2023/10/04 by Hao Chen, Abhishek Gupta, Chen, Hao +5
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2310.02941
openalex publication_date 2023/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies Hoeffding's inequality for Markov chains under the generalized concentrability condition defined via integral probability metric (IPM). The generalized concentrability condition establishes a framework that interpolates and extends the existing hypotheses of Markov chain Hoeffding-type inequalities. The flexibility of our framework allows Hoeffding's inequality to be applied beyond the ergodic Markov chains in the traditional sense. We demonstrate the utility by applying our framework to several non-asymptotic analyses arising from the field of machine learning, including (i) a generalization bound for empirical risk minimization with Markovian samples, (ii) a finite sample guarantee for Ployak-Ruppert averaging of SGD, and (iii) a new regret bound for rested Markovian bandits with general state space.