A Concentration Bound for TD(0) with Function Approximation
This provides theoretical guarantees for reinforcement learning algorithms in practical online settings, though it is incremental as it builds on existing stochastic approximation methods.
The paper tackles the problem of analyzing TD(0) with linear function approximation under online learning with samples from a single Markov chain path, deriving a concentration bound for all sufficiently large n.
We derive a concentration bound of the type `for all $n \geq n_0$ for some $n_0$' 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.