Improved High-Probability Bounds for the Temporal Difference Learning Algorithm via Exponential Stability

• URL: http://arxiv.org/abs/2310.14286v2
• Date: Sat, 15 Jun 2024 08:29:03 GMT
• Title: Improved High-Probability Bounds for the Temporal Difference Learning Algorithm via Exponential Stability
• Authors: Sergey Samsonov, Daniil Tiapkin, Alexey Naumov, Eric Moulines,
• Abstract summary: We show that a simple algorithm with a universal and instance-independent step size is sufficient to obtain near-optimal variance and bias terms. Our proof technique is based on refined error bounds for linear approximation together with the novel stability result for the product of random matrices.
• Score: 17.771354881467435
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we consider the problem of obtaining sharp bounds for the performance of temporal difference (TD) methods with linear function approximation for policy evaluation in discounted Markov decision processes. We show that a simple algorithm with a universal and instance-independent step size together with Polyak-Ruppert tail averaging is sufficient to obtain near-optimal variance and bias terms. We also provide the respective sample complexity bounds. Our proof technique is based on refined error bounds for linear stochastic approximation together with the novel stability result for the product of random matrices that arise from the TD-type recurrence.

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