Improved Sample Complexity for Incremental Autonomous Exploration in MDPs
This work provides an incremental improvement in sample complexity for autonomous exploration in MDPs, primarily benefiting researchers working on reinforcement learning in unknown environments.
This paper addresses the problem of exploring an unknown environment without a reward function, aiming to learn a set of epsilon-optimal goal-conditioned policies for states incrementally reachable within L steps. The proposed algorithm, DisCo, achieves a sample complexity of O(L^5 S_{L+epsilon} Gamma_{L+epsilon} A epsilon^{-2}), which improves upon prior work in epsilon and L, albeit with an additional Gamma_{L+epsilon} factor.
We investigate the exploration of an unknown environment when no reward function is provided. Building on the incremental exploration setting introduced by Lim and Auer [1], we define the objective of learning the set of $ε$-optimal goal-conditioned policies attaining all states that are incrementally reachable within $L$ steps (in expectation) from a reference state $s_0$. In this paper, we introduce a novel model-based approach that interleaves discovering new states from $s_0$ and improving the accuracy of a model estimate that is used to compute goal-conditioned policies to reach newly discovered states. The resulting algorithm, DisCo, achieves a sample complexity scaling as $\tilde{O}(L^5 S_{L+ε} Γ_{L+ε} A ε^{-2})$, where $A$ is the number of actions, $S_{L+ε}$ is the number of states that are incrementally reachable from $s_0$ in $L+ε$ steps, and $Γ_{L+ε}$ is the branching factor of the dynamics over such states. This improves over the algorithm proposed in [1] in both $ε$ and $L$ at the cost of an extra $Γ_{L+ε}$ factor, which is small in most environments of interest. Furthermore, DisCo is the first algorithm that can return an $ε/c_{\min}$-optimal policy for any cost-sensitive shortest-path problem defined on the $L$-reachable states with minimum cost $c_{\min}$. Finally, we report preliminary empirical results confirming our theoretical findings.