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Stochastic Weakly Convex Optimization Beyond Lipschitz Continuity
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abstract
This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the stochastic subgradient method, preserve the $\mathcal{O} ( 1 / \sqrt{K})$ convergence rate with constant failure rate. Our analyses rest on rather weak assumptions: the Lipschitz parameter can be either bounded by a general growth function of $\|x\|$ or locally estimated through independent random samples.
Forward citations
Cited by 2 Pith papers
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An Adaptive Proximal Framework for Stochastic Weakly Convex Optimization
Introduces APS, an adaptive proximal method achieving O(ε^{-2}) iteration complexity for ε-stationary points of ρ-weakly convex functions with unknown ρ in deterministic and stochastic settings.
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Revisiting Randomized Smoothing: Nonsmooth Nonconvex Optimization Beyond Global Lipschitz Continuity
For functions satisfying an (α,β) subgradient growth condition, the paper's variance-reduced randomized smoothing method reaches a (δ,ε)-Goldstein stationary point in Õ(d^{3/2}δ^{-1}ε^{-3}) function evaluations with h...
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