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

arXiv: https://arxiv.org/abs/2411.19132 · HTML: https://mlsanity.com/paper/2411.19132/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2024.

## Built on by (most cited first, 5 of 5)

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- [Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systems](https://mlsanity.com/paper/2603.07092/) (2026)
- [PAC-Bayesian Certificates for Quadratic Closed-Loop Control](https://mlsanity.com/paper/2606.28281/) (2026)
- [A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification](https://mlsanity.com/paper/2608.29789/) (2026)

## Abstract (arXiv)

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.