Authors: Vinit Ranjan, Jisun Park, Bartolomeo Stellato
Organizations: Department of Operations Research and Financial Engineering, Princeton University. · Department of Operations Research and Financial Engineering, Princeton University, and Research Institute of Mathematics, Seoul National University. · Research Institute of Mathematics, Seoul National University.
We propose a distributionally robust approach to learning hyperparameters for first-order methods in convex optimization. Given a dataset of problem instances, we minimize a Wasserstein distributionally robust version of the performance estimation problem (PEP) over algorithm parameters such as step sizes. Our framework unifies two extremes: as the robustness radius vanishes, we recover classical learning to optimize (L2O); as it grows, we recover worst-case optimal algorithm design via PEP. We solve the resulting problem with stochastic gradient descent, differentiating through the solution of an inner semidefinite program at each step. We prove high-probability bounds showing that the true risk of the learned algorithm is at most the in-sample L2O optimum plus a slack that shrinks with the sample size, and is no worse than the worst-case PEP bound. On unconstrained quadratic minimization, LASSO, and linear programming benchmarks, our learned algorithms achieve strong out-of-sample performance with certifiable robustness, outperforming both worst-case optimal and vanilla L2O baselines.
The literature has proposed various robust alternatives to empirical risk minimisation to address failure modes such as distribution shift, label noise and finite-sample degeneracies. Examples include distributionally robust optimization, label smoothing, vicinal risk minimization, and Mixup. However, such approaches are typically developed in isolation, forcing practitioners to commit a priori to a single failure mode even when the dominant mode for the task is unclear. To address this, we organize a broad class of existing methods along three common design axes and derive a tractable training procedure that decomposes robust learning into sequential stages (reference distribution enrichment, input-space perturbation, label-space perturbation, and sample-level aggregation), each with a choice of stance (pessimistic, neutral, or optimistic). This results in a unified design space in which joint hyperparameter optimization can compose and configure robustness strategies suited to the task at hand. Across tabular, image, and reward modeling benchmarks, joint hyperparameter optimization is competitive with the best single-method baseline in each setting, offering a reliable default for practitioners who do not know a priori which failure mode dominates their task.
Jonas Hanselle, Valentin Margraf, Clemens Damke +1
Distributional shifts arise when the target deployment environment differs from the source environment that generated the training data. Robust learning frameworks such as Distributionally Robust Optimization (DRO) and Robust Satisficing (RS) aim to address this challenge, yet their finite-sample guarantees under such shifts, and their systematic comparison, remain underexplored: existing analyses typically establish guarantees either in the source environment or for adversarial worst-case performance over an ambiguity set. This paper instead studies generalization error in the target environment---the excess loss under the shifted target distribution. Our contributions are threefold. First, we derive finite-sample generalization error bounds in the shifted target environment for both DRO and RS. These bounds explicitly characterize the trade-off between reduced sensitivity to shift and the regularization penalty induced by each method's robustness hyperparameter, and they avoid the curse of dimensionality associated with Wasserstein empirical concentration. Second, when partial shift information such as shift magnitude or direction is available, we propose information-directed hyperparameter calibrations and compare the two methods given the same information. Under these calibrations, and in the partial-information regimes we study, DRO and RS exhibit complementary theoretical and empirical behavior. Finally, we apply the framework to a network lot-sizing problem, using it to interpret how robust policies respond to positive shifts in the demand distribution. Together, these results fill a gap in understanding the statistical properties of robust learning methods under distributional shifts and provide a principled basis for comparing DRO and RS.
Distributionally robust optimization (DRO) is widely used for decision-making under uncertainty, but its adversarial focus on worst-case loss can lead to overly conservative policies. To mitigate this, we study ex-ante Distributionally Robust Regret Optimization (DRRO) with Wasserstein ambiguity sets, designed to balance robustness with upside potential. We develop a theory of Wasserstein DRRO (WDRRO) paralleling Wasserstein DRO. Under smoothness and regularity, WDRRO selects among ERM optima by a first-order gradient-discrepancy rule. If the ERM optimizer is unique, first-order sensitivity vanishes and a second-order expansion governs deviations. For convex quadratics ERM and DRRO coincide for any radius. We then study regimes where these assumptions fail: nondifferentiable max-affine losses, discrete references, and larger radii, where WDRRO can differ from ERM and WDRO. We show that computing WDRRO regret is NP-hard even without bilinear terms. Nevertheless, we develop exact algorithms, a tractable convex relaxation with guarantees, and experiments showing tightness and loss-dependent behavior.