Develops infinite-horizon stationary robust mean-field games incorporating distributional uncertainty, proves equilibrium existence via fixed-point on contractive Bellman operator, gives convergent algorithm, and derives finite-population approximation bounds under contractive regime.
On the Convergence Rate of Stochastic Mirror Descent for Nonsmooth Nonconvex Optimization
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abstract
In this paper, we investigate the non-asymptotic stationary convergence behavior of Stochastic Mirror Descent (SMD) for nonconvex optimization. We focus on a general class of nonconvex nonsmooth stochastic optimization problems, in which the objective can be decomposed into a relatively weakly convex function (possibly non-Lipschitz) and a simple non-smooth convex regularizer. We prove that SMD, without the use of mini-batch, is guaranteed to converge to a stationary point in a convergence rate of $ \mathcal{O}(1/\sqrt{t}) $. The efficiency estimate matches with existing results for stochastic subgradient method, but is evaluated under a stronger stationarity measure. Our convergence analysis applies to both the original SMD and its proximal version, as well as the deterministic variants, for solving relatively weakly convex problems.
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cs.LG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Stationary Robust Mean-Field Games under Model Mismatches
Develops infinite-horizon stationary robust mean-field games incorporating distributional uncertainty, proves equilibrium existence via fixed-point on contractive Bellman operator, gives convergent algorithm, and derives finite-population approximation bounds under contractive regime.