Quantile Optimization via Multiple-Timescale Local Search for Black-Box Functions

Author:

Hu Jiaqiao1ORCID,Song Meichen1ORCID,Fu Michael C.23ORCID

Affiliation:

1. Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, New York 11794;

2. Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742;

3. Institute for Systems Research, University of Maryland, College Park, Maryland 20742

Abstract

Black-Box Quantile Optimization via Finite-Difference-Based Gradient Approximation Risk management necessitates consideration of metrics such as quantiles to supplement conventional mean performance measures. In “Quantile Optimization via Multiple-Timescale Local Search for Black-Box Functions,” J. Hu, M. Song, and M. C. Fu consider the problem where the goal is to optimize the quantile of a black-box output. They introduce two new iterative multitimescale stochastic approximation algorithms utilizing finite-difference-based gradient estimators. The first algorithm requires 2d + 1 samples of the black-box function per iteration, where d is the number of decision variables. The second employs a simultaneous-perturbation-based gradient estimator that uses only three samples per iteration, irrespective of the number of decision variables. The authors prove strong local convergence for both algorithms and analyze their finite-time convergence rates through a novel fixed-point argument. These algorithms perform well across a varied set of benchmark problems.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

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