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- W4319792367 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 $tilde{mathcal{O}}(LS^{rightarrow}_{L}Aln^{12}(S^{rightarrow}_{L})/epsilon^2)$, outperforming existing algorithms and matching for the first time the lower bound proved by Cai et al. (2022) up to logarithmic factors." @default.
- W4319792367 created "2023-02-11" @default.
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- W4319792367 date "2023-02-07" @default.
- W4319792367 modified "2023-09-27" @default.
- W4319792367 title "Layered State Discovery for Incremental Autonomous Exploration" @default.
- W4319792367 doi "https://doi.org/10.48550/arxiv.2302.03789" @default.
- W4319792367 hasPublicationYear "2023" @default.
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