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Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization

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arxiv 2311.10053 v2 pith:WCDCJST4 submitted 2023-11-16 math.OC cs.LGmath.DS

Severin Maier , Camille Castera , Peter Ochs This is my paper · ORCID
classification math.OCcs.LGmath.DS
keywords dampingsystemclosed-loopalgorithmconvergenceconvexlyapunovoptimal
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We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are almost exclusively achieved by non-autonomous methods via open-loop damping (e.g., Nesterov's algorithm), we show that our system, featuring a closed-loop damping, exhibits a rate arbitrarily close to the optimal one. We do so by coupling the damping and the speed of convergence of the system via a well-chosen Lyapunov function. By discretizing our system we then derive an algorithm and present numerical experiments supporting our theoretical findings.

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  1. Stochastic Adaptive Gradient Descent Without Descent

    cs.LG 2025-09 conditional novelty 6.0 of 10

    A new adaptive step-size for SGD, built on the AdaGD Lyapunov function, provably converges in several convex settings without tuned hyper-parameters.

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