Layered State Discovery for Incremental Autonomous Exploration

02/07/2023
by   Liyu Chen, et al.
0

We study the autonomous exploration (AX) problem proposed by Lim Auer (2012). In this setting, the objective is to discover a set of ϵ-optimal policies reaching a set 𝒮_L^→ 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 𝒪̃(LS^→_L(1+ϵ)Γ_L(1+ϵ) A ln^12(S^→_L(1+ϵ))/ϵ^2), where S^→_L(1+ϵ) is the number of states that are incrementally L(1+ϵ)-controllable, A is the number of actions, and Γ_L(1+ϵ) 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 𝒪̃(LS^→_LAln^12(S^→_L)/ϵ^2), outperforming existing algorithms and matching for the first time the lower bound proved by Cai et al. (2022) up to logarithmic factors.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset