# No-Regret Exploration in Goal-Oriented Reinforcement Learning

Many popular reinforcement learning problems (e.g., navigation in a maze, some Atari games, mountain car) are instances of the so-called episodic setting or stochastic shortest path (SSP) problem, where an agent has to achieve a predefined goal state (e.g., the top of the hill) while maximizing the cumulative reward or minimizing the cumulative cost. Despite its popularity, most of the literature studying the exploration-exploitation dilemma either focused on different problems (i.e., fixed-horizon and infinite-horizon) or made the restrictive loop-free assumption (which implies that no same state can be visited twice during any episode). In this paper, we study the general SSP setting and introduce the algorithm UC-SSP whose regret scales as O(c_max^3/2 c_min^-1/2 D S √( A D K)) after K episodes for any unknown SSP with S non-terminal states, A actions, an SSP-diameter of D and positive costs in [c_min, c_max]. UC-SSP is thus the first learning algorithm with vanishing regret in the theoretically challenging setting of episodic RL.

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