Layered State Discovery for Incremental Autonomous Exploration

• URL: http://arxiv.org/abs/2302.03789v1
• Date: Tue, 7 Feb 2023 22:58:12 GMT
• Title: Layered State Discovery for Incremental Autonomous Exploration
• Authors: Liyu Chen, Andrea Tirinzoni, Alessandro Lazaric, Matteo Pirotta
• Abstract summary: Layered Autonomous Exploration (LAE) is a novel algorithm for AX that attains a sample complexity of $tildemathcalO(LSrightarrow_LAln12(Srightarrow_LAln12(Srightarrow_LAln12(Srightarrow_LAln12(Srightar row_LAln12(Srightarrow_LAln12
• Score: 106.37656068276901
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the autonomous exploration (AX) problem proposed by Lim & Auer (2012). In this setting, the objective is to discover a set of $\epsilon$-optimal policies reaching a set $\mathcal{S}_L^{\rightarrow}$ of incrementally $L$-controllable states. We introduce a novel layered decomposition of the set of incrementally $L$-controllable states that is based on the iterative application of a state-expansion operator. We leverage these results to design Layered Autonomous Exploration (LAE), a novel algorithm for AX that attains a sample complexity of $\tilde{\mathcal{O}}(LS^{\rightarrow}_{L(1+\epsilon)}\Gamma_{L(1+\epsilon)} A \ln^{12}(S^{\rightarrow}_{L(1+\epsilon)})/\epsilon^2)$, where $S^{\rightarrow}_{L(1+\epsilon)}$ is the number of states that are incrementally $L(1+\epsilon)$-controllable, $A$ is the number of actions, and $\Gamma_{L(1+\epsilon)}$ is the branching factor of the transitions over such states. LAE improves over the algorithm of Tarbouriech et al. (2020a) by a factor of $L^2$ and it is the first algorithm for AX that works in a countably-infinite state space. Moreover, we show that, under a certain identifiability assumption, LAE achieves minimax-optimal sample complexity of $\tilde{\mathcal{O}}(LS^{\rightarrow}_{L}A\ln^{12}(S^{\rightarrow}_{L})/\epsilon^2)$, outperforming existing algorithms and matching for the first time the lower bound proved by Cai et al. (2022) up to logarithmic factors.

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