Maximizing the Value of Predictions in Control: Accuracy Is Not Enough

TL;DR

This paper investigates how stochastic predictions can improve control performance, introducing a framework to quantify their value beyond mere accuracy, and deriving bounds that highlight the importance of prediction quality in various control settings.

Contribution

It develops a general framework for modeling the joint distribution of predictions and disturbances, introduces the concept of prediction power, and derives bounds demonstrating the fundamental benefits of stochastic predictions in control.

Findings

Prediction power can be explicitly quantified in LQR settings.

Weakly dependent predictions can still provide significant performance improvements.

Fundamental bounds show the importance of prediction quality over accuracy alone.

Abstract

We study the value of stochastic predictions in online optimal control with random disturbances. Prior work provides performance guarantees based on prediction error but ignores the stochastic dependence between predictions and disturbances. We introduce a general framework modeling their joint distribution and define "prediction power" as the control cost improvement from the optimal use of predictions compared to ignoring the predictions. In the time-varying Linear Quadratic Regulator (LQR) setting, we derive a closed-form expression for prediction power and discuss its mismatch with prediction accuracy and connection with online policy optimization. To extend beyond LQR, we study general dynamics and costs. We establish a lower bound of prediction power under two sufficient conditions that generalize the properties of the LQR setting, characterizing the fundamental benefit of incorporating stochastic predictions. We apply this lower bound to non-quadratic costs and show that even weakly dependent predictions yield significant performance gains.