Welcome to the 'Optimal Stopping Seminar,' run by the students and postdocs of Columbia University.
The seminar meets in-person in Columbia University on Firdays at 5:00 pm in Math room 507.
This seminar is the logical continuation of the seminar held in Spring 2025 - Optimal Stopping Theory: Methods and Techniques - Spring 2025.
If you would like to come or to be added on the mailing list, please email gg2793@columbia.edu.
| Date and time | Speaker | Title and abstract |
|---|---|---|
| Friday, November 7, 5:00 pm | Andres Riveros Valdevenito | TBA
TBA |
| Date and time | Speaker | Title and abstract |
|---|---|---|
| Friday, November 14, 5:00 pm | Christian Fiedler | From Online Vector Balancing to Mean-Field Stochastic Control
Online vector balancing problems (OVBPs) are a central task in discrepancy theory. Given a finite stream of vectors $v_1,\dots ,v_n\in\mathbb{R}^n$, the goal is to adaptively choose signs $\varepsilon_k\in\{\pm 1\}$ so that the signed sum $\sum_{k=1}^{n}\varepsilon_k v_k$ is small in every coordinate. Such problems have been studied extensively from an algorithmic point of view. We examine the OVBP from the new perspective of stochastic control. Under i.i.d. Gaussian inputs $v_k\sim\mathcal{N}(0,I_n)$ we conjecture that the mean-field scaling limit is characterized by a continuous-time stochastic control problem of novel type. In it, one steers a Brownian motion with an $L^2$-constrained drift to minimize the $L^\infty$-norm of the state at the terminal time 1. We provide strong partial results supporting this convergence. We establish the value of the limiting control problem as a lower bound for the asymptotic value of the OVBP. More significantly, we also show that restricting the limiting problem to a suitable class of controls yields an upper bound on the asymptotic value. This connection suggests new avenues for algorithm design for OVBP based on stochastic control. |
| Friday, November 21, 5:00 pm | No seminar (24th Northeast Probability Seminar) |
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| Friday, November 28, 5:00 pm | No seminar (Thanksgiving) |
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| Friday, December 5, 5:00 pm | Raphael Grondin | TBA
TBA |
| Date and time | Speaker | Title and abstract |
|---|---|---|
| Friday, September 19, 5:00 pm | Steven Campbell | A Tractable Triple Problem in Sequential Inference: Filtering, Control, and Stopping
We study a Bayesian sequential inference problem for the drift of a Brownian motion in which the observer not only chooses their stopping and decision rules, but also controls the rate at which information is acquired. This extension introduces a cost for information acquisition, transforming the classical formulation of Shiryaev (1967) into a joint problem of filtering, control, and optimal stopping. Problems of this kind arise in adaptive experimental design and real-time inference across domains such as healthcare, finance, and engineering, where information is costly and decision-making must be timely. Our framework accommodates a host of classification losses and general running costs on the control process. Despite the added complexity, the problem admits a remarkably simple and semi-explicit solution that exhibits structural parallels with the classical setting. This work highlights a rare instance in which a triple problem-combining inference, control, and stopping-remains analytically tractable. Based on joint work with Georgy Gaitsgori and Richard Groenewald. |
| Friday, September 26, 5:00 pm | Georgy Gaitsgori | An Optimal Stoping Problem with Drift Uncertainty
We consider an optimal stopping problem for a diffusion process whose drift is given by an unobservable Bernoulli random variable. The goal, unlike problems of sequential testing, is to stop the diffusion so as to minimize the terminal convex cost in the presence of the running cost per unit of elapsed time. We show that under suitable assumptions on the terminal cost (e.g., it is a power function), the problem admits a semi-explicit characterization. We also provide examples where the continuation region consists of multiple disjoint intervals. The talk is based on an ongoing project with Ioannis Karatzas. |
| Friday, October 3, 5:00 pm | Raphael Grondin | An introduction to entropy estimation in information theory (Part 1)
I will present the foundational results of Shannon, covering his famous Source Coding Theorem and Universal Codes. I will cover the celebrated Shannon-McMilan-Breiman theorem while motivating the famous result of Lempel and Ziv on estimating the entropy of a single ergodic source. If time permits, I will start presenting the theory for estimating the relative entropy of two given random sources \P, \Q and talk about the famous Wyner problem on waiting times and the various relative entropy estimation algorithms known and studied in the literature. |
| Friday, October 10, 5:00 pm | No seminar (Stony Brook probability day) | |
| Friday, October 17, 5:00 pm | No seminar |
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| Friday, October 24, 5:00 pm | No seminar (9th Eastern Conference on Mathematical Finance) |
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| Friday, October 31, 5:00 pm | Manuel Arnese | Sharp propagation of chaos for mean field Langevin dynamics and mean field control
We establish the sharp rate of propagation of chaos for McKean--Vlasov equations with coefficients that are non-linear in the measure argument; we then apply our results to Wasserstein gradient flows, mean field games and mean field control. Our arguments combine a version of the BBGKY hierarchy with ideas from the literature on weak propagation of chaos and analysis on the space of measures. |