Garivier, Aurélien Hadiji, Hédi Menard, Pierre Stoltz, Gilles

In the context of K–armed stochastic bandits with distribution only assumed to be supported by [0, 1], we introduce a new algorithm, KL-UCB-switch, and prove that is enjoys simultaneously a distribution-free regret bound of optimal order √ KT and a distribution-dependent regret bound of optimal order as well, that is, matching the κ ln T lower boun...

Chabane, Lydia Chetrite, Raphael Verley, Gatien

We study the fluctuations of systems modeled by Markov jump processes with periodic generators. We focus on observables defined through time-periodic functions of the system's states or transitions. Using large deviation theory, canonical biasing and generalized Doob transform, we characterize the asymptotic fluctuations of such observables after a...

Abeille, Marc Lazaric, Alessandro

We derive an alternative proof for the regret of Thompson sampling (\ts) in the stochastic linear bandit setting. While we obtain a regret bound of order $\widetilde{O}(d^{3/2}\sqrt{T})$ as in previous results, the proof sheds new light on the functioning of the \ts. We leverage on the structure of the problem to show how the regret is related to t...

Azais, Jean-Marc Delmas, Céline

Let X = {X(t) : t ∈ R N } be an isotropic Gaussian random field with real values. In a first part we study the mean number of critical points of X with index k using random matrices tools. We obtain an exact expression for the probability density of the eigenvalue of rank k of a N-GOE matrix. We deduce some exact expressions for the mean number of ...

Abi Jaber, Eduardo Miller, Enzo Pham, Huyên

We provide an exhaustive treatment of Linear-Quadratic control problems for a class of stochastic Volterra equations of convolution type, whose kernels are Laplace transforms of certain signed matrix measures which are not necessarily finite. These equations are in general neither Markovian nor semimartingales, and include the fractional Brownian m...

Chazottes, J.-R Moles, J Ugalde, E

We consider the full shift $T:\Omega\to\Omega$ where $\Omega=A^{\mathbb{N}}$, $A$ being a finite alphabet. For a class ofpotentials which contains in particular potentials $\phi$ with variation decreasing like $O(n^{-\alpha})$ for some $\alpha>2$, we prove that their corresponding equilibrium state $\mu_\phi$ satisfies a Gaussian concentration boun...

Le Ny, Arnaud

This review-type paper is based on a talk given at the conference États de la Recherche en Mécanique statistique, which took place at IHP in Paris (December 10-14, 2018). We revisit old results from the 80's about one dimensional long-range polynomially decaying Ising models (often called Dyson models in dimension one) and describe more recent resu...

Guillin, Arnaud Personne, Arnaud Strickler, Edouard

The paper is devoted to the study of the asymptotic behaviour of Moran process in random environment, say random selection. In nite population, the Moran process may be degenerate in nite time, thus we will study its limiting process in large population which is a Piecewise Deterministic Markov Process, when the random selection is a Markov jump pr...

Jusselin, Paul Mastrolia, Thibaut

Going from a scaling approach for birth/death processes, we investigate the convergence of solutions to BSDEs driven a sequence of converging martingales. We apply our results to non-Markovian stochastic control problems for discrete population models. In particular we describe how the values and optimal controls of control problems converge when t...

Varvenne, Maylis

The main objective of the paper is to study the long-time behavior of general discrete dynamics driven by an ergodic stationary Gaussian noise. In our main result, we prove existence and uniqueness of the invariant distribution and exhibit some upper-bounds on the rate of convergence to equilibrium in terms of the asymptotic behavior of the covaria...