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We consider the infinitehorizon, discretetime fullinformation control...
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Online Learning of the Kalman Filter with Logarithmic Regret
In this paper, we consider the problem of predicting observations genera...
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Kalman Filter Tuning with Bayesian Optimization
Many state estimation algorithms must be tuned given the state space pro...
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Regretoptimal Estimation and Control
We consider estimation and control in linear timevarying dynamical syst...
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NoRegret Prediction in Marginally Stable Systems
We consider the problem of online prediction in a marginally stable line...
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Optimizing the Energy Efficiency of Unreliable Memories for Quantized Kalman Filtering
This paper presents a quantized Kalman filter implemented using unreliab...
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Stochastic firstorder methods: nonasymptotic and computeraided analyses via potential functions
We provide a novel computerassisted technique for systematically analyz...
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RegretOptimal Filtering
We consider the problem of filtering in linear statespace models (e.g., the Kalman filter setting) through the lens of regret optimization. Different assumptions on the driving disturbance and the observation noise sequences give rise to different estimators: in the stochastic setting to the celebrated Kalman filter, and in the deterministic setting of bounded energy disturbances to H_∞ estimators. In this work, we formulate a novel criterion for filter design based on the concept of regret between the estimation error energy of a clairvoyant estimator that has access to all future observations (a socalled smoother) and a causal one that only has access to current and past observations. The regretoptimal estimator is chosen to minimize this worstcase difference across all boundedenergy noise sequences. The resulting estimator is adaptive in the sense that it aims to mimic the behavior of the clairvoyant estimator, irrespective of what the realization of the noise will be and thus interpolates between the stochastic and deterministic approaches. We provide a solution for the regret estimation problem at two different levels. First, we provide a solution at the operator level by reducing it to the Nehari problem. Second, for statespace models, we explicitly find the estimator that achieves the optimal regret. From a computational perspective, the regretoptimal estimator can be easily implemented by solving three Riccati equations and a single Lyapunov equation. For a statespace model of dimension n, the regretoptimal estimator has a statespace structure of dimension 3n. We demonstrate the applicability and efficacy of the estimator in a variety of problems and observe that the estimator has average and worstcase performances that are simultaneously close to their optimal values. We therefore argue that regretoptimality is a viable approach to estimator design.
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