Hoeffding's Inequality for Markov Chains under Generalized Concentrability Condition
This work provides theoretical tools for analyzing Markovian data in machine learning, though it appears incremental as it extends existing frameworks.
This paper extends Hoeffding's inequality to Markov chains under a generalized concentrability condition, enabling applications beyond traditional ergodic chains. It demonstrates utility through three machine learning applications, including generalization bounds and regret bounds.
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.