A Kernel Loss for Solving the Bellman Equation
This addresses convergence issues in reinforcement learning algorithms for researchers and practitioners, though it is incremental as it builds on prior work like residual gradient.
The paper tackles the problem of value function learning in reinforcement learning, where existing methods like Q-learning lack convergence guarantees, by proposing a novel kernel loss function that ensures reliable optimization with standard gradient methods and achieves effective performance in benchmarks.
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 variant of Bellman operator that is 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 without risking divergence. 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. Our approach may be combined with general function classes such as neural networks, on either on- or off-policy data, and is shown to work reliably and effectively in several benchmarks.