# Follow the Clairvoyant: an Imitation Learning Approach to Optimal Control

arXiv: https://arxiv.org/abs/2211.07389 · HTML: https://mlsanity.com/paper/2211.07389/

## 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 16 references that are in the map.
- First posted on arXiv 14 Nov 2022.

## 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)

- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [Imitation Learning with Stability and Safety Guarantees](https://mlsanity.com/paper/2012.09293/) (2020)
- [Model Predictive Contouring Control for Time-Optimal Quadrotor Flight](https://mlsanity.com/paper/2108.13205/) (2021)
- [Regret-optimal Estimation and Control](https://mlsanity.com/paper/2106.12097/) (2021)
- [A System Level Approach to Controller Synthesis](https://mlsanity.com/paper/1610.04815/) (2016)
- [Competitive Control](https://mlsanity.com/paper/2107.13657/) (2021)
- [Safe Control with Minimal Regret](https://mlsanity.com/paper/2203.00358/) (2022)
- [A System Level Approach to Regret Optimal Control](https://mlsanity.com/paper/2202.13763/) (2022)
- [Optimal Competitive-Ratio Control](https://mlsanity.com/paper/2206.01782/) (2022)

## Abstract (arXiv)

We consider control of dynamical systems through the lens of competitive analysis. Most prior work in this area focuses on minimizing regret, that is, the loss relative to an ideal clairvoyant policy that has noncausal access to past, present, and future disturbances. Motivated by the observation that the optimal cost only provides coarse information about the ideal closed-loop behavior, we instead propose directly minimizing the tracking error relative to the optimal trajectories in hindsight, i.e., imitating the clairvoyant policy. By embracing a system level perspective, we present an efficient optimization-based approach for computing follow-the-clairvoyant (FTC) safe controllers. We prove that these attain minimal regret if no constraints are imposed on the noncausal benchmark. In addition, we present numerical experiments to show that our policy retains the hallmark of competitive algorithms of interpolating between classical H2 and H_∞ control laws - while consistently outperforming regret minimization methods in constrained scenarios thanks to the superior ability to chase the clairvoyant.