Abstract: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.
| Subjects: | Machine Learning (cs.LG); Optimization and Control (math.OC) |
| Cite as: | arXiv:2605.06585 [cs.LG] |
| (or arXiv:2605.06585v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.06585 arXiv-issued DOI via DataCite (pending registration) |
From: Vinit Ranjan [view email]
[v1]
Thu, 7 May 2026 17:14:15 UTC (2,499 KB)
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