Improved High-Probability Bounds for the Temporal Difference Learning Algorithm via Exponential Stability
This work addresses the need for improved theoretical guarantees in reinforcement learning, offering incremental advancements in bounding TD learning performance.
The paper tackles the problem of obtaining sharp performance bounds for temporal difference (TD) methods in policy evaluation for discounted Markov decision processes, showing that a simple algorithm with a universal step size and tail averaging achieves near-optimal variance and bias terms with provided sample complexity bounds.
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.