Provable Multi-Objective Reinforcement Learning with Generative Models

Multi-objective reinforcement learning (MORL) is an extension of ordinary, single-objective reinforcement learning (RL) that is applicable to many real world tasks where multiple objectives exist without known relative costs. We study the problem of single policy MORL, which learns an optimal policy given the preference of objectives. Existing methods require strong assumptions such as exact knowledge of the multi-objective Markov decision process, and are analyzed in the limit of infinite data and time. We propose a new algorithm called model-based envelop value iteration (EVI), which generalizes the enveloped multi-objective $Q$-learning algorithm in Yang, 2019. Our method can learn a near-optimal value function with polynomial sample complexity and linear convergence speed. To the best of our knowledge, this is the first finite-sample analysis of MORL algorithms.