# Provable imitation learning for control of instability in partially-observed Vlasov--Poisson equations

arXiv: https://arxiv.org/abs/2605.05081 · HTML: https://mlsanity.com/paper/2605.05081/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 6 May 2026.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 9 of 9)

- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Reinforcement and Imitation Learning via Interactive No-Regret Learning](https://mlsanity.com/paper/1406.5979/) (2014)
- [A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems](https://mlsanity.com/paper/1912.01825/) (2019)
- [Toward the Fundamental Limits of Imitation Learning](https://mlsanity.com/paper/2009.05990/) (2020)
- [Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning](https://mlsanity.com/paper/2407.15007/) (2024)
- [Solving PDE-constrained Control Problems Using Operator Learning](https://mlsanity.com/paper/2111.04941/) (2021)
- [Neural Operators for Bypassing Gain and Control Computations in PDE Backstepping](https://mlsanity.com/paper/2302.14265/) (2023)
- [The Pitfalls of Imitation Learning when Actions are Continuous](https://mlsanity.com/paper/2503.09722/) (2025)
- [Controlling a Vlasov-Poisson plasma by a Particle-In-Cell method based on a Monte Carlo framework](https://mlsanity.com/paper/2304.02083/) (2023)

## Abstract (arXiv)

We consider the stabilization of Vlasov--Poisson plasma dynamics, a central control problem in nuclear fusion. Our focus is the gap between what an ideal controller would use and what experiments can actually observe: while optimal policy may rely on the full phase-space state, practical feedback is typically limited to sparse macroscopic diagnostics. We therefore study imitation learning methods that distill a fully observed expert policy into controllers operating only on macroscopic measurements. We show the stability guarantees of the learned policy, where the error floor depends on the minimal behavior cloning loss achievable under the observation constraints. We further characterize this minimal loss in terms of a notion of entropy that quantifies the complexity of the initial distribution. Our results demonstrates the theoretical feasibility of learning stabilizing feedback policies for kinetic plasma dynamics from macroscopic observations, and exhibits the adaptivity of the learning approach to low-complexity structures. Through extensive numerical experiments, we validate our theory and show that the learned policies can stabilize the system using only macroscopic observations, within a significantly longer time horizon than non-adaptive baseline controllers.