Path Integral Bottleneck: An Algorithm-Agnostic Framework of Computation and Control

Executing a control sequence requires computation. While this is a simple observation, developing a framework that relates a controller's required computation to its ability to successfully control a system (e.g. lower control cost) is challenging, especially when the controller appears on alternative compute platforms (e.g. biological neural networks). More specifically, we want a framework where, given an observed closed-loop trajectory, we can quantify the computation effort needed to produce that trajectory. To enable effective comparisons of closed-loop systems across alternative compute platforms, we present the Path Integral Bottleneck (PI-IB), a method to produce an analytical, algorithm-agnostic description of the compute-control relationship. With the PI-IB framework, we can plot tradeoffs between performance and computation effort for any given plant description and control cost function. Simulations of the cart-pole reveal fundamental control-compute tradeoffs, exposing regions where the task performance-per-compute is higher than others.