Fourier Policy Gradients
This work addresses a fundamental bottleneck in reinforcement learning by potentially reducing variance in policy gradients, which could impact the development of next-generation RL algorithms, though it appears incremental as it builds on existing expected policy gradient methods.
The paper tackles the problem of high variance in policy gradient updates for reinforcement learning by proposing a Fourier analysis technique that converts integrals into convolutions and multiplications, enabling analytical solutions that capture low variance benefits across diverse settings, including arbitrary policies and unified sample-based estimators.
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.