I work on probability theory at the interface of stochastic processes and machine learning, aiming to build rigorous, quantitative laws for discrete-time stochastic algorithms beyond diffusion approximations.

Themes

  • Stochastic recurrence / exit times: rigorous finite-time and rare-event behavior for discrete stochastic dynamics motivated by SGD-like updates.
  • Metastability & Edge of Stability: understanding stability thresholds and large excursions that drive regime switches during training.
  • Anisotropic noise & generalization: linking directional noise, landscape geometry, and algorithmic notions of flatness (e.g., via escape times or stability margins).

Previous Projects

  • Exit-time theory for Kesten’s stochastic recurrence equations: scaling laws for mean exit times and their connection to heavy-tailed stationary behavior.

Current Projects

  • CFR+ convergence rates: asymptotic rates for Counterfactual Regret Minimization+ in imperfect-information games (Poker), with provable exponents in simple benchmark games.
  • A metastability-based theory for EoS driven by rare events and non-Gaussian effects.
  • Trajectory-aware, data-dependent generalization theory grounded in the regions actually visited by training.