pilot-optimizer 0.1.0.post2

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

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

Project Page  |  Paper  |  PyPI

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PILOT is an online adaptive optimizer that adjusts its update behavior during training. Instead of applying a fixed update rule from the first step to the last, PILOT reads a gradient-direction agreement signal and reshapes the update through a lightweight learned policy — no offline search, no meta-training, no second-order estimation.

Installation

pip install pilot-optimizer

Or install from source

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

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 for agreement signal
    eta_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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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

Full results with all baselines in the paper.

Training Curves

Training loss (left, middle) and validation accuracy (right) across FashionMNIST (top) and CIFAR-10 (bottom) over 30 epochs.

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Loss Landscape

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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Method

PILOT monitors gradient-direction agreement (cosine similarity between successive gradients, smoothed into a running signal) and feeds it through a learned polynomial to produce three control knobs:

• Momentum reliance — trust the accumulated trend vs. react to the current gradient
• Variance normalization — how aggressively to apply adaptive scaling
• Sign compression — use full gradient magnitudes vs. compress toward ±1

Only 3(d+1) learnable coefficients (9 for degree 2). Initialized so PILOT starts as Adam and learns to deviate. The policy is updated each step via analytic meta-gradients at negligible cost. See the paper for the full derivation.

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Hyperparameters

Parameter	Description	Default / Range
lr	Learning rate	1e-3
betas	Moment coefficients	(0.9, 0.999)
weight_decay	Decoupled weight decay	0.01
gamma	Agreement signal smoothing	0.85–0.99
eta_phi	Policy learning rate	5e-4–5e-2
degree	Polynomial degree	1–4

Tuned configurations from the paper

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

Selected via Bayesian optimization (TPE + ASHA early stopping, 30–40 trials).

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Experiment Setup

30 epochs · cross-entropy loss · cosine annealing LR · batch size 128 · AMP · 3-epoch linear warmup for ResNet-18. Benchmarked on NVIDIA V100 GPUs. See the paper for full details.

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Citation

@article{altuuaim2026pilot,
  title   = {PILOT: Policy-Informed Learned Optimization for
             Adaptive Deep Network Training},
  author  = {Altuuaim, Sattam and Ayash, Lama and
             Mubashar, Muhammad and Khan, Naeemullah},
  journal = {arXiv preprint arXiv:2605.24570},
  year    = {2026}
}

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License

MIT