Optimizing Automatic Differentiation with Deep Reinforcement Learning

TL;DR

This paper introduces a novel deep reinforcement learning approach to optimize Jacobian computations in automatic differentiation, achieving significant reductions in multiplications and runtime without approximations.

Contribution

It presents a new RL-based method for finding optimal elimination orders in Jacobian computation, improving efficiency over existing methods while maintaining exact results.

Findings

Achieves up to 33% reduction in multiplications compared to state-of-the-art methods.

Demonstrates real runtime improvements with an efficient JAX implementation.

Validates the approach across diverse scientific domains.

Abstract

Computing Jacobians with automatic differentiation is ubiquitous in many scientific domains such as machine learning, computational fluid dynamics, robotics and finance. Even small savings in the number of computations or memory usage in Jacobian computations can already incur massive savings in energy consumption and runtime. While there exist many methods that allow for such savings, they generally trade computational efficiency for approximations of the exact Jacobian. In this paper, we present a novel method to optimize the number of necessary multiplications for Jacobian computation by leveraging deep reinforcement learning (RL) and a concept called cross-country elimination while still computing the exact Jacobian. Cross-country elimination is a framework for automatic differentiation that phrases Jacobian accumulation as ordered elimination of all vertices on the computational graph where every elimination incurs a certain computational cost. We formulate the search for the optimal elimination order that minimizes the number of necessary multiplications as a single player game which is played by an RL agent. We demonstrate that this method achieves up to 33% improvements over state-of-the-art methods on several relevant tasks taken from diverse domains. Furthermore, we show that these theoretical gains translate into actual runtime improvements by providing a cross-country elimination interpreter in JAX that can efficiently execute the obtained elimination orders.