Overcoming the Spectral Bias of Neural Value Approximation

TL;DR

This paper addresses the spectral bias in neural value approximation for reinforcement learning by introducing Fourier feature networks, leading to faster convergence, improved stability, and state-of-the-art results on continuous control tasks.

Contribution

It proposes a simple modification using Fourier features to overcome spectral bias in neural value functions, enhancing performance and stability in off-policy reinforcement learning.

Findings

FFN achieves state-of-the-art performance on continuous control tasks.

Faster convergence and improved off-policy stability.

Elimination of target networks without divergence issues.

Abstract

Value approximation using deep neural networks is at the heart of off-policy deep reinforcement learning, and is often the primary module that provides learning signals to the rest of the algorithm. While multi-layer perceptron networks are universal function approximators, recent works in neural kernel regression suggest the presence of a spectral bias, where fitting high-frequency components of the value function requires exponentially more gradient update steps than the low-frequency ones. In this work, we re-examine off-policy reinforcement learning through the lens of kernel regression and propose to overcome such bias via a composite neural tangent kernel. With just a single line-change, our approach, the Fourier feature networks (FFN) produce state-of-the-art performance on challenging continuous control domains with only a fraction of the compute. Faster convergence and better off-policy stability also make it possible to remove the target network without suffering catastrophic divergences, which further reduces TD}(0)'s estimation bias on a few tasks.