A unified recursion framework for stochastic variance-reduced estimation yields high-probability bounds and the first Õ(ε^{-3}) oracle complexity for stochastic optimization with expectation constraints.
First-order methods for nonsmooth nonconvex functional constrained optimization with or without slater points.SIAM Journal on Optimization, 35(2):1300–1329, 2025
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Heat kernel regularization ensures the regularized Hessian stays asymptotically nondegenerate near nonsmooth minimizers of the form |x|^a, making the continuation equation locally solvable for small t.
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Unified High-Probability Analysis of Stochastic Variance-Reduced Estimation
A unified recursion framework for stochastic variance-reduced estimation yields high-probability bounds and the first Õ(ε^{-3}) oracle complexity for stochastic optimization with expectation constraints.
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From Nonsmooth Minima to Smooth Branches via Heat Kernel Regularization
Heat kernel regularization ensures the regularized Hessian stays asymptotically nondegenerate near nonsmooth minimizers of the form |x|^a, making the continuation equation locally solvable for small t.