Orateur
Description
Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein distributionally robust optimization can reduce conservatism by being data-driven, but it often leads to large problems with prohibitive solution times. In this talk, we introduce Mean Robust Optimization, a general framework that combines the best of both worlds by constructing data-driven uncertainty sets based on compressed data, significantly improving computational tractability. By varying the number of clusters, Mean Robust Optimization balances computational complexity and conservatism, and effectively bridges robust and Wasserstein distributionally robust optimization. We show finite-sample performance guarantees and explicitly control the potential pessimism introduced by any clustering procedure. We further extend Mean Robust Optimization to sequential decision problems with streaming data, by dynamically updating the clusters to efficiently adjust the uncertainty sets. We illustrate the benefits of our framework on several numerical examples, obtaining significant computational speedups with little-to-no effect on the solution quality.
