Mixed Strategies for Robust Optimization of Unknown Objectives [article]

Pier Giuseppe Sessa, Ilija Bogunovic, Maryam Kamgarpour, Andreas Krause
2020 arXiv   pre-print
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
more » ... 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.
arXiv:2002.12613v2 fatcat:egt4hxnbcngclc4j3kgqibyfry