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

TL;DR

The paper introduces the Path Integral Bottleneck framework, an analytical method to quantify the relationship between computation effort and control performance across different platforms, revealing fundamental tradeoffs.

Contribution

It provides an algorithm-agnostic framework to analyze and compare control systems' computation and performance tradeoffs using observed trajectories.

Findings

Fundamental control-compute tradeoffs identified in simulations.

Regions with higher performance-per-compute efficiency discovered.

Framework applicable to various control platforms and cost functions.

Abstract

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.