Conformal Prediction for Distribution-free Optimal Control of Linear Stochastic Systems

TL;DR

This paper introduces a conformal prediction-based method for distribution-free optimal control of linear stochastic systems with unknown noise, providing probabilistic guarantees and two design approaches for control and prediction regions.

Contribution

It presents a novel conformal prediction framework for joint chance constraints in linear stochastic control, with two methods for designing feedback controllers and prediction regions.

Findings

Guarantees probabilistic control performance independent of data size.

Two methods for designing control and prediction regions: direct optimization and S-procedure.

Ensures reliable probabilistic guarantees for stochastic systems.

Abstract

We address an optimal control problem for linear stochastic systems with unknown noise distributions and joint chance constraints using conformal prediction. Our approach involves designing a feedback controller to maintain an error system within a prediction region (PR). We define PRs as sublevel sets of a nonconformity score over error trajectories, enabling the handling of joint chance constraints. We propose two methods to design feedback control and PRs: one through direct optimization over error trajectory samples, and the other indirectly using the $S$-procedure with a disturbance ellipsoid obtained from data. By tightening constraints with PRs, we solve a relaxed problem to synthesize a feedback policy. Our method ensures reliable probabilistic guarantees based on marginal coverage, independent of data size.