A Concentration Bound for TD(0) with Function Approximation

We derive uniform all-time concentration bound of the type ‘for all [Formula: see text] for some [Formula: see text]’ for TD(0) with linear function approximation. We work with online TD learning with samples from a single sample path of the underlying Markov chain. This makes our analysis significantly different from offline TD learning or TD learning with access to independent samples from the stationary distribution of the Markov chain. We treat TD(0) as a contractive stochastic approximation algorithm with both martingale and Markov noises. Markov noise is handled using the Poisson equation, and the lack of almost-sure guarantees on boundedness of iterates is handled using the concept of relaxed concentration inequalities. Funding: The work of V. S. Borkar was supported in part by the S. S. Bhatnagar Fellowship from the Government of India.