A Kernel Loss for Solving the Bellman Equation

TL;DR

This paper introduces a new kernel loss function for value function learning in reinforcement learning that ensures convergence and can be optimized with standard gradient methods, improving stability over traditional Bellman-based approaches.

Contribution

The paper proposes a novel kernel loss function for Bellman equation solutions that guarantees convergence and is compatible with neural networks and standard gradient optimization.

Findings

Works reliably with neural networks and off-policy data

Avoids divergence issues common in Bellman-based methods

Effective in multiple benchmark environments

Abstract

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.