# Fourier Policy Gradients

arXiv: https://arxiv.org/abs/1802.06891 · HTML: https://mlsanity.com/paper/1802.06891/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2018.

## Built on by (most cited first, 3 of 3)

- [Bayesian Bellman Operators](https://mlsanity.com/paper/2106.05012/) (2021)
- [Fourier Controller Networks for Real-Time Decision-Making in Embodied Learning](https://mlsanity.com/paper/2405.19885/) (2024)
- [Taylor TD-learning](https://mlsanity.com/paper/2302.14182/) (2023)

## Abstract (arXiv)

We propose a new way of deriving policy gradient updates for reinforcement learning. Our technique, based on Fourier analysis, recasts integrals that arise with expected policy gradients as convolutions and turns them into multiplications. The obtained analytical solutions allow us to capture the low variance benefits of EPG in a broad range of settings. For the critic, we treat trigonometric and radial basis functions, two function families with the universal approximation property. The choice of policy can be almost arbitrary, including mixtures or hybrid continuous-discrete probability distributions. Moreover, we derive a general family of sample-based estimators for stochastic policy gradients, which unifies existing results on sample-based approximation. We believe that this technique has the potential to shape the next generation of policy gradient approaches, powered by analytical results.