Learning to optimize with guarantees: a complete characterization of linearly convergent algorithms

arXiv:2508.00775v2 Announce Type: replace-cross Abstract: The design of many classical optimization algorithms is driven by the certification of linear convergence rates over classes of optimization problems. In this paper, we consider the problem of improving the average-case performance of an algorithm over a specific distribution of problem instances. While this task can be tackled by embedding trainable components into the algorithm updates, a key challenge is to preserve worst-case guarantees across the entire problem class. For classes of composite optimization problems, we show that all

Source: arXiv cs.LG — read the full report at the original publisher.

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