Accurate Parameter Estimation for Risk-aware Autonomous Systems

Sarker, Arnab; Fisher, P. H.; Gaudio, Joseph E.; Annaswamy, Anuradha M.

doi:10.48550/arxiv.2006.12687

Cited by 2 publications

(2 citation statements)

References 18 publications

(51 reference statements)

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“…Can we design inputs to respect constraints such as constraints on frequencies? [SGA20] suggests that efficient estimation is possible under general conditions on the inputs. More general noise.…”

Section: Process Noisementioning

confidence: 99%

Improved rates for prediction and identification of partially observed linear dynamical systems

Lee¹

2020

Preprint

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Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. A natural question is how to do so with non-asymptotic statistical rates depending on the inherent dimensionality (order) d of the system, rather than on the sufficient rollout length or on 1 1−ρ(A) , where ρ(A) is the spectral radius of the dynamics matrix. We develop the first algorithm that given a single trajectory of length T with gaussian observation noise, achieves a near-optimal rate of ‹ Oin H 2 error for the learned system. We also give bounds under process noise and improved bounds for learning a realization of the system. Our algorithm is based on low-rank approximation of Hankel matrices of geometrically increasing sizes.

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Section: Process Noisementioning

confidence: 99%

Improved rates for prediction and identification of partially observed linear dynamical systems

Lee¹

2020

Preprint

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“…[23] considers the non linear dynamical systems of the form x t+1 = Aφ(x t , u t ) + η t which φ is a known non-linearity and matrix A is to be estimated. [24,25] consider essentially linear dynamics but allow for certain non-linearities that can be modeled as process noise. All these again differ from the model we consider.…”

Section: Introductionmentioning

confidence: 99%

Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systems

Jain¹,

Kowshik²,

Nagaraj³

et al. 2021

Preprint

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We consider the setting of vector valued non-linear dynamical systems X t+1 = φ(A * X t ) + η t , where η t is unbiased noise and φ : R → R is a known link function that satisfies certain expansivity property. The goal is to learn A * from a single trajectory X 1 , • • • , X T of dependent or correlated samples. While the problem is well-studied in the linear case, where φ is identity, with optimal error rates even for non-mixing systems, existing results in the non-linear case hold only for mixing systems. In this work, we improve existing results for learning nonlinear systems in a number of ways: a) we provide the first offline algorithm that can learn non-linear dynamical systems without the mixing assumption, b) we significantly improve upon the sample complexity of existing results for mixing systems, c) in the much harder one-pass, streaming setting we study a SGD with Reverse Experience Replay (SGD − RER) method, and demonstrate that for mixing systems, it achieves the same sample complexity as our offline algorithm, d) we justify the expansivity assumption by showing that for the popular ReLU link function -a non-expansive but easy to learn link function with i.i.d. samples -any method would require exponentially many samples (with respect to dimension of X t ) from the dynamical system. We validate our results via. simulations and demonstrate that a naive application of SGD can be highly sub-optimal. Indeed, our work demonstrates that for correlated data, specialized methods designed for the dependency structure in data can significantly outperform standard SGD based methods.Preprint. Under review.

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Accurate Parameter Estimation for Risk-aware Autonomous Systems

Cited by 2 publications

References 18 publications

Improved rates for prediction and identification of partially observed linear dynamical systems

Improved rates for prediction and identification of partially observed linear dynamical systems

Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systems

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