Mixed Strategies for Robust Optimization of Unknown Objectives

TL;DR

This paper introduces GP-MRO, a sample-efficient algorithm for robust optimization of unknown objectives that learns to find effective mixed strategies against worst-case scenarios, outperforming deterministic approaches.

Contribution

The paper presents a novel algorithm combining Gaussian process confidence bounds with online learning to efficiently discover robust mixed strategies for unknown objectives.

Findings

GP-MRO effectively learns robust mixed strategies with fewer samples.

Mixed strategies outperform deterministic ones in robustness and performance.

Theoretical bounds on sample complexity are established for different GP kernels.

Abstract

We consider robust optimization problems, where the goal is to optimize an unknown objective function against the worst-case realization of an uncertain parameter. For this setting, we design a novel sample-efficient algorithm GP-MRO, which sequentially learns about the unknown objective from noisy point evaluations. GP-MRO seeks to discover a robust and randomized mixed strategy, that maximizes the worst-case expected objective value. To achieve this, it combines techniques from online learning with nonparametric confidence bounds from Gaussian processes. Our theoretical results characterize the number of samples required by GP-MRO to discover a robust near-optimal mixed strategy for different GP kernels of interest. We experimentally demonstrate the performance of our algorithm on synthetic datasets and on human-assisted trajectory planning tasks for autonomous vehicles. In our simulations, we show that robust deterministic strategies can be overly conservative, while the mixed strategies found by GP-MRO significantly improve the overall performance.