Learning to Learn by Zeroth-Order Oracle

TL;DR

This paper extends the learning to learn framework to zeroth-order optimization, using neural networks to learn gradient approximation and query strategies, resulting in improved convergence in black-box tasks.

Contribution

It introduces a neural network-based optimizer for zeroth-order optimization that learns gradient estimation and sampling strategies, outperforming traditional algorithms.

Findings

Outperforms hand-designed algorithms in convergence rate.

Effective in practical ZO tasks like black-box adversarial attacks.

Demonstrates the learned optimizer's superiority through extensive experiments.

Abstract

In the learning to learn (L2L) framework, we cast the design of optimization algorithms as a machine learning problem and use deep neural networks to learn the update rules. In this paper, we extend the L2L framework to zeroth-order (ZO) optimization setting, where no explicit gradient information is available. Our learned optimizer, modeled as recurrent neural network (RNN), first approximates gradient by ZO gradient estimator and then produces parameter update utilizing the knowledge of previous iterations. To reduce high variance effect due to ZO gradient estimator, we further introduce another RNN to learn the Gaussian sampling rule and dynamically guide the query direction sampling. Our learned optimizer outperforms hand-designed algorithms in terms of convergence rate and final solution on both synthetic and practical ZO optimization tasks (in particular, the black-box adversarial attack task, which is one of the most widely used tasks of ZO optimization). We finally conduct extensive analytical experiments to demonstrate the effectiveness of our proposed optimizer.