Near-Optimal Sample Complexity for Recursive Entropic Risk Reinforcement Learning with a Generative Model

Amirparsa Bahrami, Oliver Mortensen, Mohammad Sadegh Talebi

In this paper, we study the sample complexities of value and policy learning in finite discounted Markov decision processes (MDPs) under recursive entropic risk preferences with risk parameter \(β\neq 0\), assuming access to a generative model of the MDP. We provide a refined analysis of model-based risk-sensitive Q-value iteration (MB-RS-QVI), a plug-in model-based method introduced in prior work, and derive \((\varepsilon,δ)\)-PAC guarantees for both learning the optimal \(Q\)-value function and an \(\varepsilon\)-optimal policy. Our bounds improve the exponential dependence on the effective horizon \(1/(1-γ)\) compared with the best existing guarantees for this setting. In particular, they match the existing lower bounds in their exponential dependence on \(|β|/(1-γ)\), as well as in \(S\), \(A\), \(\varepsilon\), and \(|β|\), up to logarithmic factors. Consequently, our analysis removes the exponential gap between the previously known upper and lower bounds, leaving only a polynomial gap in the effective horizon.