Author

D. Belomestny

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Preprint Aug 2026

Beyond Marginal Validity: Finite-Sample Guarantees for Localized Conformal Prediction

Conformal prediction endows arbitrary black-box predictors with finite-sample, distribution-free marginal coverage, yet marginal validity can hide severe covariate-specific miscalibration, while exact distribution-free conditional coverage is finite-sample unattainable. Randomly localized conformal prediction (RLCP) mi...

Anton Conrad, R. Isaev, D. Belomestny et al. · 0 citations

#machine learning Preprint Sep 2026

Conformalized Quantile Regression and Minimax Limits of Fixed-Score Calibration under Known Covariate Shift

In this paper, we study nonasymptotic $L^p$ error bounds for interval length and conditional coverage in split conformalized quantile regression (CQR). Our bounds rely on local regularity conditions and accuracy guarantees for the estimated quantiles. We further instantiate our bounds for quantile regression with spars...

R. Isaev, Anton Conrad, D. Belomestny et al. · 0 citations

Review Jul 2026

Mathematical methods of reinforcement learning

Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin the design and analysis of modern algorithms in RL. We begin from Markov decision processes (MDPs) and Bellman operators, emphasizing contrac...

D. Belomestny, Alexander V. Gasnikov, E. Gladin et al. · Успехи математических наук · 0 citations

#machine learning Preprint Aug 2026

Uniform Statistical Convergence of Empirical Sinkhorn Potentials with Exponential and Polynomial Dependence on the Regularization Parameter

We study the empirical Sinkhorn estimator of the entropic optimal transport potentials under the uniform loss. Since the potentials are only unique up to additive constants, we measure the error using the quotient supremum norm, defined as $d_\infty([u],[v]) = \inf_{a\in\mathbb{R}}\|u-v-a\|_\infty$. For a fixed regular...

D. Belomestny · 0 citations