Convex empirical risk minimization is a basic tool in machine learning and statistics. We
provide new algorithms and matching lower bounds for differentially private convex …

Abstract We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability
distribution $\nu= e^{-f} $ on $\R^ n $. We prove a convergence guarantee in Kullback …

This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo
method with emphasis on probabilistic machine learning. Second, it reviews the main …

Various aspects of the theory of random walks on graphs are surveyed. In particular,
estimates on the important parameters of access time, commute time, cover time and mixing …

Historically, there is a close connection between geometry and optImization. This is
illustrated by methods like the gradient method and the simplex method, which are …

For simple random walk on a N-vertex graph, the mean time to cover all vertices is at least
cN log (N), where c> 0 is an absolute constant. This is deduced from a more general result …

Abstract Inverse Reinforcement Learning (IRL) is the problem of learning the reward function
underlying a Markov Decision Process given the dynamics of the system and the behaviour …

The presence of uncertainty in a system description has always been a critical issue in
control. The main objective of Randomized Algorithms for Analysis and Control of Uncertain …

We consider the problem of Bayesian learning on sensitive datasets and present two simple
but somewhat surprising results that connect Bayesian learning to “differential privacy”, a …

We show that the problem of counting the number of linear extensions of a given partially
ordered set is# P-complete. This settles a long-standing open question and contrssts with …