A Stochastic Record-Value Approach to Global Simulation Optimization

TL;DR

This paper introduces a modified multi-start optimization algorithm called RDMSS, which improves performance over the original DMSS in gradient-based black-box optimization tasks by leveraging stochastic process analysis and empirical testing.

Contribution

It proposes a revised version of DMSS, called RDMSS, tailored for gradient-based inner searches, with theoretical analysis and empirical validation of its effectiveness.

Findings

RDMSS outperforms DMSS in gradient-based optimization scenarios.

Theoretical analysis supports the stochastic stopping criteria used in RDMSS.

Numerical experiments demonstrate RDMSS's improved efficiency and robustness.

Abstract

Black-box optimization is ubiquitous in machine learning, operations research and engineering simulation. Black-box optimization algorithms typically do not assume structural information about the objective function and thus must make use of stochastic information to achieve statistical convergence to a globally optimal solution. One such class of methods is multi-start algorithms which use a probabilistic criteria to: determine when to stop a single run of an iterative optimization algorithm, also called an inner search, when to perform a restart, or outer search, and when to terminate the entire algorithm. Zabinsky, Bulger & Khompatraporn introduced a record-value theoretic multi-start framework called Dynamic Multi-start Sequential Search (DMSS). We observe that DMSS performs poorly when the inner search method is a deterministic gradient-based search. In this thesis, we present an algorithmic modification to DMSS and empirically show that the Revised DMSS (RDMSS) algorithm can outperform DMSS in gradient-based settings for a broad class of objective test functions. We give a theoretical analysis of a stochastic process that was constructed specifically as an inner search stopping criteria within RDMSS. We discuss computational considerations of the RDMSS algorithm. Finally, we present numerical results to determine its effectiveness.