Thinking Fast and Slow: Optimization Decomposition Across Timescales

TL;DR

This paper introduces a theoretical framework for designing multi-timescale controllers that decompose global control problems into fast reactive and slow predictive components, achieving near-optimal performance.

Contribution

It proposes a novel approach to temporal decomposition of control problems, inspired by network utility maximization, and introduces the MRPC method for near-optimal multi-timescale control.

Findings

Multi-timescale decomposition can be near-optimal.

MRPC maintains low cost within a constant factor of the offline optimal.

The framework applies to decentralized control systems with different reaction speeds.

Abstract

Many real-world control systems, such as the smart grid and human sensorimotor control systems, have decentralized components that react quickly using local information and centralized components that react slowly using a more global view. This paper seeks to provide a theoretical framework for how to design controllers that are decomposed across timescales in this way. The framework is analogous to how the network utility maximization framework uses optimization decomposition to distribute a global control problem across independent controllers, each of which solves a local problem; except our goal is to decompose a global problem temporally, extracting a timescale separation. Our results highlight that decomposition of a multi-timescale controller into a fast timescale, reactive controller and a slow timescale, predictive controller can be near-optimal in a strong sense. In particular, we exhibit such a design, named Multi-timescale Reflexive Predictive Control (MRPC), which maintains a per-timestep cost within a constant factor of the offline optimal in an adversarial setting.