Finite-Time Analysis of Whittle Index based Q-Learning for Restless Multi-Armed Bandits with Neural Network Function Approximation

• URL: http://arxiv.org/abs/2310.02147v1
• Date: Tue, 3 Oct 2023 15:34:21 GMT
• Title: Finite-Time Analysis of Whittle Index based Q-Learning for Restless Multi-Armed Bandits with Neural Network Function Approximation
• Authors: Guojun Xiong, Jian Li
• Abstract summary: We present Neural-Q-Whittle, a Whittle index based Q-learning algorithm for RMAB with neural network function approximation. Despite the empirical success of deep Q-learning, the non-asymptotic convergence rate of Neural-Q-Whittle remains unclear.
• Score: 13.30475927566957
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Whittle index policy is a heuristic to the intractable restless multi-armed bandits (RMAB) problem. Although it is provably asymptotically optimal, finding Whittle indices remains difficult. In this paper, we present Neural-Q-Whittle, a Whittle index based Q-learning algorithm for RMAB with neural network function approximation, which is an example of nonlinear two-timescale stochastic approximation with Q-function values updated on a faster timescale and Whittle indices on a slower timescale. Despite the empirical success of deep Q-learning, the non-asymptotic convergence rate of Neural-Q-Whittle, which couples neural networks with two-timescale Q-learning largely remains unclear. This paper provides a finite-time analysis of Neural-Q-Whittle, where data are generated from a Markov chain, and Q-function is approximated by a ReLU neural network. Our analysis leverages a Lyapunov drift approach to capture the evolution of two coupled parameters, and the nonlinearity in value function approximation further requires us to characterize the approximation error. Combing these provide Neural-Q-Whittle with $\mathcal{O}(1/k^{2/3})$ convergence rate, where $k$ is the number of iterations.

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