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Poster
Layered State Discovery for Incremental Autonomous Exploration
Liyu Chen · Andrea Tirinzoni · Alessandro Lazaric · Matteo Pirotta

Thu Jul 27 01:30 PM -- 03:00 PM (PDT) @ Exhibit Hall 1 #724
in Poster Session 5 »
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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Author Information

Liyu Chen (USC)
Andrea Tirinzoni (Facebook AI Research)
Alessandro Lazaric (Facebook AI Research)
Matteo Pirotta (META)

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