Title: Wasserstein Distributionally Robust Minimax Regret Optimization for Multimodal Machine Learning
Primary area: learning theory
Keywords: Wasserstein Distributionally Robust Optimization, Minimax Regret Optimization, Multimodal Machine Learning, Robust Fusion, Convex Optimization, Precision Oncology

Abstract: Learning robust multimodal predictors under distributional uncertainty remains challenging, as empirical risk minimization (ERM) is brittle to modality-specific perturbations and standard distributionally robust optimization (DRO), by minimizing worst-case risk, may yield overly conservative solutions under heterogeneous noise. 
We introduce **Wasserstein Distributionally Robust Minimax Regret Optimization (WDRO-MRO)**, a framework that unifies Wasserstein DRO with minimax regret. By minimizing worst-case *regret* relative to the oracle predictor, WDRO-MRO provides a decision-centric robustness notion that directly bounds performance degradation under heterogeneous shifts. A modality-weighted Wasserstein cost further enables selective protection of vulnerable modalities. 
Theoretically, WDRO-MRO establishes a solid foundation: existence and uniqueness of minimax regret solutions under convex losses, convexity and strong duality of the formulation, and sensitivity characterizations of optimal regret with respect to ambiguity radii and modality weights. We also provide statistical guarantees including consistency, finite-sample generalization bounds, $O(N^{-1/2})$ convergence rates, and explicit sample complexity. Algorithmically, WDRO-MRO admits tractable convex reformulations (LP, SOCP, SDP, and power-cone programs) and introduces a dual-game algorithm that couples strong-dual reformulations with an exponentiated-weights adversary update, yielding an oracle-free no-regret procedure.
Empirically, on the HANCOCK multimodal healthcare dataset, WDRO-MRO maintains competitive average accuracy and improves robustness and fairness compared to ERM and standard DRO, without incurring excessive conservatism.

TL;DR: This paper proposes WDRO-MRO for multimodal learning that admits tractable convex reformulations with statistical guarantees and, on HANCOCK, improves accuracy, robustness, and fairness under distribution shift.