Regularized Q-Learning with Linear Function Approximation

Jiachen Xi, Alfredo Garcia, Petar Momcilovic
Computer Science, Artificial Intelligence, Artificial Intelligence (cs.AI)
2024-01-26 00:00:00
Several successful reinforcement learning algorithms make use of regularization to promote multi-modal policies that exhibit enhanced exploration and robustness. With functional approximation, the convergence properties of some of these algorithms (e.g. soft Q-learning) are not well understood. In this paper, we consider a single-loop algorithm for minimizing the projected Bellman error with finite time convergence guarantees in the case of linear function approximation. The algorithm operates on two scales: a slower scale for updating the target network of the state-action values, and a faster scale for approximating the Bellman backups in the subspace of the span of basis vectors. We show that, under certain assumptions, the proposed algorithm converges to a stationary point in the presence of Markovian noise. In addition, we provide a performance guarantee for the policies derived from the proposed algorithm.
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