14 citations · 58 across the 23 of their papers we have counts for
25 papers
Regularised double shuffle relations for planar Arborified Zeta Values
Pierre Catoire, Pierre J. Clavier, Ku-Yu Fan
We endow spaces of decorated planar rooted trees with new dendriform and tridendrifrom algebra structures and provide their combinatorial description. We then show that the planar…
Tridendriform and dendriform Zeta Values from Schroeder trees
Pierre Catoire, Pierre Clavier, Douglas Modesto da Fraga Candido
To build new generalisations of Multiple Zeta Values, we define new spaces of formal series and formal integrals. We show that they are tridendriform and dendriform algebras. This…
TRAPs, Generalisations of MZVs, Locality and Resurgence for Quantum Field Theories
Pierre J. Clavier
This thesis presents some mathematical results related to quantum field theory. The first chapter is dedicated to TRAPs and how they could be used to rigorously define Feynman rule…
Coalgebras, bialgebras and Rota-Baxter algebras from shuffles of rooted forests
Pierre J. Clavier, Douglas Modesto
We construct and study new generalisations to rooted trees and forests of some properties of shuffles of words. First, we build a coproduct on rooted trees which, together with the…
VITS : Variational Inference Thompson Sampling for contextual bandits
Pierre Clavier, Tom Huix, Alain Durmus
In this paper, we introduce and analyze a variant of the Thompson sampling (TS) algorithm for contextual bandits. At each round, traditional TS requires samples from the current po…
Towards Minimax Optimality of Model-based Robust Reinforcement Learning
Pierre Clavier, Erwan Le Pennec, Matthieu Geist
We study the sample complexity of obtaining an -optimal policy in \emph{Robust} discounted Markov Decision Processes (RMDPs), given only access to a generative model of the nomi…