samsara-rl 0.0.5

Vectorized Reinforcement Learning Library

Samsara RL

A vectorized NumPy implementation of foundational reinforcement learning algorithms, following David Silver's RL lecture series, Sutton and Barto book and other papers cited when referenced. Built for clarity, learning as well as speed.

Applications of RL include robotic manipulation, LLM fine-tuning, financial portfolio management, and control systems.

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Table of Contents

1. Installation
2. Quick Start
3. Planning
   • MDP Structure
   • Policy Iteration
   • Value Iteration
4. Model-Free Prediction
   • Monte Carlo
   • TD Learning
5. Model-Free Control
   • SARSA
   • Q-Learning
6. Function Approximation

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Installation

pip install samsara-rl

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Quick Start

from samsara_rl.mdp.grid_world.grid_world_mdp import GridWorldMDP
from samsara_rl.planning.policy_iteration import PolicyIteration

mdp = GridWorldMDP()
pi = PolicyIteration(mdp)
policy = pi.find_optimal_policy()

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Planning

Planning algorithms assume full knowledge of environment dynamics (transition probabilities and reward function). While not "true RL" — agents never have access to dynamics in practice — planning provides the theoretical foundation all RL algorithms build on.

MDP Structure

MDPs are represented as NumPy arrays. The included GridWorldMDP implements the 4x4 grid world from David Silver's Lecture 3.

Attribute	Shape	Description
state_action_transition_matrix	(S, A, S')	T(s, a, s') — transition probabilities
reward_matrix	(S, A, S')	R(s, a, s') — reward for each transition

Policy Iteration

Alternates between evaluating the current policy using the Bellman expectation equation and improving it greedily until the policy stops changing.

PolicyIteration(mdp, bellman_tolerance)

Argument	Type	Default	Description
mdp	MDP		MDP instance to solve
bellman_tolerance	float	0.01	Convergence threshold for policy evaluation

find_optimal_policy(max_iter)

Argument	Type	Default	Description
max_iter	int	99	Maximum number of policy iteration steps

Value Iteration

Applies the Bellman optimality equation directly each iteration. Equivalent to policy iteration with k=1 evaluation steps per improvement. Policy is extracted once at convergence.

ValueIteration(mdp, bellman_tolerance)

Argument	Type	Default	Description
mdp	MDP		MDP instance to solve
bellman_tolerance	float	0.01	Convergence threshold for value iteration

Examples

from samsara_rl.mdp.grid_world.grid_world_mdp import GridWorldMDP
from samsara_rl.planning.policy_iteration import PolicyIteration
from samsara_rl.planning.value_iteration import ValueIteration

mdp = GridWorldMDP()

policy = PolicyIteration(mdp, bellman_tolerance=0.001).find_optimal_policy(max_iter=50)
policy = ValueIteration(mdp, bellman_tolerance=0.001).find_optimal_policy()

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Model-Free Prediction

Model-free methods learn value functions directly from experience (sampled episodes) without access to the MDP's transition or reward dynamics.

Monte Carlo

Every-visit Monte Carlo prediction estimates Q(s, a) from sampled returns. After each episode, the return G_t (discounted cumulative reward from time step t onward) is computed for every visited state-action pair, and the Q-table is updated using constant-alpha learning:

Q(s, a) ← Q(s, a) + α (G_t − Q(s, a))

If the same (s, a) pair appears multiple times in an episode, each occurrence triggers an update. Returns are computed in a fully vectorized pass using a cumulative-sum trick that avoids the standard reverse loop over time steps.

MonteCarloPrediction(mdp, policy, alpha, gamma)

Argument	Type	Default	Description
mdp	MDP		MDP instance to sample episodes from
policy	array		Stochastic policy of shape (S, A)
alpha	float	0.01	Learning rate for incremental Q updates
gamma	float	1	Discount factor

evaluate(max_iter)

Argument	Type	Default	Description
max_iter	int	10000	Number of episodes to sample from

TD(λ)

TD(λ) learns Q(s, a) online using one-step bootstrapping with eligibility traces. After each step, the TD error is computed against the expected Q-value of the next state under the current policy, and all previously visited state-action pairs are updated proportionally to their eligibility:

δ = R + γ E_π[Q(S', ·)] − Q(S, A)

Q(s, a) ← Q(s, a) + α δ e(s, a)

Eligibility traces use the replacing variant — on each visit to (s, a), the trace is set to 1 rather than incremented. All traces decay by γλ at each time step. Traces are reset to zero between episodes.

TemporalDifference(mdp, policy, alpha, gamma, _lambda)

Argument	Type	Default	Description
mdp	MDP		MDP instance to sample episodes from
policy	array		Stochastic policy of shape (S, A)
alpha	float	0.01	Learning rate for incremental Q updates
gamma	float	0.9	Discount factor
_lambda	float	0.4	Trace decay parameter (0 = TD(0), 1 = TD(1))

evaluate(max_iter)

Argument	Type	Default	Description
max_iter	int	1000	Number of episodes to sample from

Examples

from samsara_rl.mdp.grid_world.grid_world_mdp import GridWorldMDP
from samsara_rl.prediction.monte_carlo import MonteCarloPrediction
from samsara_rl.prediction.td import TemporalDifference
from samsara_rl.utils.policy.policy_utils import init_uniform_random

mdp = GridWorldMDP()
policy = init_uniform_random(mdp)

mc = MonteCarloPrediction(mdp, policy, alpha=0.01, gamma=0.9)
mc.evaluate(max_iter=10000)

td = TemporalDifference(mdp, policy, alpha=0.01, gamma=0.9, _lambda=0.4)
td.evaluate(max_iter=10000)

# V(s) for the random policy (expected value over actions)
v_mc = mc.q_table.mean(axis=1).reshape(4, 4)
v_td = td.q_table.mean(axis=1).reshape(4, 4)

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Model-Free Control

Control algorithms learn an optimal policy by interleaving evaluation and improvement on every step. Both SARSA and Q-Learning build on the TD(λ) engine, using ε-greedy exploration to balance exploitation with discovery of new state-action pairs.

SARSA

On-policy TD control. Bootstraps from a sampled next action A' drawn from the current policy — the name comes from the quintuple (S, A, R, S', A'). Because the bootstrap target reflects the exploratory policy, SARSA's Q values account for the cost of occasional random actions.

δ = R + γ Q(S', A') − Q(S, A)

Sarsa(mdp, policy, alpha, gamma)

Argument	Type	Default	Description
mdp	MDP		MDP instance to sample episodes from
policy	array		Initial stochastic policy of shape (S, A)
alpha	float	0.01	Learning rate for incremental Q updates
gamma	float	0.9	Discount factor

evaluate(max_iter)

Argument	Type	Default	Description
max_iter	int	5000	Number of episodes to run

Q-Learning

Off-policy TD control. Bootstraps from the greedy action max_a Q(S', a) regardless of the action actually taken. This means Q-Learning converges to the optimal Q* even while following an exploratory ε-greedy policy.

δ = R + γ max_a Q(S', a) − Q(S, A)

QLearning(mdp, policy, alpha, gamma)

Argument	Type	Default	Description
mdp	MDP		MDP instance to sample episodes from
policy	array		Initial stochastic policy of shape (S, A)
alpha	float	0.01	Learning rate for incremental Q updates
gamma	float	0.9	Discount factor

evaluate(max_iter)

Argument	Type	Default	Description
max_iter	int	5000	Number of episodes to run

Examples

from samsara_rl.mdp.grid_world.grid_world_mdp import GridWorldMDP
from samsara_rl.control.tabular.sarsa import Sarsa
from samsara_rl.control.tabular.q_learning import QLearning
from samsara_rl.utils.policy.policy_utils import init_uniform_random

mdp = GridWorldMDP()
policy = init_uniform_random(mdp)

sarsa = Sarsa(mdp, policy, alpha=0.01, gamma=0.9)
sarsa.evaluate(max_iter=5000)

ql = QLearning(mdp, policy, alpha=0.01, gamma=0.9)
ql.evaluate(max_iter=5000)

# Optimal value per state (best action)
v_sarsa = sarsa.agent.q_table.max(axis=1).reshape(4, 4)
v_ql = ql.agent.q_table.max(axis=1).reshape(4, 4)

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Function Approximation

TODO