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Description

We study distributionally robust contextual optimization, where a decision maker seeks a context-dependent policy that minimizes the worst-case expected loss over an ambiguity set of joint distributions of covariates and outcomes. Standard approaches first reformulate the worst-case expectation into a tractable finite-dimensional program and then solve an outer policy-optimization problem, typically over a parametric class (e.g., affine rules or neural nets). However, this workflow often obscures the inherent tractability of many contextual OR models, where non-robust policy optimization reduces to simple conditional optimization. To leverage this feature, we invoke a minimax interchange to recast the robust problem as a maximization over distributions, which we solve via a generative approach. Concretely, we compute a least-favorable distribution using a particle-based first-order method, and then recover the robust policy as an optimal response to this distribution. Focusing on Sinkhorn uncertainty sets, we establish global convergence guarantees in the large-particle regime.