Learning to Learn by Zeroth-Order Oracle

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. Learning to learn (L2L) is a recently proposed meta-learning framework where we leverage deep neural networks to learn optimization algorithms automatically. The most common choice for the learned optimizer is recurrent neural network (RNN) since it can capture long-term dependencies and propose parameter updates based on knowledge of previous iterations. By training RNN op-timizers on predefined optimization tasks, the optimizers are capable of learning to explore the loss landscape and adaptively choose descent directions and steps (Lv et al., 2017).