MaLGa center, Dipartimento di Matematica
Università degli Studi di Genova · Genoa, Italy
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.
Research papers on probability, learning, control, and distributions.
High-probability bounds for the convergence of a Markov chain’s occupation measure in MMD, separating the roles of the spectral gap and kernel relaxation, with an application to one-step prediction from a single trajectory.
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.
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.
Studies learning from one dependent trajectory, giving guarantees for prediction and extensions to higher-order systems, finite-state dynamics, and Koopman operators.
A reproducible benchmark for unsupervised domain adaptation across images, text, biomedical, and tabular data, with particular attention to realistic model selection.
Learns a data-dependent kernel between probability distributions by maximizing entropy in an embedding space, yielding useful geometry for downstream tasks.
Selected open-source work at the intersection of machine learning, reinforcement learning, and reproducibility.
A scikit-learn and PyTorch-compatible library for domain adaptation, with estimators, pipelines, and tools for evaluating methods under distribution shift.
An OpenAI Gym-compatible research environment for Age of Empires II, exposing game observations and actions for reinforcement learning agents.
A reproduction of a PPO agent for the μRTS strategy game using Stable-Baselines3, including training, evaluation, and profiling scripts.
A compact reproduction of an attention-based driving agent, trained with covariance matrix adaptation evolution strategy on the CarRacing environment.
A streamlined reproduction of EMP-SSL, with attention to reproducible training and efficient use of GPU memory for fast experiments.
Email: oleksii.kachaiev@gmail.com