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UID:13109-1741262400-1741266900@seasevents.nmsdev7.com
SUMMARY:IDEAS/STAT Optimization Seminar: "Data-Driven Algorithm Design and Verification for Parametric Convex Optimization"
DESCRIPTION:Zoom link \nhttps://upenn.zoom.us/j/98220304722 \n  \nAbstract\nWe present computational tools for analyzing and designing first-order methods in parametric convex optimization. These methods are popular for their low per-iteration cost and warm-starting capabilities. However\, precisely quantifying the number of iterations required to compute high-quality solutions remains a key challenge\, especially in real-time applications. First\, we introduce a numerical framework for verifying the worst-case performance of first-order methods in parametric quadratic optimization. We formulate this as a mixed-integer linear program that maximizes the infinity norm of the fixed-point residual after a given number of iterations. Our approach captures a broad class of gradient\, projection\, and proximal iterations through affine or piecewise-affine constraints\, with strong polyhedral formulations. To improve scalability\, we incorporate bound-tightening techniques that exploit operator-theoretic bounds. Numerical results show that our method closely matches true worst-case performance\, achieving significant reductions in worst-case fixed-point residuals compared to standard convergence analyses. Second\, we present a data-driven approach for analyzing the performance of first-order methods using statistical learning theory. We establish generalization guarantees for classical optimizers using sample convergence bounds and for learned optimizers using the Probably Approximately Correct (PAC)-Bayes framework. We then apply this framework to learn accelerated first-order methods by directly minimizing the PAC-Bayes bound over key algorithmic parameters (e.g.\, gradient steps and warm-starts). Numerical experiments demonstrate that our approach provides strong generalization guarantees for both classical and learned optimizers\, with statistical bounds that closely match true out-of-sample performance.
URL:https://seasevents.nmsdev7.com/event/ideas-stat-optimization-seminar-bartolomeo-stellato/
LOCATION:Amy Gutmann Hall\, Room 414\, 3333 Chestnut Street\, Philadelphia\, 19104\, United States
CATEGORIES:Seminar,Colloquium
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