pilot-optimizer 0.1.0

PILOT: Policy-Informed Learned Optimization for Adaptive Deep Network Training

PILOT: Policy-Informed Learned Optimization for Adaptive Deep Network Training

PILOT is an online adaptive optimizer that adjusts its update behavior during training using gradient-direction agreement as a signal of local optimization stability.

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Overview

Most optimizers use a fixed update structure throughout training — a static balance between momentum, normalization, and sign-based updates that cannot respond to how the loss landscape evolves.

PILOT introduces a learnable policy that continuously modulates three core update primitives:

• Momentum reliance — how much to rely on accumulated gradient history vs. the current gradient
• Variance-normalization strength — how aggressively to apply adaptive scaling
• Sign-based behavior — how much to compress gradient magnitudes toward ±1

The policy is conditioned on a smoothed gradient-direction agreement signal, which serves as a compact online descriptor of local update consistency. It is updated online during training using a one-step meta-gradient estimate — no offline search, no meta-training phase, no second-order estimation.

PILOT follows a distinct trajectory through the loss surface and converges to a lower-loss region compared to Adam, AdamW, Lion, and Sophia.

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Key Results

CNN Architecture

Dataset	Optimizer	Accuracy (%) ↑	Val Loss ↓	Loss Var. ↓
FashionMNIST	Adam	93.28	0.1957	0.0033
FashionMNIST	AdamW	93.22	0.1944	0.0034
FashionMNIST	Lion	92.91	0.2091	0.0041
FashionMNIST	AdaBelief	93.66	0.1822	0.0046
FashionMNIST	PILOT (Ours)	94.13	0.1719	0.0045
CIFAR-10	Adam	79.91	0.5794	0.0103
CIFAR-10	Lion	80.87	0.5487	0.0105
CIFAR-10	PILOT (Ours)	81.94	0.5302	0.0073

ResNet-18 Architecture

Dataset	Optimizer	Accuracy (%) ↑	Val Loss ↓	Loss Var. ↓
FashionMNIST	AdaBelief	95.33	0.1711	0.0056
FashionMNIST	PILOT (Ours)	95.71	0.2690	0.0030
CIFAR-10	Adam	93.18	0.2140	0.0073
CIFAR-10	AdamW	92.90	0.2514	0.0066
CIFAR-10	PILOT (Ours)	93.42	0.2496	0.0001

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Method

Gradient-Direction Agreement

At each step, PILOT computes the cosine similarity between successive gradients:

$$r_t = \frac{g_t^\top g_{t-1}}{|g_t|2 , |g{t-1}|_2 + \epsilon}$$

This is smoothed via an exponential moving average:

$$\rho_t = \gamma \rho_{t-1} + (1 - \gamma) r_t$$

Positive values indicate stable, aligned gradients. Values near zero indicate noise. Negative values indicate directional disagreement.

Learnable Policy

The smoothed signal $\rho_t$ is fed through polynomial functions followed by sigmoid activations to produce three scalar control variables:

$$p_{m,t} = \sigma(f(\rho_t; \phi_m)), \quad p_{v,t} = \tfrac{1}{2}\sigma(f(\rho_t; \phi_v)), \quad p_{s,t} = \sigma(f(\rho_t; \phi_s))$$

The total number of learnable policy parameters is $3(d+1)$, where $d$ is the polynomial degree.

Update Rule

$$\theta_{t+1} = \theta_t - \eta \frac{(|n_t| + \epsilon_n)^{1 - p_{s,t}} \odot \text{sign}(n_t)}{\hat{v}t^{,p{v,t}} + \epsilon}$$

where $n_t = p_{m,t} \hat{m}t + (1 - p{m,t}) g_t$ is the policy-controlled blend of momentum and current gradient.

This formulation recovers Adam ($p_m=1, p_v=0.5, p_s=0$) and sign-based updates ($p_s=1, p_v=0$) as special cases.

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Installation

pip install pilot-optimizer

Or install from source:

git clone https://github.com/SattamAltwaim/PILOT.git
cd PILOT
pip install -e .

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Usage

from pilot import PILOT

optimizer = PILOT(
    model.parameters(),
    lr=1e-3,
    betas=(0.9, 0.999),
    weight_decay=1e-4,
    gamma=0.95,        # smoothing coefficient for agreement signal
    lr_phi=0.01,       # policy learning rate
    degree=2           # polynomial degree
)

for batch in dataloader:
    loss = criterion(model(x), y)
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

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Hyperparameters

Parameter	Description	Typical Range
lr	Model learning rate	1e-4 – 1e-3
betas	Moment coefficients	(0.9, 0.999)
gamma	Agreement signal smoothing	0.85 – 0.99
lr_phi	Policy learning rate	5e-4 – 5e-2
degree	Polynomial degree	1 – 4

Configuration-Specific Selections

Dataset	Architecture	γ	η_φ	Degree
CIFAR-10	CNN	0.882	0.00312	1
CIFAR-10	ResNet-18	0.950	0.00500	2
FashionMNIST	CNN	0.950	0.01000	2
FashionMNIST	ResNet-18	0.957	0.00273	3

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Experiments

Experiments use 30 epochs, cross-entropy loss, cosine annealing LR schedule, batch size 128, and AMP. ResNet-18 configurations include a 3-epoch linear warmup.

# CNN on CIFAR-10
python train.py --dataset cifar10 --arch cnn --optimizer pilot

# ResNet-18 on FashionMNIST
python train.py --dataset fashionmnist --arch resnet18 --optimizer pilot