Functional Regularization for Reinforcement Learning via Learned Fourier Features

TL;DR

This paper introduces a Fourier basis embedding architecture for deep reinforcement learning that enhances sample efficiency and stability by controlling frequency fitting, supported by theoretical analysis and empirical results.

Contribution

It presents a novel learned Fourier feature architecture for RL, with theoretical insights linking initial variance tuning to functional regularization, improving learning stability and efficiency.

Findings

Improved sample efficiency in RL benchmarks.

Theoretically links Fourier basis variance to regularization.

Empirical benefits over baseline methods.

Abstract

We propose a simple architecture for deep reinforcement learning by embedding inputs into a learned Fourier basis and show that it improves the sample efficiency of both state-based and image-based RL. We perform infinite-width analysis of our architecture using the Neural Tangent Kernel and theoretically show that tuning the initial variance of the Fourier basis is equivalent to functional regularization of the learned deep network. That is, these learned Fourier features allow for adjusting the degree to which networks underfit or overfit different frequencies in the training data, and hence provide a controlled mechanism to improve the stability and performance of RL optimization. Empirically, this allows us to prioritize learning low-frequency functions and speed up learning by reducing networks' susceptibility to noise in the optimization process, such as during Bellman updates. Experiments on standard state-based and image-based RL benchmarks show clear benefits of our architecture over the baselines. Website at https://alexanderli.com/learned-fourier-features