# PIPPS: Flexible Model-Based Policy Search Robust to the Curse of Chaos

## TL;DR

This paper reveals that the exploding gradient problem in deep learning and reinforcement learning is due to chaos-like behavior in nonlinear computations, and introduces PIPPS, a robust model-based policy search framework that improves gradient estimation efficiency.

## Contribution

The paper identifies chaos as a key factor in gradient instability and proposes PIPPS, a flexible policy search method with the total propagation algorithm for improved gradient estimation.

## Key findings

- Likelihood ratio gradients are robust to chaos.
- PIPPS matches previous data-efficient algorithms.
- Total propagation can outperform reparameterization gradients by up to 10^6 times.

## Abstract

Previously, the exploding gradient problem has been explained to be central in deep learning and model-based reinforcement learning, because it causes numerical issues and instability in optimization. Our experiments in model-based reinforcement learning imply that the problem is not just a numerical issue, but it may be caused by a fundamental chaos-like nature of long chains of nonlinear computations. Not only do the magnitudes of the gradients become large, the direction of the gradients becomes essentially random. We show that reparameterization gradients suffer from the problem, while likelihood ratio gradients are robust. Using our insights, we develop a model-based policy search framework, Probabilistic Inference for Particle-Based Policy Search (PIPPS), which is easily extensible, and allows for almost arbitrary models and policies, while simultaneously matching the performance of previous data-efficient learning algorithms. Finally, we invent the total propagation algorithm, which efficiently computes a union over all pathwise derivative depths during a single backwards pass, automatically giving greater weight to estimators with lower variance, sometimes improving over reparameterization gradients by $10^6$ times.