2024/05/24 by Peter Richtárik, Richtárik, Peter, Abdurakhmon Sadiev +3 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2405.15941
openalex publication_date 2024/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness against imperfect tuning, a trait not shared by the dominant stochastic gradient descent (SGD) algorithm. A framework of assumptions that we introduce encompasses methods employing techniques such as variance reduction and arbitrary sampling. A cornerstone of our general theoretical approach is a parametric assumption on the iterates, correction and control vectors. We establish a single theorem that ensures linear convergence under this assumption and the μ-strong convexity of the loss function, and without the need to invoke smoothness. This integral theorem reinstates best known complexity and convergence guarantees for several existing methods which demonstrates the robustness of our approach. We expand our study by developing three new variants of SPPM, and through numerical experiments we elucidate various properties inherent to them.