We study the Sampled-Max Subgradient Method (SMax-SGM) for large convex finite-max problems. Each iteration maximizes over a fresh random subset of the $N$ components and takes one subgradient of the sampled maximizer. The method is therefore stochastic subgradient descent on a sampled-max surrogate. We bound the surro...
E. Gladin, Анна Фёдорровна Попова, Georgii Babinskii· 0 citations
Motivated by the computational challenges of large-scale Cox regression, we study stochastic minimization of LogSumExp objectives over large sets. Mini-batch normalizer estimates generally yield biased gradients. We instead use a softplus surrogate that introduces one auxiliary scalar per normalizer and admits unbiased...
This work derives a finite-sample comparison of clipped and unclipped Polyak-Ruppert averaged SGD under finite conditional $p$-th moments, and gives explicit accuracy and confidence conditions under which, for $p>2$, the Gaussian term dominates the unclipped deviation bound, so clipping need not improve its leading ord...
A. Suvorikova, E. Gladin, D. Dvinskikh et al.· 0 citations
Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin the design and analysis of modern algorithms in RL. We begin from Markov decision processes (MDPs) and Bellman operators, emphasizing contrac...
D. Belomestny, Alexander V. Gasnikov, E. Gladin et al.· Успехи математических наук· 0 citations
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