arXiv Machine Learning By Xiaomian Yang, Sungho Shin

Learning Linear Systems under Heavy-Tailed Noise: A Non-Asymptotic Analysis from A Single Trajectory

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arXiv:2610. 00637v1 Announce Type: new Abstract: We establish non-asymptotic sample complexity bounds for the least-squares estimation of vector autoregressive models for exponentially stable systems with heavy-tailed noise based on a single observed trajectory.

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arXiv Machine Learning
Jul 21

Concentration and Mean-Square Bounds for Contractive Stochastic Approximation: A Unified Elementary Approach

arXiv:2607. 17595v1 Announce Type: new Abstract: We establish mean-square and concentration bounds for stochastic approximation (SA) with arbitrary norm contractive mappings, under a multiplicative noise model where the noise may scale affinely with the norm of the iterates, and the iterates are potentially unbounded.

By Siddharth Chandak
arXiv Machine Learning
Aug 27

Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systems

The paper studies least squares parameter estimation for discrete‑time, unstable, closed‑loop nonlinear stochastic systems with linearly parametrised uncertainty and additive i.i.d. process noise. By perturbing the control policy with exploratory input and assuming a sub‑exponential input‑to‑state growth property, the authors derive non‑asymptotic bounds on the estimation error whenever the state trajectory remains in an informative region of the state space. When the entire state space is informative, the bounds hold with high probability for all time steps, and the authors illustrate the applicability of their results with examples that extend beyond existing work.

By Seth Siriya, Jingge Zhu, Dragan Ne\v{s}i\'c, Ye Pu