Overcoming The Spectral Bias of Neural Value Approximation

Ge Yang, Anurag Ajay, Pulkit Agrawal

Keywords: spectral bias, neural value approximation, Q learning, reinforcement learning, neural tangent kernels, kernel regression

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 \textit{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. Code and analysis available at https://geyang.github.io/ffn.

One-sentence Summary: Overcoming the spectral bias of neural value approximation via fourier features

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2206.04672/code)