
SLIP: Learning to Predict in Unknown Dynamical Systems with LongTerm Memory
We present an efficient and practical (polynomial time) algorithm for on...
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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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Robust guarantees for learning an autoregressive filter
The optimal predictor for a linear dynamical system (with hidden state a...
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Sample Complexity of Kalman Filtering for Unknown Systems
In this paper, we consider the task of designing a Kalman Filter (KF) fo...
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RegretOptimal Filtering
We consider the problem of filtering in linear statespace models (e.g.,...
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Online Algorithms For Parameter Mean And Variance Estimation In Dynamic Regression Models
We study the problem of estimating the parameters of a regression model ...
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Stochastic Online Optimization using Kalman Recursion
We study the Extended Kalman Filter in constant dynamics, offering a bay...
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Online Learning of the Kalman Filter with Logarithmic Regret
In this paper, we consider the problem of predicting observations generated online by an unknown, partially observed linear system, which is driven by stochastic noise. For such systems the optimal predictor in the mean square sense is the celebrated Kalman filter, which can be explicitly computed when the system model is known. When the system model is unknown, we have to learn how to predict observations online based on finite data, suffering possibly a nonzero regret with respect to the Kalman filter's prediction. We show that it is possible to achieve a regret of the order of polylog(N) with high probability, where N is the number of observations collected. Our work is the first to provide logarithmic regret guarantees for the widely used Kalman filter. This is achieved using an online leastsquares algorithm, which exploits the approximately linear relation between future observations and past observations. The regret analysis is based on the stability properties of the Kalman filter, recent statistical tools for finite sample analysis of system identification, and classical results for the analysis of leastsquares algorithms for time series. Our regret analysis can also be applied for state prediction of the hidden state, in the case of unknown noise statistics but known statespace basis. A fundamental technical contribution is that our bounds hold even for the class of nonexplosive systems, which includes the class of marginally stable systems, which was an open problem for the case of online prediction under stochastic noise.
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