No-Regret Exploration in Goal-Oriented Reinforcement Learning
This addresses a theoretical gap for researchers in reinforcement learning, providing a foundational algorithm for goal-oriented tasks like navigation, though it is incremental in extending no-regret methods to a broader SSP setting.
The paper tackles the exploration-exploitation dilemma in general stochastic shortest path (SSP) reinforcement learning problems without restrictive assumptions, introducing UC-SSP as the first no-regret algorithm with a proven regret bound of $\widetilde{\mathcal{O}}( D S \sqrt{ A D K})$ after $K$ episodes.
Many popular reinforcement learning problems (e.g., navigation in a maze, some Atari games, mountain car) are instances of the episodic setting under its stochastic shortest path (SSP) formulation, where an agent has to achieve a goal state while minimizing the cumulative cost. Despite the popularity of this setting, the exploration-exploitation dilemma has been sparsely studied in general SSP problems, with most of the theoretical literature focusing on different problems (i.e., fixed-horizon and infinite-horizon) or making the restrictive loop-free SSP assumption (i.e., no state can be visited twice during an episode). In this paper, we study the general SSP problem with no assumption on its dynamics (some policies may actually never reach the goal). We introduce UC-SSP, the first no-regret algorithm in this setting, and prove a regret bound scaling as $\displaystyle \widetilde{\mathcal{O}}( D S \sqrt{ A D K})$ after $K$ episodes for any unknown SSP with $S$ states, $A$ actions, positive costs and SSP-diameter $D$, defined as the smallest expected hitting time from any starting state to the goal. We achieve this result by crafting a novel stopping rule, such that UC-SSP may interrupt the current policy if it is taking too long to achieve the goal and switch to alternative policies that are designed to rapidly terminate the episode.