Target-based Surrogates for Stochastic Optimization

TL;DR

This paper introduces a framework for constructing surrogate functions in a target space to efficiently optimize expensive stochastic functions, with theoretical guarantees and practical benefits demonstrated in supervised and imitation learning tasks.

Contribution

The paper proposes a novel target-based surrogate optimization framework that reduces the cost of gradient computations and provides convergence guarantees, applicable to stochastic and full-batch settings.

Findings

Surrogate functions serve as global upper bounds on the loss in the full-batch setting.

The $SSO$ algorithm offers theoretical guarantees for convex function minimization.

Experiments show improved efficiency and effectiveness in supervised and imitation learning tasks.

Abstract

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a \emph{target space} (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the $SSO$ algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for $SSO$ when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of $SSO$.