UCB Momentum Q-learning: Correcting the bias without forgetting
This addresses bias correction in Q-learning for tabular episodic MDPs, offering a novel algorithm with theoretical guarantees, though it is incremental in improving regret bounds.
The paper tackles the bias issue in Q-learning for reinforcement learning by proposing UCBMQ, which adds a momentum term and uses optimism to achieve a regret bound of O(√(H³SAT) + H⁴SA), matching the lower bound for large T and improving second-order term scaling.
We propose UCBMQ, Upper Confidence Bound Momentum Q-learning, a new algorithm for reinforcement learning in tabular and possibly stage-dependent, episodic Markov decision process. UCBMQ is based on Q-learning where we add a momentum term and rely on the principle of optimism in face of uncertainty to deal with exploration. Our new technical ingredient of UCBMQ is the use of momentum to correct the bias that Q-learning suffers while, at the same time, limiting the impact it has on the second-order term of the regret. For UCBMQ, we are able to guarantee a regret of at most $O(\sqrt{H^3SAT}+ H^4 S A )$ where $H$ is the length of an episode, $S$ the number of states, $A$ the number of actions, $T$ the number of episodes and ignoring terms in poly-$\log(SAHT)$. Notably, UCBMQ is the first algorithm that simultaneously matches the lower bound of $Ω(\sqrt{H^3SAT})$ for large enough $T$ and has a second-order term (with respect to the horizon $T$) that scales only linearly with the number of states $S$.