A Kernel Loss for Solving the Bellman Equation

Value function learning plays a central role in many state-of-the-art reinforcement learning algorithms. Many popular algorithms like Q-learning do not optimize any objective function, but are fixed-point iterations of some variants of Bellman operator that are not necessarily a contraction. As a result, they may easily lose convergence guarantees, as can be observed in practice. In this paper, we propose a novel loss function, which can be optimized using standard gradient-based methods with guaranteed convergence. The key advantage is that its gradient can be easily approximated using sampled transitions, avoiding the need for double samples required by prior algorithms like residual gradient.