Mean Robust Optimization

Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions because of pessimistic assumptions on the uncertain parameters. Wasserstein distributionally robust optimization can reduce conservatism by being closely data-driven, but it often leads to very large problems with prohibitive solution times. We introduce mean robust optimization, a general framework that combines the best of both worlds by providing a trade-off between computational effort and conservatism. Using machine learning, we define uncertainty sets and constraints around clustered data points, undergoing a significant size reduction while preserving key properties. We show finite-sample performance guarantees and conditions for which clustering does not increase conservatism, and otherwise provide bounds on the effect on conservatism. Numerical examples illustrate the high efficiency and performance preservation of our approach.