• Corpus ID: 233715120

# Regret-Optimal Full-Information Control

@article{Sabag2021RegretOptimalFC,
title={Regret-Optimal Full-Information Control},
author={Oron Sabag and Gautam Goel and Sahin Lale and Babak Hassibi},
journal={ArXiv},
year={2021},
volume={abs/2105.01244}
}
• Published 4 May 2021
• Mathematics, Computer Science
• ArXiv
We consider the infinite-horizon, discrete-time fullinformation control problem. Motivated by learning theory, as a criterion for controller design we focus on regret, defined as the difference between the LQR cost of a causal controller (that has only access to past and current disturbances) and the LQR cost of a clairvoyant one (that has also access to future disturbances). In the full-information setting, there is a unique optimal non-causal controller that in terms of LQR cost dominates all…

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## References

SHOWING 1-10 OF 23 REFERENCES

### Regret-Optimal Controller for the Full-Information Problem

• Mathematics, Computer Science
2021 American Control Conference (ACC)
• 2021
The regret-optimal control problem can be reduced to a Nehari extension problem, i.e., to approximate an anticausal operator with a causal one in the operator norm, andSimulations over a range of plants demonstrates that the regret- optimal controller interpolates nicely between the H2 and the H∞ optimal controllers, and generally has H1 and H2 costs that are simultaneously close to their optimal values.

### Regret-optimal measurement-feedback control

• Mathematics
L4DC
• 2021
It is shown that in the measurement-feedback setting, unlike in the full-information setting, there is no single offline controller which outperforms every other offline controller on every disturbance, and a new $H_2$-optimal offline controller is proposed as a benchmark for the online controller to compete against.

### Regret-Optimal Filtering

• Computer Science
AISTATS
• 2021
The regret-optimal estimator is the causal estimator that minimizes the worst-case regret across all bounded-energy noise sequences and is represented as a finite-dimensional state-space whose parameters can be computed by solving three Riccati equations and a single Lyapunov equation.

### The Power of Linear Controllers in LQR Control

• Computer Science
ArXiv
• 2020
The Linear Quadratic Regulator framework considers the problem of regulating a linear dynamical system perturbed by environmental noise and fully characterize the optimal offline policy and shows that it has a recursive form in terms of the optimal online policy and future disturbances.

• Computer Science, Mathematics
COLT
• 2011
The construction of the condence set is based on the recent results from online least-squares estimation and leads to improved worst-case regret bound for the proposed algorithm, and is the the rst time that a regret bound is derived for the LQ control problem.

### Explore More and Improve Regret in Linear Quadratic Regulators

• Computer Science, Mathematics
ArXiv
• 2020
A framework for adaptive control that exploits the characteristics of linear dynamical systems and deploys additional exploration in the early stages of agent-environment interaction to guarantee sooner design of stabilizing controllers is proposed.

### Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis

• Computer Science
NeurIPS
• 2019
This paper designs online algorithms, Receding Horizon Gradient-based Control (RHGC), that utilize the predictions through finite steps of gradient computations, and provides a fundamental limit of the dynamic regret for any online algorithms by considering linear quadratic tracking problems.

### Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator

• Computer Science, Mathematics
NeurIPS
• 2018
This work presents the first provably polynomial time algorithm that provides high probability guarantees of sub-linear regret on this problem of adaptive control of the Linear Quadratic Regulator, where an unknown linear system is controlled subject to quadratic costs.

### Logarithmic Regret for Online Control

• Computer Science
NeurIPS
• 2019
It is shown that the optimal regret in this fundamental setting can be significantly smaller, scaling as polylog(T), achieved by two different efficient iterative methods, online gradient descent and online natural gradient.

### Logarithmic Regret for Adversarial Online Control

• Computer Science, Mathematics
ICML
• 2020
A new algorithm for online linear-quadratic control in a known system subject to adversarial disturbances is introduced, giving the first algorithm with logarithmic regret for arbitrary adversarial disturbance sequences, provided the state and control costs are given by known quadratic functions.