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Regret-Optimal Filtering

Sabag, Oron and Hassibi, Babak (2021) Regret-Optimal Filtering. Proceedings of Machine Learning Research, 130 . pp. 2629-2637. ISSN 1938-7228.

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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 to all future observations (a so-called smoother) and a causal one that only has access to current and past observations. The regret-optimal estimator is the causal estimator that minimizes the worst-case regret across all bounded-energy noise sequences. We provide a solution for the regret filtering problem at two levels. First, an horizon-independent solution at the operator level is obtained by reducing the regret to the well-known Nehari problem. Secondly, our main result for state-space models is an explicit estimator that achieves the optimal regret. The regret-optimal estimator is represented as a finite-dimensional state-space whose parameters can be computed by solving three Riccati equations and a single Lyapunov equation. We demonstrate the applicability and efficacy of the estimator in a variety of problems and observe that the estimator has average and worst-case performances that are simultaneously close to their optimal values.

Item Type:Article
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URLURL TypeDescription Paper
Sabag, Oron0000-0002-7907-1463
Additional Information:© 2021 by the author(s). The work of OS is partially supported by the ISEF postdoctoral fellowship.
Funding AgencyGrant Number
Israel Scholarship Education Foundation (ISEF)UNSPECIFIED
Record Number:CaltechAUTHORS:20210225-132748732
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108213
Deposited By: George Porter
Deposited On:01 Mar 2021 15:00
Last Modified:30 Aug 2021 20:58

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