Reward-free Model-based Reinforcement Learning With Linear Function Approximation

Abstract

We study the model-based reward-free reinforcement learning with linear function approximation for episodic Markov decision processes (MDPs). In this setting, the agent works in two phases. In the exploration phase, the agent interacts with the environment and collects samples without the reward. In the planning phase, the agent is given a specific reward function and uses samples collected from the exploration phase to learn a good policy. We propose a new provably efficient algorithm, called UCRL-RFE under the Linear Mixture MDP assumption, where the transition probability kernel of the MDP can be parameterized by a linear function over certain feature mappings defined on the triplet of state, action, and next state. We show that to obtain an \(\epsilon\)-optimal policy for arbitrary reward function, UCRL-RFE needs to sample at most \(\tilde\{\mathcal\{O\}\}(H^5d^2\epsilon^\{-2\})\) episodes during the exploration phase. Here, \(H\) is the length of the episode, \(d\) is the dimensio

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