Minibatch Stochastic Three Points Method for Unconstrained Smooth Minimization

TL;DR

This paper introduces MiSTP, a new zero-order optimization algorithm that efficiently minimizes unconstrained smooth functions using stochastic three points, suitable for scenarios with only approximate function evaluations.

Contribution

It extends the stochastic three points method to a minibatch setting, providing a novel zero-order approach with complexity analysis for both convex and nonconvex problems.

Findings

Effective in nonconvex and convex settings

Demonstrates competitive performance on machine learning tasks

Provides theoretical complexity bounds

Abstract

In this paper, we propose a new zero order optimization method called minibatch stochastic three points (MiSTP) method to solve an unconstrained minimization problem in a setting where only an approximation of the objective function evaluation is possible. It is based on the recently proposed stochastic three points (STP) method (Bergou et al., 2020). At each iteration, MiSTP generates a random search direction in a similar manner to STP, but chooses the next iterate based solely on the approximation of the objective function rather than its exact evaluations. We also analyze our method's complexity in the nonconvex and convex cases and evaluate its performance on multiple machine learning tasks.