\dm_csml_event_details UCL ELLIS

New deviation inequalities for Markov chains, with applications to stochastic optimization and empirical risk minimization


Pierre Alquier


ESSEC Business School Singapore


Friday, 31 March 2023




Function Space, UCL Centre for Artificial Intelligence, 1st Floor, 90 High Holborn, London WC1V 6BH



Event series

DeepMind/ELLIS CSML Seminar Series


Many deviation inequalities were recently proven for Markov chains based on martingale techniques. However, such inequalities rely strongly on the assumption that the chain is homogeneous and contractive. Such an assumption is not satisfied in many practical situations, a typical example being the iterates of SGD. In this paper, we extend these techniques to prove deviation inequalities for a class of non-homogeneous Markov chains. I will introduce these inequalities and then focus on two applications: empirical risk minimization for time series, and stochastic optimization. This is based on a joint work with Xiequan Fan (Tianjin University) and Paul Doukhan (Université de Cergy-Pontoise): https://linkinghub.elsevier.com/retrieve/pii/S0304414922001600 (published version) https://arxiv.org/abs/2102.08685 (open-access version)


Pierre Alquier is a professor in statistics at ESSEC Business School in the ASIA-PACIFIC Campus in Singapore. He was previously a researcher at RIKEN AIP in Tokyo. Previously, he held various academic positions in Europe, including Professor of Statistics at ENSAE Paris and Senior Lecturer in Statistics at UCD Dublin. He is currently a senior member of the PC for COLT 2023 and editor for the Journal of Machine Learning Research and Transactions on Machine Learning Research.