Wasserstein Regularization for 0-1 Loss

Wasserstein distributionally robust optimization (DRO) finds robust solutions by hedging against data perturbation specified by distributions in a Wasserstein ball. The robustness is linked to the regularization effect, which has been studied for continuous losses in various settings. However, existing results cannot be simply applied to the 0-1 loss, which is frequently seen in uncertainty … Read more

Decision-making with Side Information: A Causal Transport Robust Approach

We consider stochastic optimization with side information where, prior to decision making, covariate data are available to inform better decisions.¬†In particular, we propose to consider a distributionally robust formulation based on causal transport distance.¬†Compared with divergence and Wasserstein metric, the causal transport distance is better at capturing the information structure revealed from the conditional distribution … Read more

Data-driven Multistage Distributionally Robust Optimization with Nested Distance

We study multistage distributionally robust linear optimization, where the uncertainty set is a ball of distributions defined through the nested distance (Pflug and Pichler 2012) centered at a scenario tree. This choice of uncertainty set, as opposed to alternatives like the Wasserstein distance between stochastic processes, takes account of information evolution, making it hedge against … Read more

Optimal Robust Policy for Feature-Based Newsvendor

We study policy optimization for the feature-based newsvendor, which seeks an end-to-end policy that renders an explicit mapping from features to ordering decisions. Unlike existing works that restrict the policies to some parametric class which may suffer from sub-optimality (such as affine class) or lack of interpretability (such as neural networks), we aim to optimize … Read more

Contextual Decision-making under Parametric Uncertainty and Data-driven Optimistic Optimization

We consider decision-making problems with contextual information, in which the reward function involves uncertain parameters that can be predicted using covariates. To quantify the uncertainty of the reward, we propose a new parameter uncertainty set based on a supervised learning oracle. We show that the worst/best-case reward over the proposed parameter uncertainty set serves as … Read more

Sinkhorn Distributionally Robust Optimization

We study distributionally robust optimization (DRO) with Sinkhorn distance—a variant of Wasserstein distance based on entropic regularization. We derive convex programming dual reformulation for general nominal distributions, transport costs, and loss functions. Compared with Wasserstein DRO, our proposed approach offers enhanced computational tractability for a broader class of loss functions, and the worst-case distribution exhibits … Read more

Reliable Off-policy Evaluation for Reinforcement Learning

In a sequential decision-making problem, off-policy evaluation estimates the expected cumulative reward of a target policy using logged trajectory data generated from a different behavior policy, without execution of the target policy. Reinforcement learning in high-stake environments, such as healthcare and education, is often limited to off-policy settings due to safety or ethical concerns, or … Read more

Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality

Wasserstein distributionally robust optimization (DRO) aims to find robust and generalizable solutions by hedging against data perturbations in Wasserstein distance. Despite its recent empirical success in operations research and machine learning, existing performance guarantees for generic loss functions are either overly conservative due to the curse of dimensionality, or plausible only in large sample asymptotics. … Read more

Wasserstein Distributionally Robust Optimization and Variation Regularization

Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although the connection between Wasserstein DRO and regularization has been established in several settings, existing results often require restrictive assumptions, such as smoothness or convexity, that are not satisfied by … Read more

Distributionally Robust Stochastic Optimization with Dependence Structure

Distributionally robust stochastic optimization (DRSO) is a framework for decision-making problems under certainty, which finds solutions that perform well for a chosen set of probability distributions. Many different approaches for specifying a set of distributions have been proposed. The choice matters, because it affects the results, and the relative performance of different choices depend on … Read more