2015/05/11 by Wesley Cowan, Cowan, Wesley, Michael N. Katehakis +1 · 1 citation
Computer Science · Decision Sciences · Mathematics · #62L10 #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Search Problems #Reinforcement Learning in Robotics #Risk and Portfolio Optimization #cs.LG #msc:62L10 #stat.ML
paper · pdf · doi:10.48550/arxiv.1505.02865
openalex publication_date 2015/05/11 · arxiv created 2015/12/17 · arxiv updated 2015/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to provide further understanding into the structure of the sequential allocation ("stochastic multi-armed bandit", or MAB) problem by establishing probability one finite horizon bounds and convergence rates for the sample (or "pseudo") regret associated with two simple classes of allocation policies π. For any slowly increasing function g, subject to mild regularity constraints, we construct two policies (the g-Forcing, and the g-Inflated Sample Mean) that achieve a measure of regret of order O(g(n)) almost surely as n → ∞, bound from above and below. Additionally, almost sure upper and lower bounds on the remainder term are established. In the constructions herein, the function g effectively controls the "exploration" of the classical "exploration/exploitation" tradeoff.