Sample Complexity and Overparameterization Bounds for Projection-Free Neural TD Learning

03/02/2021 ∙ by Semih Cayci, et al. ∙ 0

We study the dynamics of temporal-difference learning with neural network-based value function approximation over a general state space, namely, Neural TD learning. Existing analysis of neural TD learning relies on either infinite width-analysis or constraining the network parameters in a (random) compact set; as a result, an extra projection step is required at each iteration. This paper establishes a new convergence analysis of neural TD learning without any projection. We show that the projection-free TD learning equipped with a two-layer ReLU network of any width exceeding poly(ν,1/ϵ) converges to the true value function with error ϵ given poly(ν,1/ϵ) iterations or samples, where ν is an upper bound on the RKHS norm of the value function induced by the neural tangent kernel. Our sample complexity and overparameterization bounds are based on a drift analysis of the network parameters as a stopped random process in the lazy training regime.

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