Gradient-Based Adaptive Stochastic Search for Non-Differentiable Optimization

TL;DR

This paper introduces a gradient-based stochastic search algorithm that efficiently solves non-differentiable optimization problems by transforming them into differentiable problems on the sampling distribution's parameter space.

Contribution

It presents a novel method combining stochastic search robustness with gradient speed by optimizing the sampling distribution parameters.

Findings

Converges reliably on complex optimization problems.

Achieves faster convergence than traditional stochastic methods.

Demonstrates effectiveness through numerical experiments.

Abstract

In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized distribution model over the solution space. The basic idea is to convert the original (possibly non-differentiable) problem into a differentiable optimization problem on the parameter space of the parameterized sampling distribution, and then use a direct gradient search method to find improved sampling distributions. Thus, the algorithm combines the robustness feature of stochastic search from considering a population of candidate solutions with the relative fast convergence speed of classical gradient methods by exploiting local differentiable structures. We analyze the convergence and converge rate properties of the proposed algorithm, and carry out numerical study to illustrate its performance.