TILOS-HDSI Seminar: Machine learning for discrete optimization: Theoretical foundations
2026-05-06 11:00 - 12:00 (America/Los_Angeles) | HDSI 123 and Virtual, 3234 Matthews Ln, La Jolla, CA, 92093, United States
Ellen Vitercik, Stanford University
Abstract: Many of the most important optimization problems in practice are massive in scale, mathematically complex, and involve numerous unknown parameters. Machine learning offers a powerful way to address these challenges by uncovering hidden structure across problem instances, but integrating predictions into algorithms raises fundamental questions: which architectures align with combinatorial structure, and how can we ensure robustness to error? This talk presents two case studies. First, we show how graph neural networks can approximate the optimal dynamic program for online matching, yielding algorithms that generalize across graph sizes and achieve strong empirical performance. Second, we investigate calibration as a principled interface between machine learning and decision-making, demonstrating through rent-or-buy and job scheduling problems that calibrated predictions yield both theoretical guarantees and practical improvements. This is joint work with Alexandre Hayderi, Amin Saberi, Anders Wikum, and Judy Hanwen Shen.

Ellen Vitercik is an Assistant Professor at Stanford University with a joint appointment between the Management Science & Engineering department and the Computer Science department. Her research interests include machine learning, algorithm design, discrete and combinatorial optimization, and the interface between economics and computation. Before joining Stanford, she spent a year as a Miller Postdoctoral Fellow at UC Berkeley and received a PhD in Computer Science from Carnegie Mellon University. Her research has been recognized with a Schmidt Sciences AI2050 Early Career Fellowship, an NSF CAREER award, the SIGecom Doctoral Dissertation Award, and the CMU School of Computer Science Distinguished Dissertation Award, among other honors.

Optimization for ML and AI Seminar: Self-play Algorithms for Math Theorem Proving
2026-05-08 11:00 - 12:00
Tengyu Ma, Stanford University
Abstract: I will discuss RL algorithms for automated theorem proving with LLMs, especially in the possible future regime where we run out of high-quality training data. To keep improving the models with limited data, we draw inspiration from mathematicians, who continuously develop new results, partly by proposing novel conjectures or exercises and attempting to solve them. We design the Self-play Theorem Prover (STP) that simultaneously takes on two roles, conjecturer and prover, each providing training signals to the other. At the end of the talk, I will mention a recent paper on extending the algorithm to include another role, Guide, which helps guide the conjecturer to generate clean and relevant conjectures, and a few other related works in using AI for math.

Tengyu Ma is an assistant professor of computer science at Stanford University. His research interests broadly include topics in machine learning, algorithms and their theory, such as deep learning, (deep) reinforcement learning, pre-training / foundation models, robustness, non-convex optimization, distributed optimization, and high-dimensional statistics.

TILOS-HDSI Seminar: ComPO: Preference Alignment via Comparison Oracles
2026-05-13 11:00 - 12:00
Tianyi Lin, Columbia University
Direct alignment methods are increasingly used for aligning large language models (LLMs) with human preferences. However, these methods suffer from the likelihood displacement, which can be driven by noisy preference pairs that induce similar likelihood for preferred and dis-preferred responses. To address this issue, we consider doing derivative-free optimization based on comparison oracles. First, we propose a new preference alignment method via comparison oracles and provide convergence guarantees for its basic mechanism. Second, we improve our method using some heuristics and conduct the experiments to demonstrate the flexibility and compatibility of practical mechanisms in improving the performance of LLMs using noisy preference pairs. Evaluations are conducted across multiple base and instruction-tuned models with different benchmarks. Experimental results show the effectiveness of our method as an alternative to addressing the limitations of existing methods. A highlight of our work is that we evidence the importance of designing specialized methods for preference pairs with distinct likelihood margins.

Tianyi Lin is an assistant professor in the Department of Industrial Engineering and Operations Research (IEOR) at Columbia University. His research interests lie in generative artificial intelligence, optimization for machine learning, game theory, social and economic network, and optimal transport. He obtained his Ph.D. in Electrical Engineering and Computer Science at UC Berkeley, where he was advised by Professor Michael Jordan and was associated with the Berkeley Artificial Intelligence Research (BAIR) group. From 2023 to 2024, he was a postdoctoral researcher at the Laboratory for Information & Decision Systems (LIDS) at Massachusetts Institute of Technology, working with Professor Asuman Ozdaglar. Prior to that, he received a B.S. in Mathematics from Nanjing University, a M.S. in Pure Mathematics and Statistics from University of Cambridge and a M.S. in Operations Research from UC Berkeley.

Optimization for ML and AI Seminar: A non-equilibrium phase transition with broken ergodicity leads to double descent and benign overfitting in machine learning
2026-05-15 11:00 - 12:00
Nigel Goldenfeld, UC San Diego Department of Physics and HDSI
Abstract: The remarkable ability of modern neural networks to generalize improves with increasing network capacity, even when the number of model parameters or effective degrees of freedom exceeds the number of training data points. This phenomenon is all the more surprising given that generalization error diverges when the number of model parameters approaches a critical value from below. Here we use dynamical mean field theory to show, in a simple setting of linear regression, that this so-called “double descent” behavior is the outcome of a phase transition in the stochastic field theory describing the training process. We calculate the critical exponents and scaling function of the double descent phase transition, and show that it is marked by a breakdown of the fluctuation-dissipation theorem associated with broken ergodicity. The corresponding response function has the same functional form as the simple London model of the superconducting transition, with the rigidity of the wave function corresponding to the neural network’s ability to generalize accurately. Our results are distinct from earlier work, because we calculate the time-dependence specifically, not just the equilibrium solutions. This is what enables us to identify the origin of the emergent behavior.
Work performed with Chan Li.

Nigel Goldenfeld holds the Chancellor’s Distinguished Professorship in Physics at UC San Diego, which he joined in Fall 2021 after 36 years at the University of Illinois at Urbana-Champaign (UIUC). Nigel’s research spans condensed matter theory, the theory of living systems, hydrodynamics and non-equilibrium statistical physics.
Nigel received his PhD in theoretical physics from the University of Cambridge (UK) in 1982, and from 1982-1985 was a postdoctoral fellow at the Institute for Theoretical Physics at UC Santa Barbara, where his work on the dynamics of snowflake growth helped launch the modern theory of pattern formation in nature. He joined the condensed matter theory group at the Department of Physics at UIUC in 1985, where his work was instrumental to the discovery of d-wave pairing in high temperature superconductors. Nigel’s interests in biology include microbial ecology, evolution and systems biology. He was a founding member of the Institute for Genomic Biology at UIUC, where he led the Biocomplexity Group and directed the NASA Astrobiology Institute for Universal Biology. During the COVID-19 pandemic, he pivoted from his experience in mathematical modeling of bacteria and viruses to computational epidemiology, advising the Governor of Illinois, and helping devise, set up and run the COVID saliva testing system at UIUC, which provided ~12 hour turnaround of PCR tests to the 50,000 people in the campus community and eventually to over 1700 schools and other institutions in Illinois and beyond. Nigel has served on the editorial boards of several journals, including The Philosophical Transactions of the Royal Society, Physical Biology and the International Journal of Theoretical and Applied Finance. Selected honors include: Alfred P. Sloan Foundation Fellow, University Scholar of the University of Illinois, the Xerox Award for research, the A. Nordsieck award for excellence in graduate teaching and the American Physical Society’s Leo P. Kadanoff Prize 2020. Nigel is a Fellow of the American Physical Society, a Fellow of the American Academy of Arts and Sciences, a Fellow of the Royal Society (UK) and a Member of the US National Academy of Sciences.

TILOS-HDSI Seminar: Inference-Time Algorithms: A Theoretical Lens on Tractability and Error Propagation
2026-05-20 11:00 - 12:00
Andrej Risteski, Carnegie Mellon University
Abstract: Modern AI systems are increasingly built by placing trained models inside larger computational loops. Inference-time algorithms are a basic instance of this idea: they use one or more trained models at test time to incorporate new information, exploit pretrained models as priors, and trade computational effort for accuracy, sample quality, or control. Examples include generator-verifier search for reasoning, diffusion models for solving inverse problems, and reward-guided generation. Theoretically, this revisits a classical question from optimization and theoretical computer science: what can be done with access to an oracle? Here, however, the oracles are new and non-standard: they model the capabilities of large pretrained models, making them powerful, but also imperfect because they are learned. This combination leads to new questions about algorithm design and error propagation.
This talk studies two central aspects of this paradigm: computational efficiency and error propagation. The first vignette considers generator-verifier systems, and shows how stochastic backtracking can trade additional computation for accuracy, giving a principled version of test-time scaling even with imperfect learned oracles. The second vignette studies diffusion steering: when can we efficiently bias a pretrained diffusion model toward higher-reward samples while staying close to the original model? We show that tractability depends strongly on both the reward structure and the alignment objective, and that simple primitives—such as sampling from linear tilts—can be surprisingly useful for handling richer reward classes.
Based on https://arxiv.org/abs/2510.03149, https://arxiv.org/abs/2602.16570, https://arxiv.org/abs/2605.11361.

Andrej Risteski is an Associate Professor at the Machine Learning Department in Carnegie Mellon University. Prior to that, he was a Norbert Wiener Research Fellow jointly in the Applied Math department and IDSS at MIT. Dr. Risteski received his PhD in the Computer Science Department at Princeton University under the advisement of Sanjeev Arora.
Dr. Risteski’s research interests lie in the intersection of machine learning, statistics, and theoretical computer science, spanning topics like (probabilistic) generative models, algorithmic tools for learning and inference, representation and self-supervised learning, out-of-distribution generalization and applications of neural approaches to natural language processing and scientific domains. The broad goal of his research is principled and mathematical understanding of statistical and algorithmic problems arising in modern machine learning paradigms.
