Abstract: This paper studies a gradient temporal difference (GTD) algorithm using neural network (NN) function approximators to minimize the mean squared Bellman error (MSBE). For off-policy learning, we show that the minimum MSBE problem can be recast into a min-max optimization involving a pair of over-parameterized primal-dual NNs. The resultant formulation can then be tackled using a neural GTD algorithm. We analyze the convergence of the proposed algorithm with a 2-layer ReLU NN architecture using $m$ neurons and prove that it computes an approximate optimal solution to the minimum MSBE problem as $m \rightarrow \infty$.