Regularized Q-Learning with Linear Function Approximation

• URL: http://arxiv.org/abs/2401.15196v2
• Date: Sun, 28 Jul 2024 16:35:05 GMT
• Title: Regularized Q-Learning with Linear Function Approximation
• Authors: Jiachen Xi, Alfredo Garcia, Petar Momcilovic,
• Abstract summary: We consider a bi-level optimization formulation of regularized Q-learning with linear functional approximation. We show that, under certain assumptions, the proposed algorithm converges to a stationary point in the presence of Markovian noise.
• Score: 2.765106384328772
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Regularized Markov Decision Processes serve as models of sequential decision making under uncertainty wherein the decision maker has limited information processing capacity and/or aversion to model ambiguity. With functional approximation, the convergence properties of learning algorithms for regularized MDPs (e.g. soft Q-learning) are not well understood because the composition of the regularized Bellman operator and a projection onto the span of basis vectors is not a contraction with respect to any norm. In this paper, we consider a bi-level optimization formulation of regularized Q-learning with linear functional approximation. The {\em lower} level optimization problem aims to identify a value function approximation that satisfies Bellman's recursive optimality condition and the {\em upper} level aims to find the projection onto the span of basis vectors. This formulation motivates a single-loop algorithm with finite time convergence guarantees. The algorithm operates on two time-scales: updates to the projection of state-action values are `slow' in that they are implemented with a step size that is smaller than the one used for `faster' updates of approximate solutions to Bellman's recursive optimality equation. 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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