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.
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.
arXiv:2411. 01982v2 Announce Type: replace-cross Abstract: We study the problem of learning controlled stochastic differential equations (SDEs) \[ dX_t = b(t,X_t,u_t)\,dt + \sigma(t,X_t,u_t)\,dW_t, \] whose drift and diffusion depend nonlinearly on time, state, and control values.
arXiv:2609.08740v1 Announce Type: new Abstract: In this paper we derive a Probably Approximately Correct (PAC)-Bayesian error bound for partially observed linear time-invariant (LTI) stochastic dynam...
arXiv:2609. 20409v1 Announce Type: new Abstract: Two-timescale stochastic approximation (TTSA) is a fundamental tool for analyzing coupled iterative algorithms in reinforcement learning, optimization, and stochastic control.
arXiv:2602. 12756v2 Announce Type: replace Abstract: Large Language Models (LLMs) have recently shown exceptional potential in time series forecasting (TSF), leveraging their inherent sequential reasoning capabilities to model complex temporal dynamics.
arXiv:2603. 14762v3 Announce Type: replace-cross Abstract: We study supervisory switching control for partially-observed linear dynamical systems.
arXiv:2607. 22399v1 Announce Type: cross Abstract: We consider the problem of learning from a single finite trajectory of an ergodic stochastic dynamical system.
arXiv:2609.37787v1 Announce Type: new Abstract: Adam is widely observed to remain stable even when the objective deviates significantly from global smoothness. Under the generalized smoothness framew...
Accurately learning nonlinear dynamics from a finite-duration experiment requires the efficient collection of informative data. We address this challenge for stochastic controlled nonlinear dynamical...
The paper presents a theoretical study of Adam in non‑stationary stochastic optimization, distinguishing two regimes: Euclidean tracking under adaptive strong monotonicity and high‑probability projected stationarity for general smooth objectives. It derives finite‑time bounds that decompose into initialization, objective drift, first‑moment tracking error (β₁), and preconditioner perturbation (β₂), and characterizes burn‑in times for constant and step‑decay schedules. The analysis reveals a noise–drift tradeoff, showing that in noise‑dominated settings Adam’s adaptive mechanisms can improve guarantees, while in drift‑dominated settings they may worsen tracking, potentially making vanilla SGD preferable.
arXiv:2609. 18127v1 Announce Type: new Abstract: Many real-world processes exhibit long-range dependence, where the current state depends on a slowly decaying trace of past states rather than on the most recent state alone.
arXiv:2406. 07746v4 Announce Type: replace-cross Abstract: We propose a computationally efficient algorithm that achieves anytime regret of order $\mathcal{O}(\sqrt{t})$, with explicit dependence on the system dimensions and on the solution of the Discrete Algebraic Riccati Equation (DARE).