Author

Oleksii Kachaiev

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Preprint Sep 2026

A short operator proof of Hoeffding inequalities for Markov chains

We give a short operator-theoretic proof of the sharp Hoeffding inequality for additive functionals of a Markov chain on a general state space with an $L^2(\pi)$ spectral gap, recovering the bound of Fan et al. (2021). We further show that the same argument yields the Hoeffding inequality of Neeman et al. (2024) for Ma...

Oleksii Kachaiev · 0 citations

Jul 2026

Learning Ergodic Dynamical Systems from a Finite Trajectory

This work first focuses on estimating the optimal one-step prediction function by nonlinear least squares, and derive high-probability guarantees measured with respect to the invariant measure of the process, and extends the framework to higher-order systems and finite-state spaces.

Oleksii Kachaiev, S. Villa, Lorenzo Rosasco · arXiv.org · 0 citations

Preprint Jul 2026

Learning to control switching nonlinear systems with Koopman operator regression

This work quantifies the sub-optimality of the model predictive control strategy, both in the case of exact Koopman dynamics, and in the case of learned ones, in the case of model predictive control systems with finite action spaces.

Edoardo Caldarelli, Oleksii Kachaiev, C. Molinari et al. · 0 citations