Robust Out-of-Distribution Stochastic Optimization

TL;DR

This paper introduces a robust stochastic optimization framework that learns an uncertainty set over distributions from relevant data, providing strong out-of-distribution guarantees and superior decision-making performance in unseen scenarios.

Contribution

It proposes a novel data-driven approach using RKHS to model distribution uncertainty, with theoretical guarantees and practical algorithms for robust out-of-distribution optimization.

Findings

Outperforms existing methods in out-of-distribution scenarios.

Provides theoretical guarantees for generalization and robustness.

Demonstrates effectiveness on newsvendor and portfolio problems.

Abstract

Data-driven decision-making under uncertainty typically presumes the collection of historical data from an unknown target probability distribution. However, one may have no access to any data from the target distribution prior to decision-making. To address this challenge, we propose robust out-of-distribution stochastic optimization, a novel data-driven framework that effectively utilizes relevant data distributions for robust decision-making under unseen distributions. A key feature of our framework is that all data distributions are assumed to be randomly generated from a meta-distribution over distributions. To describe uncertainty in distribution generation, we propose to learn a data-driven uncertainty set in a reproducing kernel Hilbert space (RKHS) from relevant data distributions, with adjustable conservatism. We then incorporate this set into a min-max stochastic program to derive robust decisions. Notably, under randomness of distribution generation, we establish rigorous out-of-distribution generalization guarantees for the uncertainty set as well as the solution. To ease problem-solving in RKHS, an approximate parametrization with a provably bounded suboptimality and a row generation strategy are presented. Extensive numerical experiments on multi-item newsvendor and portfolio optimization demonstrate the superior out-of-distribution performance of our decision-making framework under unseen data distribution, even when only a small or moderate number of relevant sources are available.