A short operator proof of Hoeffding inequalities for Markov chains
A direct operator proof of sharp Hoeffding bounds for Markov chains with an L² spectral gap, extending the same argument to Markov-dependent random matrices.
arXiv:2609.23098PDF ↗
01 / Research
Learning from evolving systems.
I study dynamical systems through probability and statistical learning. My recent work has focused on two related questions: what can we learn about a system from a single observed trajectory, and what can we say about its behavior over long time horizons? The first concerns learning and prediction from dependent data; the second includes quantitative bounds for the convergence of occupation measures toward invariant distributions. I use tools from Markov chains, concentration inequalities, kernel methods, and operator theory. I am also interested in applying ideas and tools from dynamical systems to optimization, flows, and optimal transport.
Previously, I was a Principal Software Engineer at Riot Games, serving as tech lead of the AI/ML team working on League of Legends.
02 / Publications & preprints
Selected writing.
Research papers on probability, learning, control, and distributions.
-
-
Learning to control switching nonlinear systems with Koopman operator regression
Learns a switching predictive model for nonlinear dynamics from data, then uses it in model predictive control, with bounds for learning error and control performance.
arXiv:2607.11344PDF ↗ -
Learning Ergodic Dynamical Systems from a Finite Trajectory
Studies learning from one dependent trajectory, giving guarantees for prediction and extensions to higher-order systems, finite-state dynamics, and Koopman operators.
arXiv:2607.22399PDF ↗ -
SKADA-Bench: Benchmarking Unsupervised Domain Adaptation Methods with Realistic Validation On Diverse Modalities
A reproducible benchmark for unsupervised domain adaptation across images, text, biomedical, and tabular data, with particular attention to realistic model selection.
arXiv:2407.11676Code ↗ -
Learning to Embed Distributions via Maximum Kernel Entropy
Learns a data-dependent kernel between probability distributions by maximizing entropy in an embedding space, yielding useful geometry for downstream tasks.
03 / Research engineering
Tools & experiments.
Selected open-source work at the intersection of machine learning, reinforcement learning, and reproducibility.
-
Python · Domain adaptation SKADA ↗
A scikit-learn and PyTorch-compatible library for domain adaptation, with estimators, pipelines, and tools for evaluating methods under distribution shift.
-
Python · Learning environments PyAge2 ↗
An OpenAI Gym-compatible research environment for Age of Empires II, exposing game observations and actions for reinforcement learning agents.
-
Python · Reinforcement learning Gym-μRTS with Stable-Baselines3 ↗
A reproduction of a PPO agent for the μRTS strategy game using Stable-Baselines3, including training, evaluation, and profiling scripts.
-
PyTorch · Neuroevolution Self-interpretable car-racing agent ↗
A compact reproduction of an attention-based driving agent, trained with covariance matrix adaptation evolution strategy on the CarRacing environment.
-
PyTorch · Self-supervised learning SSL in One Epoch ↗
A streamlined reproduction of EMP-SSL, with attention to reproducible training and efficient use of GPU memory for fast experiments.
04 / Contact
Get in touch.
Email: oleksii.kachaiev@gmail.com