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Proximal random reshuffling under local Lipschitz continuity
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abstract
We study proximal random reshuffling (PRR) for minimizing the sum of locally Lipschitz or locally smooth functions and a proper lower semicontinuous convex function without assuming coercivity or the existence of limit points. The algorithmic guarantees pertaining to near approximate stationarity rely on a new tracking lemma linking the iterates to trajectories of conservative fields. One of the novelties in the analysis consists in handling set-valued mappings with unbounded values. In the locally smooth case, it improves the known convergence rate from nearly $O(k^{-1/4})$ to nearly $o(k^{-1/2})$.
Forward citations
Cited by 2 Pith papers
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Stochastic Saddle Avoidance Beyond Unit Excitation and Smoothness: A Pathwise Lyapunov-Perron Framework
A new pathwise Lyapunov-Perron framework proves almost sure saddle avoidance for stochastic recursions without unit excitation, covering SGD, mirror descent, proximal stochastic gradient, and random reshuffling.
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Improved Last-Iterate Convergence of Shuffling Gradient Methods for Nonsmooth Convex Optimization
For nonsmooth convex finite-sum optimization, random reshuffling and single shuffle achieve last-iterate rates up to n^{1/4} and n^{1/2} faster than proximal gradient descent, with random reshuffling suffix average ma...
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