Abstract

The classical Langevin diffusion provides a natural algorithm for sampling from a given (continuous) distribution, which can be viewed as the unique minimizer of an energy functional over the space of probability measures. More recently, many problems in machine learning and statistics require sampling from distributions which are characterized as minimizers of similar energy functionals over a smaller, constrained set of probability measures. Key examples are (regularized) optimal transport, for which the constraint set consists of couplings of some given marginals, as well as variational inference in Bayesian statistics for which a variety of constraint sets are used, the most popular two being Gaussians and product measures. This talk will discuss new stochastic dynamics arising as variants of the Langevin dynamics which are well-suited for these kinds of constrained sampling problems. These dynamics can be viewed as gradient flows on submanifolds of the Wasserstein space of probability measures (although this talk assumes no prior knowledge of gradient flow theory). Based in part on joint work with Giovanni Conforti and Soumik Pal.

Speaker's Bio

Daniel is an associate professor in the Department of Industrial Engineering and Operations Research at Columbia University. He was an NSF postdoctoral fellow in the Division of Applied Mathematics at Brown University from 2015 to 2017. Prior to that, he received his Ph.D. from Princeton University in 2015 and his B.S. from Carnegie Mellon University in 2010. He is a recipient of an Alfred P Sloan Fellowship, an NSF CAREER award, and a SIAG-FME early career prize. Daniel's primary research areas are mean field games and interacting particle systems, which form the mathematical foundation for a wide range of models of large-scale interactions arising in physics, engineering, economics, and finance.

Abstract

Synchronous federated learning (FL) scales poorly with the number of clients due to the straggler effect. To overcome this limitation, algorithms like FedAsync allow clients and the central server to communicate asynchronously, thus trading estimation errors for scalability and speed. While most existing analyses are based on overly simplified assumptions on delays, recent research highlights the crucial impact of these queuing dynamics on performance. Building on this insight, we make advances in both the analysis and optimization of asynchronous FL. We demonstrate that existing performance bounds can be expressed in closed form using stationary distributions of Jackson networks; in particular, this yields an explicit characterization of performance as a function of task-to-clients routing probabilities. In addition, we introduce a gradient-based optimization method to improve performance by adapting these routing probabilities. Lastly, we show that existing performance bounds do not adequately account for convergence rates relative to clock time, and we propose an alternative metric that addresses this limitation. Several experiments illustrate the performance gains of routing optimization.

This is joint work with Abdelkrim Alahyane, Matthieu Jonckheere, and Éric Moulines.

Speaker's Bio

Céline Comte is a CNRS researcher in the LAAS laboratory and the SOLACE team in Toulouse. She completed her PhD at Télécom Paris and Nokia Bell Labs in 2019. Between graduation and joining CNRS, she was a postdoctoral researcher and lecturer and then an assistant professor in the Stochastic Operations Research group at the Eindhoven University of Technology. Céline’s work focuses on performance evaluation and optimization of stochastic networks. She has been a member of the program committee of various international conferences and has also co-organized several scientific events, including YEQT XIV in June 2021 and RL4SN in June 2024.

Abstract

Machine learning (ML) has achieved great success in a variety of applications suggesting a new way to build flexible, universal, and efficient approximators for complex high-dimensional data.  These successes have inspired many researchers to apply ML to other scientific applications such as industrial engineering, scientific computing, and operational research, where similar challenges often occur. However, the luminous success of ML is overshadowed by persistent concerns that the mathematical theory of large-scale machine learning, especially deep learning, is still lacking and the trained ML predictor is always biased. In this talk, I’ll introduce a novel framework of (S)imulation-(Ca)librated (S)cientific (M)achine (L)earning (SCaSML), which can leverage the structure of stochastic simulation models to achieve the following goals: 1) make unbiased predictions even based on biased machine learning predictors; 2) beat the curse of dimensionality with an estimator suffers from it. The SCASML paradigm combines a (possibly) biased machine learning algorithm with a de-biasing step design using rigorous stochastic simulation. Theoretically, I’ll try to understand whether the SCaSML algorithms are optimal and what factors (e.g., smoothness, dimension, and boundness) determine the improvement of the convergence rate. Empirically, I’ll introduce different estimators that enable unbiased and trustworthy estimation for physical quantities with a biased machine learning estimator. Applications include but are not limited to estimating the moment of a function, simulating high-dimensional stochastic processes, uncertainty quantification using bootstrap methods, and randomized linear algebra.

Speaker's Bio

Dr.Yiping Lu is an assistant professor of Industrial Engineering & Management Science, at Northwestern University. Previously we worked as Courant instructors at the Courant Institute of Mathematical Sciences, New York University from 2023-2024. He received my Ph.D. degree in applied math from Stanford University in 2023 and my Bachelor’s degree in applied math from Peking University in 2019.  The long-term goal of Yiping's research is to develop a hybrid scientific research discipline that combines domain knowledge (differential equation, stochastic process, control,…), machine learning, and (randomized) experiments. To this end, I’m working on an interdisciplinary research approach across probability and statistics, machine learning, numerical algorithms, control theory, signal processing/inverse problems, and operations research. Yiping was a recipient of the Conference on Parsimony and Learning (CPAL) Rising Star Award in 2024, the Rising Star in Data Science from the University of Chicago in 2022, the Stanford Interdisciplinary Graduate Fellowship, and the SenseTime Scholarship in 2021 for undergraduates in AI in 2019. He also serves as an area chair/senior PC member for NeurIPS and AISTATS. Homepage: https://2prime.github.io/

Abstract

A/B tests have been used at scale by data-driven enterprises to guide decisions and test innovative ideas to improve core business metrics such as revenue and customer satisfaction. Meanwhile, non-stationarities often arise in such business metrics. These non-stationarities may include the time-of-day effect, the day-of-week effect, week-to-week distribution changes, longer-term changes. In this presentation, we discuss a few perspectives related to such non-stationarities in A/B tests. 

Speaker's Bio

Zeyu Zheng is an associate professor in the Department of Industrial Engineering and Operations Research, College of Engineering at University of California Berkeley. He received a Ph.D. in Management Science and Engineering (2018), Ph.D. minor in Statistics (2018) and M.A. in Economics (2016) from Stanford University, and B.S. in Mathematics (2012) from Peking University. He directs the Berkeley Artificial Intelligence and Simulation Lab. His research team works on simulation, inference, generative AI models, stochastic optimization, experiment design and non-stationary learning. 

Abstract

In this talk, we explore the non-asymptotic sample complexity for the pure exploration problem in both contextual bandits and tabular reinforcement learning (RL), specifically focusing on identifying an ε-optimal policy from a given set of policies Π with high probability. In the bandit setting, prior work has demonstrated that it is possible to identify the best policy by focusing on estimating only the differences in behaviors between individual policies, rather than estimating each policy’s behavior independently, leading to significant improvements in sample efficiency. However, the best-known approaches for tabular RL fail to exploit this idea and instead estimate the behavior of each policy individually. We investigate whether this efficiency can be extended to RL by estimating only the differences in policy behaviors, and we present a nuanced answer. For contextual bandits, we show that such an approach is indeed sufficient. However, for tabular RL, we establish that it is not, revealing a key distinction between the two settings. Nevertheless, we propose a new approach inspired by this observation, showing that it is nearly sufficient to estimate behavior differences in RL when anchored by a reference policy. Our algorithm leverages this insight to provide the tightest known bound on the sample complexity of tabular RL, offering both theoretical advancements and practical implications for reinforcement learning research.

Speaker's Bio

Kevin Jamieson is an Associate Professor in the Paul G. Allen School of Computer Science & Engineering at the University of Washington. He received his B.S. in 2009 from the University of Washington under the advisement of Maya Gupta, his M.S. in 2010 from Columbia University under the advisement of Rui Castro, and his Ph.D. in 2015 from the University of Wisconsin - Madison under the advisement of Robert Nowak, all in electrical engineering. He returned to the University of Washington as faculty in 2017 after a postdoc in the AMP lab at the University of California, Berkeley working with Benjamin Recht. Jamieson's work has been recognized by an NSF CAREER award and Amazon Faculty Research award.