2024/11/27 by Borna Sayedana, Sayedana, Borna, Peter E. Caines +3
Engineering · #Advanced Research in Systems and Signal Processing #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2411.18551
openalex publication_date 2024/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the concentration properties of cumulative reward in Markov Decision Processes (MDPs), focusing on both asymptotic and non-asymptotic settings. We introduce a unified approach to characterize reward concentration in MDPs, covering both infinite-horizon settings (i.e., average and discounted reward frameworks) and finite-horizon setting. Our asymptotic results include the law of large numbers, the central limit theorem, and the law of iterated logarithms, while our non-asymptotic bounds include Azuma-Hoeffding-type inequalities and a non-asymptotic version of the law of iterated logarithms. Additionally, we explore two key implications of our results. First, we analyze the sample path behavior of the difference in rewards between any two stationary policies. Second, we show that two alternative definitions of regret for learning policies proposed in the literature are rate-equivalent. Our proof techniques rely on a martingale decomposition of cumulative reward, properties of the solution to the policy evaluation fixed-point equation, and both asymptotic and non-asymptotic concentration results for martingale difference sequences.