training signal. Use for deterministic evals.

    # ── Budget ────────────────────────────────────────────────────────────
    max_episodes=None,                      # hard cap; None = run until DORMANT

    # ── Convergence detection (BackoffScheduler) ──────────────────────────
    base_interval=1,                        # eval every N episodes at the start
    backoff_factor=2.0,                     # multiply interval by this on each non-improvement
    max_interval_episodes=100,              # interval cap  -  never wait more than this
    plateau_threshold=5,                    # consecutive non-improvements → COOLING
    dormant_threshold=20,                   # consecutive non-improvements → DORMANT (stop)
                                            # off-policy agents (DQN, SAC) auto-set to 15  - 
                                            # replay buffer scores are noisier than on-policy
    score_smoothing=2,                      # rolling mean window applied before comparing scores;
                                            # filters single-episode noise from convergence signals

    # ── Improvement margin ────────────────────────────────────────────────
    improvement_margin=0.0,                 # fixed minimum gain to count as improvement
    noise_k=2.0,                            # adaptive margin multiplier: effective_margin =
                                            # max(improvement_margin, noise_k × std(recent_scores))
                                            # increase if the loop stops too early on noisy envs
    score_window=20,                        # rolling window size for computing the noise floor

    # ── Degradation detection ─────────────────────────────────────────────
    rollback_on_degradation=False,          # restore best weights when degradation is detected
                                            # safe for on-policy (PPO); skip for off-policy (DQN/SAC)
    degradation_threshold=0.95,             # score must drop below best × threshold to fire
    min_episodes_before_dormant=0,          # don't declare DORMANT before this many evals;
                                            # auto-set per agent class when left at 0:
                                            # DQN=60 (epsilon decay floor timing),
                                            # SAC=30 (Q-function stabilisation)
    min_episodes_before_degradation=5,      # don't fire degradation before this many evals;
                                            # prevents false alarms during chaotic early training

    # ── Misc ──────────────────────────────────────────────────────────────
    callbacks=[],
    verbose=False,                          # print per-episode eval output (raw, smoothed, state)
)

---

Architecture

tensor_optix/
├── core/
│   ├── types.py                # EpisodeData, EvalMetrics, HyperparamSet, LoopState
│   ├── base_agent.py           # BaseAgent  -  6-method contract
│   ├── base_evaluator.py       # BaseEvaluator  -  score, combine, compare
│   ├── base_optimizer.py       # BaseOptimizer  -  suggest, on_improvement, on_plateau
│   ├── base_pipeline.py        # BasePipeline  -  episodes() generator
│   ├── loop_controller.py      # State machine + main loop
│   ├── backoff_scheduler.py    # Convergence detection + state transitions
│   ├── checkpoint_registry.py  # Snapshot storage and manifest
│   ├── normalizers.py          # RunningMeanStd, ObsNormalizer, RewardNormalizer
│   ├── trajectory_buffer.py    # compute_gae(), make_minibatches()
│   ├── noisy_linear.py         # NoisyLinear  -  factorized Gaussian noise (Rainbow)
│   ├── policy_manager.py       # PolicyManager + PolicyManagerCallback
│   ├── ensemble_agent.py       # EnsembleAgent  -  multi-policy BaseAgent wrapper
│   ├── regime_detector.py      # RegimeDetector  -  score-based regime classification
│   ├── meta_controller.py      # MetaController  -  SPAWN/PRUNE/STOP/NO_OP decisions
│   ├── her_buffer.py           # HERReplayBuffer  -  Hindsight Experience Replay
│   └── diagnostic_controller.py# DiagnosticController  -  per-episode metric aggregation
├── optimizers/
│   ├── spsa_optimizer.py       # SPSAOptimizer  -  default, all params in 2 episodes
│   ├── backoff_optimizer.py    # BackoffOptimizer  -  single-param finite difference
│   ├── momentum_optimizer.py   # MomentumOptimizer  -  gradient-signed momentum
│   └── pbt_optimizer.py        # PBTOptimizer  -  population-based exploit/explore
├── adapters/
│   ├── tensorflow/
│   │   ├── tf_agent.py         # TFAgent  -  generic REINFORCE / A2C base
│   │   └── tf_evaluator.py     # TFEvaluator  -  default scorer
│   ├── pytorch/
│   │   ├── torch_agent.py      # TorchAgent  -  generic REINFORCE / A2C base
│   │   └── torch_evaluator.py  # TorchEvaluator  -  default scorer (no TF dep)
│   └── jax/                    # NEW  -  JAX/Flax adapter
│       ├── flax_agent.py       # FlaxAgent  -  REINFORCE base, nnx.Optimizer, pickle weights
│       └── flax_evaluator.py   # FlaxEvaluator  -  total reward scorer
├── algorithms/
│   ├── tf_ppo.py               # TFPPOAgent  -  clipped surrogate, GAE-λ, n-epoch minibatch
│   ├── tf_ppo_continuous.py    # TFGaussianPPOAgent  -  continuous PPO, squashed Gaussian
│   ├── tf_dqn.py               # TFDQNAgent  -  PER replay, target net, ε-greedy
│   ├── tf_sac.py               # TFSACAgent  -  twin critics, squashed Gaussian, auto-α
│   ├── tf_td3.py               # TFTDDAgent  -  deterministic policy, delayed actor, target smoothing
│   ├── torch_ppo.py            # TorchPPOAgent (CUDA auto-detect)
│   ├── torch_ppo_continuous.py # TorchGaussianPPOAgent  -  continuous PPO (CUDA auto-detect)
│   ├── torch_dqn.py            # TorchDQNAgent (CUDA auto-detect)
│   ├── torch_sac.py            # TorchSACAgent (CUDA auto-detect)
│   ├── torch_td3.py            # TorchTD3Agent  -  TD3: twin critics, delayed actor, noise smoothing
│   ├── torch_recurrent_ppo.py  # TorchRecurrentPPOAgent  -  LSTM actor-critic, stateful act()
│   ├── torch_rainbow_dqn.py    # TorchRainbowDQNAgent  -  Double/Dueling/PER/n-step/Noisy/C51
│   └── flax_ppo.py             # FlaxPPOAgent  -  PPO via flax.nnx + optax (JAX backend)
├── distributed/                # NEW  -  async actor-learner
│   ├── async_learner.py        # AsyncActorLearner  -  IMPALA-style, POSIX shared memory
│   └── vtrace.py               # compute_vtrace_targets  -  pure-numpy V-trace IS correction
├── callbacks/
│   ├── wandb_callback.py       # WandbCallback  -  logs to Weights & Biases
│   ├── tensorboard_callback.py # TensorBoardCallback  -  logs to TensorBoard
│   └── rich_dashboard.py       # RichDashboardCallback  -  live terminal panel (requires rich)
└── pipeline/
    ├── batch_pipeline.py       # Continuous stepping, fixed windows
    ├── live_pipeline.py        # Real-time streaming with reconnect
    └── vector_pipeline.py      # Parallel envs via gymnasium.vector

Component	Responsibility
TFPPOAgent / TorchPPOAgent	Discrete PPO - GAE, clipping, entropy, n-epoch minibatch
TFGaussianPPOAgent / TorchGaussianPPOAgent	Continuous PPO - squashed Gaussian actor, same PPO core
TFDQNAgent / TorchDQNAgent	DQN with PER replay, n-step returns, target net, ε-greedy
TFSACAgent / TorchSACAgent	SAC - twin critics, auto-entropy, soft target updates
TFTDDAgent / TorchTD3Agent	TD3 - deterministic actor, twin critics, delayed updates, target smoothing
TorchRecurrentPPOAgent	LSTM actor-critic PPO - hidden state carried across steps, handles partial observability
TorchRainbowDQNAgent	Rainbow DQN - Double/Dueling/PER/n-step/Noisy Nets/C51 (all six improvements)
FlaxPPOAgent	PPO via Flax NNX + optax - XLA-compiled, convergence-parity with TorchPPOAgent
FlaxAgent	Base agent for any nnx.Module - REINFORCE update, pickle-safe weight I/O
AsyncActorLearner	IMPALA-style N-actor learner - POSIX shared memory, V-trace off-policy correction
compute_vtrace_targets	Pure-numpy V-trace IS correction (Espeholt et al. 2018)
LoopController	State machine, episode orchestration, eval, checkpoint
BackoffScheduler	Adaptive eval scheduling + convergence detection
CheckpointRegistry	Snapshot storage, best-checkpoint manifest
SPSAOptimizer	SPSA - all N params in 2 episodes, normalized space (online, within a run)
BackoffOptimizer	Two-phase finite difference hyperparameter tuning
PBTOptimizer	Population-based exploit/explore hyperparameter tuning
TrialOrchestrator	Optuna TPE trial-level HPO - N independent runs, MedianPruner (requires optuna)
PolicyManager	Rollback, spawn, prune, boost, ensemble weights, adaptive noise
MetaController	Rule-based SPAWN/PRUNE/STOP/NO_OP decisions
EnsembleAgent	Weighted-average action combining across multiple agents
RegimeDetector	Score-based regime classification (trending / ranging / volatile)
WandbCallback	Logs scores, hyperparams, and diagnostics to Weights & Biases
TensorBoardCallback	Logs to TensorBoard SummaryWriter
RichDashboardCallback	Live terminal panel - sparkline, state, hyperparams (requires rich)
VectorBatchPipeline	Parallel environment rollouts via gymnasium.vector
ObsNormalizer	Online running mean/std observation normalization
RewardNormalizer	Return-std reward scaling

---

Common Pitfalls & Best Practices

Device management

Every built-in Torch agent (TorchPPOAgent, TorchGaussianPPOAgent, TorchDQNAgent, TorchSACAgent) accepts a device parameter and moves its networks there on construction. The default is "auto", which selects CUDA if available.

agent = TorchPPOAgent(actor=actor, critic=critic, optimizer=opt,
                      hyperparams=hp, device="cuda")   # or "cpu", "auto"

The base TorchAgent adapter now also accepts device="auto" and applies it consistently in act() and load_weights(). If you subclass TorchAgent directly, pass device to super().__init__() - otherwise obs tensors and loaded checkpoints default to CPU even on a CUDA machine.

Watch out: constructing the optimizer before calling .to(device) on the model is safe because optimizers hold references to parameter tensors, not copies. But creating the optimizer after agent.load_weights() restores weights to the wrong device can leave parameters split between CPU and GPU, which causes a silent slowdown rather than an error.

Ensemble memory on GPU

Spawning agents with PolicyManager.spawn_variant() or agent_factory mode creates new networks on the target device. Calling prune() removes agents from the ensemble and automatically calls agent.teardown() on each removed agent, which moves its networks to CPU and calls torch.cuda.empty_cache().

If you remove agents from the ensemble by any other means (e.g., rebuilding _ensemble manually), call teardown() yourself:

removed = pm.prune(bottom_k=2)   # teardown() is called automatically

# If removing manually:
agent.teardown()

For long PBT-style runs with frequent spawning, monitor GPU memory with torch.cuda.memory_allocated(). If memory grows despite pruning, the likely cause is optimizer state - gradient moments accumulate per parameter. Re-creating the optimizer on each spawn (as the built-in agent_factory pattern does) avoids this.

On-policy vs. off-policy rollback

rollback_on_degradation=True is safe for PPO but harmful for DQN and SAC. Off-policy agents accumulate experience in a replay buffer across many policies. Rolling back weights without clearing the buffer means the restored policy immediately trains on transitions it never generated - corrupted Bellman targets drag it back down.

The framework handles this automatically: any agent where is_on_policy returns False skips the weight rollback even when rollback_on_degradation=True. If you write a custom off-policy agent, override the property:

@property
def is_on_policy(self) -> bool:
    return False

Wiring PolicyManager early stopping

PolicyManager.as_callback() returns a PolicyManagerCallback that stops training when the spawn budget is exhausted - but only if you wire the stop function:

pm_cb = pm.as_callback(agent, agent_factory=my_factory)
rl_opt = RLOptimizer(...)
pm_cb.set_stop_fn(rl_opt.stop)   # required  -  without this, training runs the full budget
rl_opt.add_callback(pm_cb)
rl_opt.run()

Without set_stop_fn, the callback prints the training report when the budget runs out but cannot halt the loop. Training continues until max_episodes is reached.

For the factory-mode PPO path (where agent_factory is passed to RLOptimizer and pm_cb is created inside the factory), wire the stop function inside the factory - rl_opt is already bound in the enclosing scope by the time the factory is called:

def agent_factory_full(params):
    agent = make_agent(params)
    pm_cb = pm.as_callback(agent, agent_factory=lambda: make_agent(params))
    pm_cb.set_stop_fn(rl_opt.stop)   # rl_opt is bound before run() calls this factory
    rl_opt.add_callback(pm_cb)
    return agent

rl_opt = RLOptimizer(agent_factory=agent_factory_full, ...)
rl_opt.run()

Checkpoint directory hygiene

Each run writes checkpoints to checkpoint_dir. If you reuse the same directory across restarts without clearing it, CheckpointRegistry will load stale snapshots from a previous run and roll back to them during training. Either pass a unique directory per run (include seed and timestamp) or call shutil.rmtree(ckpt_dir, ignore_errors=True) at the start of each run.

State dict key mismatches during weight averaging / spawning

average_weights() and load_weights() use PyTorch state_dict keys. If the architecture passed to a spawned agent shell differs from the one that was checkpointed (different layer names, sizes, or number of layers), load_state_dict() will raise a RuntimeError with a key mismatch message. The framework does not catch this - it is user responsibility to pass a compatible shell. The safest pattern is to use the same agent_factory for both the primary agent and all spawned variants.

---

Math & Science Reference

SPSA Gradient Estimate (SPSAOptimizer)

Δ ~ Rademacher({−1, +1}ᴺ)          ← simultaneous perturbation vector

θ⁺ = θ + c·Δ   →   f⁺ = score(θ⁺)
θ⁻ = θ − c·Δ   →   f⁻ = score(θ⁻)

ĝᵢ = (f⁺ − f⁻) / (2·c·Δᵢ)         ← unbiased estimator for all i

x  = (θ − lo) / (hi − lo)           ← normalize to [0,1]
x' = clip(x + α·ĝ, 0, 1)
θ' = lo + x' · (hi − lo)            ← denormalize

Spall (1992) proved that this two-measurement estimator is unbiased and converges at the same asymptotic rate as finite difference with N measurements. Normalizing to [0,1] before updating ensures a fixed perturbation scale c applies equally to parameters of any magnitude.

GAE-λ (trajectory_buffer.compute_gae)

δₜ = rₜ + γ·V(sₜ₊₁)·(1−dₜ) − V(sₜ)
Aₜ = δₜ + γλ·(1−dₜ)·Aₜ₊₁

The (1−dₜ) mask zeros both the bootstrap from V(sₜ₊₁) and the GAE propagation from Aₜ₊₁ simultaneously, so a single window containing multiple episode fragments is handled correctly without splitting by episode.

PPO Clipped Surrogate (TFPPOAgent / TorchPPOAgent)

rₜ(θ) = π_θ(aₜ|sₜ) / π_θ_old(aₜ|sₜ)

L_clip = E[ min(rₜ·Âₜ, clip(rₜ, 1−ε, 1+ε)·Âₜ) ]
L_vf   = E[ (V_θ(sₜ) − Rₜ)² ]
L_ent  = E[ H(π_θ(·|sₜ)) ]

L = −L_clip + c₁·L_vf − c₂·L_ent

SAC Squashed Gaussian (TFSACAgent / TorchSACAgent)

u ~ N(μ_θ(s), σ_θ(s))
a = tanh(u)

log π(a|s) = log N(u; μ, σ) − Σᵢ log(1 − tanh²(uᵢ) + ε)

Auto-entropy: L_α = −α · (log π(aₜ|sₜ) + H_target) where H_target = −dim(A).

A2C Advantage Baseline (TFAgent / TorchAgent)

Aₜ = Gₜ − V(sₜ)
∇J ≈ Σ ∇log π(aₜ|sₜ) · Âₜ

By the policy gradient theorem, subtracting V(sₜ) does not bias the gradient while reducing variance. The explained_variance diagnostic in learn() measures critic quality: 1.0 = perfect, 0.0 = useless, <0 = harmful.

PBT Perturbation Modes (PBTOptimizer)

Log-scale for learning_rate, epsilon, weight_decay:

δ_log = scale × log(high / low)
θ' = clip(θ × exp(Uniform(−δ_log, +δ_log)), low, high)

Equal probability mass per decade, following Jaderberg et al. 2017.

Detrended Volatility (RegimeDetector)

residuals    = scores − linear_regression(scores)
CV_detrended = std(residuals) / (|mean(scores)| + ε)

Avoids conflating a steadily improving score with stability.

Gap-Slope Overfitting Signal (MetaController)

gapₜ = (train_scoreₜ − val_scoreₜ) / |val_scoreₜ|
slope = linear_regression_slope(gap₀, ..., gapₙ)
slope > threshold → PRUNE

Detects active overfitting progression before gap level alone triggers.

V-trace Off-Policy Correction (compute_vtrace_targets / AsyncActorLearner)

Espeholt et al. 2018 (IMPALA). Corrects actor-lag bias when actors run an older policy μ while the learner updates to θ.

ρ_t   = π_θ(a_t|s_t) / π_μ(a_t|s_t)          ← IS ratio
ρ̄_t  = min(ρ̄, ρ_t)                            ← clipped IS weight
c̄_t  = min(c̄, ρ_t)                            ← trace coefficient

δ_t   = ρ̄_t · (r_t + γ·(1−done_t)·V(s_{t+1}) − V(s_t))

v_t   = V(s_t) + δ_t + γ·(1−done_t)·c̄_t·(v_{t+1} − V(s_{t+1}))
                                               ← backward recursion

A_t   = ρ̄_t · (r_t + γ·(1−done_t)·v_{t+1} − V(s_t))
                                               ← policy gradient advantage

With ρ̄ = c̄ = 1 and synchronous actors (μ = θ), reduces to standard on-policy GAE. The clip ρ̄ bounds the maximum IS weight, preventing gradient spikes from stale trajectories.

TD3 Target Policy Smoothing (TorchTD3Agent / TFTDDAgent)

a_noise = clip(N(0, σ), −c, c)              ← clipped Gaussian noise
a_target = clip(π_θ_tgt(s') + a_noise, a_lo, a_hi)

y = r + γ · min(Q_tgt1(s', a_target), Q_tgt2(s', a_target))

Smoothing prevents the critic from over-fitting to narrow deterministic action peaks. The actor is updated every policy_delay critic steps (default 2), giving the critic time to stabilise before actor gradients are computed.

Rainbow Categorical Distribution (TorchRainbowDQNAgent)

Distributional Bellman target (Bellemare et al. 2017):

atoms: z_i ∈ {v_min + i·Δz},   i = 0..N-1,   Δz = (v_max − v_min) / (N-1)

y     = r + γ · z_i   (projected onto support)

L     = KL(target_dist ‖ Q_dist(s, a))       ← cross-entropy loss

The 51-atom categorical distribution represents the full return distribution rather than its mean, enabling value-based agents to reason about risk.

---

neuroevo - Free-Form Topology Evolution

tensor_optix.neuroevo adds a mutable neural graph that grows and prunes itself during training. Unlike fixed-architecture networks, the compute graph is a directed graph of neurons with variable-delay edges - topology evolves alongside weights.

Install:

pip install tensor-optix[neuroevo]

Core idea

Standard networks have a fixed topology set at construction. neuroevo starts small and grows when training plateaus, using function-preserving operations - every structural change leaves the network output identical at the moment of application. Learning then breaks symmetry from that preserved baseline.

Key components

Class	Role
NeuronGraph	Mutable directed graph - the policy network
GraphAgent	BaseAgent wrapping NeuronGraph, PPO-trained
TopologyController	LoopCallback that fires grow/prune on COOLING state

Quickstart

import gymnasium as gym
from tensor_optix.neuroevo import NeuronGraph, GraphAgent, TopologyController
from tensor_optix import LoopController  # your existing loop

# Build a minimal graph: 4 inputs, 2 hidden, 3 outputs (2 actions + 1 value)
g = NeuronGraph()
for _ in range(4):
    g.add_neuron(role="input", activation="linear")
for _ in range(2):
    g.add_neuron(role="hidden", activation="tanh")
for _ in range(3):
    g.add_neuron(role="output", activation="linear")
for inp in g.input_ids:
    for hid in g.hidden_ids:
        g.add_edge(inp, hid, weight=0.1, delay=0)
for hid in g.hidden_ids:
    for out in g.output_ids:
        g.add_edge(hid, out, weight=0.1, delay=0)

agent = GraphAgent(graph=g, obs_dim=4, n_actions=2)
ctrl  = TopologyController(g, grow_op="insert_edge", grow_cooldown=20)

# Plug into any tensor-optix LoopController
loop = LoopController(agent=agent, pipeline=pipeline, callbacks=[ctrl])
loop.run()

Topology operations

All operations are function-preserving - output is identical before and after.

Grow:

• insert_neuron_on_edge(graph, edge_id) - inserts a relay neuron on an existing edge, splitting its delay
• split_neuron(graph, neuron_id) - duplicates a neuron, halves outgoing weights
• add_input_neuron(graph) - adds a new input neuron with zero-weight connections (for new task dimensions)
• add_free_edge(graph, src, dst, delay) - adds any edge with w=0

Prune:

• prune_edge(graph, edge_id) - removes a low-magnitude edge
• prune_neuron(graph, neuron_id) - redistributes signal then removes neuron
• merge_neurons(graph, id_a, id_b) - collapses two near-identical neurons into one

Variable-delay recurrence

Every edge carries a delay parameter - the number of timesteps back it reads:

h_v^(t) = σ( b_v + Σ w_{uv} · h_u^(t-d) )

delay=0 is feedforward; delay≥1 is recurrent. Both are handled by the same forward pass via per-neuron history buffers. This makes the network naturally suited to POMDPs and temporal tasks without a separate LSTM.

TopologyController trigger logic

The controller hooks into LoopController via on_plateau (fires on COOLING state - active learning, not dead):

Signal	Action
Plateau, no overfitting	GROW - insert neuron or edge
Edge |w| < threshold for N episodes	PRUNE edge
Neuron importance < threshold	PRUNE neuron
Cosine similarity > 0.95 between two neurons	MERGE

After every GROW, the BackoffScheduler is partially reset (interval halved by default) so the loop treats the grown network as a fresh start - but retains memory that this region has been hard before.

Math reference

Insert neuron on edge (u→v, w, d):

Add: (u → new, w=1.0, d₁=⌊d/2⌋)
Add: (new → v, w=w,   d₂=d−d₁)
h_new = linear passthrough at init → output preserved exactly

Split neuron v_k → v_k1, v_k2:

Incoming: both copies receive full weight
Outgoing: both copies send w/2  (sum = w)
Output preserved: w·h = w/2·h + w/2·h

New input neuron for observation dim x_i:

w_{new→j} = 0  ∀ j ∈ V
Output preserved: zero weight = silent neuron at init

---

Bio-Plausible Brain Networks

Building on neuroevo, tensor-optix 1.13.0 introduces four biologically-inspired features that can be combined to build brain-like networks.

Dale's Law

Every real neuron is either excitatory (sends positive signals) or inhibitory (sends negative signals) — it never switches. Set cell_type on any neuron and enforce_dale() is called automatically after every optimizer step.

from tensor_optix.neuroevo import NeuronGraph

g = NeuronGraph()
exc = g.add_neuron(role="hidden", activation="relu",  cell_type="excitatory")
inh = g.add_neuron(role="hidden", activation="tanh",  cell_type="inhibitory")
fre = g.add_neuron(role="hidden", activation="tanh",  cell_type="any")  # default, unconstrained

GraphAgent.learn() calls graph.enforce_dale() after every optimizer step, clamping excitatory outgoing weights to >= 0 and inhibitory to <= 0.

---

BrainNetwork

Organize neurons into named brain regions with controlled inter-region connectivity. Each region is a full NeuronGraph that can evolve independently.

from tensor_optix.neuroevo import NeuronGraph, BrainNetwork

sensory   = NeuronGraph()   # build each region ...
memory    = NeuronGraph()
executive = NeuronGraph()
motor     = NeuronGraph()

brain = BrainNetwork(name="agent_brain", output_regions=["motor"])
brain.add_region("sensory",   sensory)
brain.add_region("memory",    memory)
brain.add_region("executive", executive)
brain.add_region("motor",     motor)

# Sparse learnable pathways between regions (zero-weight at init — function preserving)
brain.add_pathway("sensory",   "memory",    n_connections=8,  delay=1)
brain.add_pathway("memory",    "executive", n_connections=4,  delay=2)
brain.add_pathway("executive", "motor",     n_connections=16, delay=0)

out = brain({"sensory": obs_tensor})  # only motor region outputs
print(brain.summary())

---

HebbianHook

Local Hebbian learning running alongside PPO. Neurons that fire together, wire together.

from tensor_optix.neuroevo import HebbianHook

# Attach to a single graph or all regions of a BrainNetwork
hook = HebbianHook.from_brain(brain, hebbian_lr=1e-3, weight_decay=1e-4)

for episode in training_loop:
    obs = env.reset()
    while not done:
        action = agent.act(obs)
        hook.record()              # snapshot co-activations after each forward pass
        obs, reward, done, _ = env.step(action)

    agent.learn(episode_data)      # PPO gradient update
    hook.apply_and_reset()         # Hebbian update + clear accumulators

Δw = η · mean(h_pre · h_post) − λ · w

Respects Dale's Law by default (respect_dale=True).

---

NeuromodulatorSignal

A global broadcast signal that reads the training regime and adjusts plasticity across the entire neuroevo stack — analogous to dopamine, norepinephrine, and acetylcholine.

from tensor_optix.neuroevo import NeuromodulatorSignal
from tensor_optix.core.regime_detector import RegimeDetector

signal = NeuromodulatorSignal(
    detector=RegimeDetector(),
    hebbian_hook=hook,          # modulates hebbian_lr
    agent=agent,                # modulates entropy_coef
    topology_controller=tc,     # modulates grow/prune thresholds
)

# In your training loop, after each episode:
regime = signal.step(metrics_history)
# "trending"  → dopamine ↑    — consolidate, lower plasticity, exploit
# "ranging"   → acetylcholine ↑ — plateau, raise plasticity, grow topology
# "volatile"  → norepinephrine ↑ — dampen Hebbian, boost exploration
print(signal.state)

All four features compose freely: BrainNetwork regions can have Dale-typed neurons, HebbianHook.from_brain() covers all of them, and NeuromodulatorSignal broadcasts regime changes to both the hook and the topology controllers of individual regions.

---

License

MIT - Copyright (c) 2026 sup3rus3r