# Pick-to-Learn for Systems and Control: Data-driven Synthesis with State-of-the-art Safety Guarantees

arXiv: https://arxiv.org/abs/2512.04781 · HTML: https://mlsanity.com/paper/2512.04781/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 58 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Builds on (most cited first, 17 of 17)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Tighter risk certificates for neural networks](https://mlsanity.com/paper/2007.12911/) (2020)
- [Formal Verification and Control with Conformal Prediction](https://mlsanity.com/paper/2409.00536/) (2024)
- [Compression, Generalization and Learning](https://mlsanity.com/paper/2301.12767/) (2023)
- [Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions](https://mlsanity.com/paper/2301.01526/) (2023)
- [Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methods](https://mlsanity.com/paper/1910.02500/) (2019)
- [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021)
- [LMI Properties and Applications in Systems, Stability, and Control Theory](https://mlsanity.com/paper/1903.08599/) (2019)
- [Stochastic Omega-Regular Verification and Control with Supermartingales](https://mlsanity.com/paper/2405.17304/) (2024)
- [Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference](https://mlsanity.com/paper/2309.09187/) (2023)
- [A PAC-Bayesian Framework for Optimal Control with Stability Guarantees](https://mlsanity.com/paper/2403.17790/) (2024)
- [Data-driven Reachability using Christoffel Functions and Conformal Prediction](https://mlsanity.com/paper/2309.08976/) (2023)
- [What Are the Odds? Improving the foundations of Statistical Model Checking](https://mlsanity.com/paper/2404.05424/) (2024)
- [Closed-loop Performance Optimization of Model Predictive Control with Robustness Guarantees](https://mlsanity.com/paper/2403.04655/) (2024)
- [Data-Driven Yet Formal Policy Synthesis for Stochastic Nonlinear Dynamical Systems](https://mlsanity.com/paper/2501.01191/) (2025)

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

- [Bound to Disagree: Generalization Bounds via Certifiable Surrogates](https://mlsanity.com/paper/2602.23128/) (2026)
- [Learning Decision-Sufficient Representations for Linear Optimization](https://mlsanity.com/paper/2603.18551/) (2026)
- [Pick-to-Learn Calibration of an MPC Policy for an Origin-to-Destination Flight Problem](https://mlsanity.com/paper/2607.16084/) (2026)
- [Preferent Compression Bounds Are Tight](https://mlsanity.com/paper/2609.36030/) (2026)
- [Learning by Compression: Risk Estimates Attain the Law-of-Large-Numbers Rate](https://mlsanity.com/paper/2610.13442/) (2026)

## Abstract (arXiv)

Data-driven methods have become paramount in modern systems and control problems characterized by growing levels of complexity. In safety-critical environments, deploying these methods requires rigorous guarantees, a need that has motivated much recent work at the interface of statistical learning and control. However, many existing approaches achieve this goal at the cost of sacrificing valuable data for testing and calibration, or by constraining the choice of learning algorithm, thus leading to suboptimal performances. In this paper, we describe Pick-to-Learn (P2L) for Systems and Control, a framework that allows any data-driven control method to be equipped with state-of-the-art safety and performance guarantees. P2L enables the use of all available data to jointly synthesize and certify the design, eliminating the need to set aside data for calibration or validation purposes. In presenting a comprehensive version of P2L for systems and control, this paper demonstrates its effectiveness across a range of core problems, including optimal control, reachability analysis, safe synthesis, and robust control. In many of these applications, P2L delivers designs and certificates that outperform commonly employed methods, and shows strong potential for broad applicability in diverse practical settings.