# Mixed Strategies for Robust Optimization of Unknown Objectives

arXiv: https://arxiv.org/abs/2002.12613 · HTML: https://mlsanity.com/paper/2002.12613/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2020.

## Built on by (most cited first, 8 of 8)

- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [Risk-averse Heteroscedastic Bayesian Optimization](https://mlsanity.com/paper/2111.03637/) (2021)
- [Movement Penalized Bayesian Optimization with Application to Wind Energy Systems](https://mlsanity.com/paper/2210.08087/) (2022)
- [Adversarial Causal Bayesian Optimization](https://mlsanity.com/paper/2307.16625/) (2023)
- [Batched Kernelized Bandits: Refinements and Extensions](https://mlsanity.com/paper/2603.12627/) (2026)
- [Bayesian Optimization for Min Max Optimization](https://mlsanity.com/paper/2107.13772/) (2021)
- [Equitable System-Prompt Selection via Constrained Mixed-Strategy GroupDRO](https://mlsanity.com/paper/2608.04339/) (2026)

## Abstract (arXiv)

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.