# Discrete fully probabilistic design: towards a control pipeline for the synthesis of policies from examples

arXiv: https://arxiv.org/abs/2112.11210 · HTML: https://mlsanity.com/paper/2112.11210/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 36 references that are in the map.
- First posted on arXiv 21 Dec 2021.

## Builds on (most cited first, 13 of 13)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [On the Sample Complexity of Stability Constrained Imitation Learning](https://mlsanity.com/paper/2102.09161/) (2021)
- [Data informativity: a new perspective on data-driven analysis and control](https://mlsanity.com/paper/1908.00468/) (2019)
- [Robust Model Predictive Path Integral Control: Analysis and Performance Guarantees](https://mlsanity.com/paper/2102.09027/) (2021)
- [Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems](https://mlsanity.com/paper/2005.04374/) (2020)
- [Learn Fast, Forget Slow: Safe Predictive Learning Control for Systems with Unknown and Changing Dynamics Performing Repetitive Tasks](https://mlsanity.com/paper/1810.06681/) (2018)
- [Willems' Fundamental Lemma for State-space Systems and its Extension to Multiple Datasets](https://mlsanity.com/paper/2002.01023/) (2020)
- [Online Markov decision processes with Kullback-Leibler control cost](https://mlsanity.com/paper/1401.3198/) (2014)
- [Learning Policies for Markov Decision Processes from Data](https://mlsanity.com/paper/1701.05954/) (2017)
- [On a probabilistic approach to synthesize control policies from example datasets](https://mlsanity.com/paper/2005.11191/) (2020)
- [On the crowdsourcing of behaviors for autonomous agents](https://mlsanity.com/paper/2010.04608/) (2020)
- [On the design of autonomous agents from multiple data sources](https://mlsanity.com/paper/2103.02020/) (2021)

## Abstract (arXiv)

We present the principled design of a control pipeline for the synthesis of policies from examples data. The pipeline, based on a discretized design which we term as discrete fully probabilistic design, expounds an algorithm recently introduced in Gagliardi and Russo (2021) to synthesize policies from examples for constrained, stochastic and nonlinear systems. Contrary to other approaches, the pipeline we present: (i) does not need the constraints to be fulfilled in the possibly noisy example data; (ii) enables control synthesis even when the data are collected from an example system that is different from the one under control. The design is benchmarked numerically on an example that involves controlling an inverted pendulum with actuation constraints starting from data collected from a physically different pendulum that does not satisfy the system-specific actuation constraints. We also make our fully documented code openly available.