2023/02/24 by Randal Douc, Douc, Randal, Sylvain Le Corff +1
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #Machine Learning (stat.ML) #Optimization and Variational Analysis #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2302.12544
openalex publication_date 2023/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces a general framework for iterative optimization algorithms and establishes under general assumptions that their convergence is asymptotically geometric. We also prove that under appropriate assumptions, the rate of convergence can be lower bounded. The convergence is then only geometric, and we provide the exact asymptotic convergence rate. This framework allows to deal with constrained optimization and encompasses the Expectation Maximization algorithm and the mirror descent algorithm, as well as some variants such as the alpha-Expectation Maximization or the Mirror Prox algorithm.Furthermore, we establish sufficient conditions for the convergence of the Mirror Prox algorithm, under which the method converges systematically to the unique minimizer of a convex function on a convex compact set.