Fast active learning for pure exploration in reinforcement learning

TL;DR

This paper introduces a novel exploration bonus scaling with 1/n for reinforcement learning, leading to faster pure-exploration learning rates and improved sample complexity bounds in reward-free settings.

Contribution

It demonstrates that using a 1/n exploration bonus accelerates pure exploration in reinforcement learning and improves sample complexity bounds for best-policy identification.

Findings

1/n bonus scales lead to faster learning rates

Improved upper bounds on exploration efficiency

Enhanced sample complexity in reward-free exploration

Abstract

Realistic environments often provide agents with very limited feedback. When the environment is initially unknown, the feedback, in the beginning, can be completely absent, and the agents may first choose to devote all their effort on exploring efficiently. The exploration remains a challenge while it has been addressed with many hand-tuned heuristics with different levels of generality on one side, and a few theoretically-backed exploration strategies on the other. Many of them are incarnated by intrinsic motivation and in particular explorations bonuses. A common rule of thumb for exploration bonuses is to use $1/\sqrt{n}$ bonus that is added to the empirical estimates of the reward, where $n$ is a number of times this particular state (or a state-action pair) was visited. We show that, surprisingly, for a pure-exploration objective of reward-free exploration, bonuses that scale with $1/n$ bring faster learning rates, improving the known upper bounds with respect to the dependence on the horizon $H$. Furthermore, we show that with an improved analysis of the stopping time, we can improve by a factor $H$ the sample complexity in the best-policy identification setting, which is another pure-exploration objective, where the environment provides rewards but the agent is not penalized for its behavior during the exploration phase.