14 papers
Conformalized Quantile Regression and Minimax Limits of Fixed-Score Calibration under Known Covariate Shift
Rustam Isaev, Anton Conrad, Denis Belomestny +2
In this paper, we study nonasymptotic error bounds for interval length and conditional coverage in split conformalized quantile regression (CQR). Our bounds rely on local reg…
Uniform Statistical Convergence of Empirical Sinkhorn Potentials with Exponential and Polynomial Dependence on the Regularization Parameter
Denis Belomestny
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 mea…
Beyond Marginal Validity: Finite-Sample Guarantees for Localized Conformal Prediction
Anton Conrad, Rustam Isaev, Denis Belomestny +2
Conformal prediction endows arbitrary black-box predictors with finite-sample, distribution-free marginal coverage, yet marginal validity can hide severe covariate-specific miscali…
Mathematical methods of reinforcement learning
Denis Belomestny, Alexander Gasnikov, Egor Gladin +5
Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin t…
Your GFlowNet Secretly Learns an Optimal Transport Plan
Ian Maksimov, Nikita Morozov, Denis Belomestny +1
Generative Flow Networks (GFlowNets) are a framework for sampling structured objects via stochastic trajectories in a directed graph. In this work, we establish a theoretical conne…
Schrödinger bridge problem via empirical risk minimization
Denis Belomestny, Alexey Naumov, Nikita Puchkin +1
We study the Schrödinger bridge problem when the endpoint distributions are available only through samples. Classical computational approaches estimate Schrödinger potentials via S…
Statistical analysis of Inverse Entropy-regularized Reinforcement Learning
Denis Belomestny, Alexey Naumov, Artemy Rubtsov +1
Inverse reinforcement learning aims to infer the reward function that explains expert behavior observed through trajectories of state--action pairs. A long-standing difficulty in c…
Tight Bounds for Schrödinger Potential Estimation in Unpaired Data Translation
Nikita Puchkin, Denis Suchkov, Alexey Naumov +1
Modern methods of generative modelling and unpaired data translation based on Schrödinger bridges and stochastic optimal control theory aim to transform an initial density to a tar…
Sample complexity of Schrödinger potential estimation
Nikita Puchkin, Iurii Pustovalov, Yuri Sapronov +3
We address the problem of Schrödinger potential estimation, which plays a crucial role in modern generative modelling approaches based on Schrödinger bridges and stochastic optimal…
Proximal Point Nash Learning from Human Feedback
Daniil Tiapkin, Daniele Calandriello, Denis Belomestny +5
Traditional Reinforcement Learning from Human Feedback (RLHF) often relies on reward models, frequently assuming preference structures like the Bradley--Terry model, which may not…
Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent
Marina Sheshukova, Sergey Samsonov, Denis Belomestny +4
In this paper, we establish the non-asymptotic validity of the multiplier bootstrap procedure for constructing the confidence sets using the Stochastic Gradient Descent (SGD) algor…
Nonasymptotic Analysis of Stochastic Gradient Descent with the Richardson-Romberg Extrapolation
Marina Sheshukova, Denis Belomestny, Alain Durmus +3
We address the problem of solving strongly convex and smooth minimization problems using stochastic gradient descent (SGD) algorithm with a constant step size. Previous works sugge…
A New Bound on the Cumulant Generating Function of Dirichlet Processes
Pierre Perrault, Denis Belomestny, Pierre Ménard +4
In this paper, we introduce a novel approach for bounding the cumulant generating function (CGF) of a Dirichlet process (DP) , using superadditivity. In par…
UVIP: Model-Free Approach to Evaluate Reinforcement Learning Algorithms
Denis Belomestny, Ilya Levin, Alexey Naumov +1
Policy evaluation is an important instrument for the comparison of different algorithms in Reinforcement Learning (RL). However, even a precise knowledge of the value function $V^π…