Reward-Free Exploration for Reinforcement Learning
This work addresses the exploration bottleneck in RL for scenarios with many reward functions or external reward shaping, offering a near-optimal solution.
The paper tackles the challenge of exploration in reinforcement learning by introducing a reward-free framework where an agent first explores an MDP without a reward function and then computes near-optimal policies for multiple given reward functions. The result is an efficient algorithm with sample complexity of Ω(S^2AH^2/ε^2) and a nearly matching lower bound, achieving ε-suboptimal policies.
Exploration is widely regarded as one of the most challenging aspects of reinforcement learning (RL), with many naive approaches succumbing to exponential sample complexity. To isolate the challenges of exploration, we propose a new "reward-free RL" framework. In the exploration phase, the agent first collects trajectories from an MDP $\mathcal{M}$ without a pre-specified reward function. After exploration, it is tasked with computing near-optimal policies under for $\mathcal{M}$ for a collection of given reward functions. This framework is particularly suitable when there are many reward functions of interest, or when the reward function is shaped by an external agent to elicit desired behavior. We give an efficient algorithm that conducts $\tilde{\mathcal{O}}(S^2A\mathrm{poly}(H)/ε^2)$ episodes of exploration and returns $ε$-suboptimal policies for an arbitrary number of reward functions. We achieve this by finding exploratory policies that visit each "significant" state with probability proportional to its maximum visitation probability under any possible policy. Moreover, our planning procedure can be instantiated by any black-box approximate planner, such as value iteration or natural policy gradient. We also give a nearly-matching $Ω(S^2AH^2/ε^2)$ lower bound, demonstrating the near-optimality of our algorithm in this setting.