Research

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 s₀. In this paper, we introduce a novel model-based approach that interleaves discovering new states from s₀ 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 Õ(L⁵S_{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 s₀ 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.