# Regret-Optimal Filtering

@inproceedings{Sabag2021RegretOptimalF, title={Regret-Optimal Filtering}, author={Oron Sabag and Babak Hassibi}, booktitle={AISTATS}, year={2021} }

We consider the problem of filtering in linear state-space models (e.g., the Kalman filter setting) through the lens of regret optimization. Specifically, we study the problem of causally estimating a desired signal, generated by a linear state-space model driven by process noise, based on noisy observations of a related observation process. We define a novel regret criterion for estimator design as the difference of the estimation error energies between a clairvoyant estimator that has access… Expand

#### 2 Citations

Regret-Optimal Full-Information Control

- Computer Science, Mathematics
- ArXiv
- 2021

The regretoptimal 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, and generally has H2 and H∞ costs that are simultaneously close to their optimal values. Expand

Regret-optimal Estimation and Control

- Computer Science, Mathematics
- ArXiv
- 2021

This work shows that the regret-optimal estimators and controllers can be derived in state-space form using operator-theoretic techniques from robust control and presents tight, data-dependent bounds on the regret incurred by the algorithms in terms of the energy of the disturbances. Expand

#### References

SHOWING 1-10 OF 33 REFERENCES

Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications

- Computer Science, Mathematics
- 1949

Extrapolation interpolation and smoothing of stationary, stationary tones interference cancellation using adaptive and stationary time series financial definition of stationary. Expand

A New Approach to Linear Filtering and Prediction Problems

- Mathematics
- 2001

The clssical filleting and prediclion problem is re-examined using the Bode-Shannon representation of random processes and the ?stat-tran-sition? method of analysis of dynamic systems. New result… Expand

Regret-Optimal Controller for the Full-Information Problem

- 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. Expand

Online Learning Robust Control of Nonlinear Dynamical Systems

- Computer Science, Engineering
- ArXiv
- 2021

This work addresses the problem of the online robust control of nonlinear dynamical systems perturbed by disturbance and proposes an online controller and presents guarantees for the metric R t when the maximum possible attenuation is given by γ, which is a system constant. Expand

Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regret

- Mathematics, Computer Science
- ICML
- 2021

This work presents the first model-free algorithm that achieves similar regret guarantees, and relies on an efficient policy gradient scheme, and a novel and tighter analysis of the cost of exploration in policy space in this setting. Expand

Regret Analysis of Distributed Online LQR Control for Unknown LTI Systems

- Computer Science, Mathematics
- ArXiv
- 2021

This work proposes a distributed variant of the online LQR algorithm where each agent computes its system estimate during an exploration stage and proves that the regret bound of the proposed algorithm scales Õ(T), implying the consensus of the network over time. Expand

Regret-Optimal Full-Information Control

- Computer Science, Mathematics
- ArXiv
- 2021

The regretoptimal 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, and generally has H2 and H∞ costs that are simultaneously close to their optimal values. Expand

Regret-optimal filtering

- Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:2629–2637, 2021.
- 2021

Regret-optimal measurement-feedback control

- Engineering, Computer Science
- 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. Expand

Sequential prediction under log-loss and misspecification

- Computer Science, Mathematics
- COLT
- 2021

Two general results for misspecified regret are shown: the existence and uniqueness of the optimal estimator, and the bound sandwiching the misspecification regret between well-specified regrets with (asymptotically) close hypotheses classes. Expand