Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimization

• URL: http://arxiv.org/abs/2401.15771v4
• Date: Fri, 17 May 2024 22:09:15 GMT
• Title: Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimization
• Authors: Nicola Bariletto, Nhat Ho,
• Abstract summary: Training machine learning and statistical models often involve optimizing a data-driven risk criterion. We propose a novel robust criterion by combining insights from Bayesian nonparametric (i.e., Dirichlet process) theory and a recent decision-theoretic model of smooth ambiguity-averse preferences. For practical implementation, we propose and study tractable approximations of the criterion based on well-known Dirichlet process representations.
• Score: 29.24821214671497
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample performance due to distributional uncertainty. In the spirit of distributionally robust optimization, we propose a novel robust criterion by combining insights from Bayesian nonparametric (i.e., Dirichlet process) theory and a recent decision-theoretic model of smooth ambiguity-averse preferences. First, we highlight novel connections with standard regularized empirical risk minimization techniques, among which Ridge and LASSO regressions. Then, we theoretically demonstrate the existence of favorable finite-sample and asymptotic statistical guarantees on the performance of the robust optimization procedure. For practical implementation, we propose and study tractable approximations of the criterion based on well-known Dirichlet process representations. We also show that the smoothness of the criterion naturally leads to standard gradient-based numerical optimization. Finally, we provide insights into the workings of our method by applying it to a variety of tasks based on simulated and real datasets.

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