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In this work, we study the problem of learning partially observed linear dynamical systems from a single sample trajectory. A major practical challenge in the existing system identification methods is the undesirable dependency of their required sample size on the system dimension: roughly speaking, they presume and rely on sample sizes that scale linearly with respect to the system dimension. Evidently, in high-dimensional regime where the system dimension is large, it may be costly, if not impossible, to collect as many samples from the unknown system. In this paper, we will remedy this undesirable dependency on the system dimension by introducing an $ell_1$-regularized estimation method that can accurately estimate the Markov parameters of the system, provided that the number of samples scale logarithmically with the system dimension. Our result significantly improves the sample complexity of learning partially observed linear dynamical systems: it shows that the Markov parameters of the system can be learned in the high-dimensional setting, where the number of samples is significantly smaller than the system dimension. Traditionally, the $ell_1$-regularized estimators have been used to promote sparsity in the estimated parameters. By resorting to the notion of weak sparsity, we show that, irrespective of the true sparsity of the system, a similar regularized estimator can be used to reduce the sample complexity of learning partially observed linear systems, provided that the true system is inherently stable.
We propose a theoretical framework for approximate planning and learning in partially observed systems. Our framework is based on the fundamental notion of information state. We provide two equivalent definitions of information state -- i) a function
Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align existing bran
We study safe, data-driven control of (Markov) jump linear systems with unknown transition probabilities, where both the discrete mode and the continuous state are to be inferred from output measurements. To this end, we develop a receding horizon es
When training the parameters of a linear dynamical model, the gradient descent algorithm is likely to fail to converge if the squared-error loss is used as the training loss function. Restricting the parameter space to a smaller subset and running th
We consider the problem of robust and adaptive model predictive control (MPC) of a linear system, with unknown parameters that are learned along the way (adaptive), in a critical setting where failures must be prevented (robust). This problem has bee