  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.
