Statistical Inference for Stochastic Gradient Descent: Beyond
Finite Variance

Co-authors: Peter Glynn, Wenhao Yang

Abstract: Stochastic gradient descent (SGD) is a foundational algorithm for iterative first order stochastic simulation optimization and general machine learning algorithms. Simulation output analysis for SGD is well understood when gradients have finite variance. However, as we will illustrate, there are several examples, in areas such machine learning, epidemiology, insurance claims, among others, in which statistical output, despite having finite variance in theory, behaves as having infinite variance over practical temporal scales. We will discuss an efficient, model-agnostic methodology for constructing confidence regions from SGD trajectories
that applies in both finite and infinite-variance regimes. The procedure is based on a joint weak convergence result for the Polyak-Ruppert averaged estimator and an empirical second-moment normalizer constructed from stochastic gradients along the SGD trajectory. This joint limit yields a self-normalized statistic in which the leading tail-dependent scaling terms cancel. We then use a subsampling calibration scheme to estimate the relevant critical values, avoiding explicit estimation of tail indices, slowly varying functions, or stable-law parameters. The resulting confidence regions are straightforward to implement and are asymptotically valid under both the
finite- and infinite-second-moment regimes. Simulation studies show reliable coverage in various settings, supporting the proposed method as a practical tool for uncertainty quantification in stochastic optimization.

Keywords: Model agnostic simulation output optimization

Session, Time and Place: Tutorial 4 | Monday, August 3rd | 16:30–18:30 | Room TBD.

Generative AI and Data Farming

Abstract: The simulation community stands at an unusual methodological vantage point. Fifty years of work on stochastic output analysis, experiment design, data farming, calibration, and uncertainty quantification have produced tools that are now needed by a much larger AI (artificial intelligence) community grappling with how to evaluate generative models. At the same time, the simulation community itself is adopting generative models in many ways, including as data sources for input modeling and surrogates for the simulation input/output behavior. In this tutorial, we begin by describing several commonly-used types of generative models, followed by a brief overview of key data farming concepts. We describe three ways generative AI models can be used in simulation practice, and demonstrate these using a large dataset on sleep activity obtained from wearable sensors. First, we use a generative adversarial network (GAN) to augment the real-world data for input modeling purposes. Second, we use data farming to assess how well this process works, and provide guidance on future data collection and assessment efforts. Third, we incorporate our GAN input model into a stylized simulation model that relates fatigue to performance. We set up a data farming experiment to investigate the impact
of different strategies on performance, and compare generative AI surrogates with other types of metamodels. Attendees will leave with a working vocabulary for the dominant generative model families, as well as demonstration materials and tools available in public GitHub repositories. We close by posing several open problems at the interface of simulation and generative AI.

Keywords: generative adversarial network, experiment design, metamodeling

Session, Time and Place: Tutorial 2 | Monday, August 3rd | 10:30–12:00 | Room TBD.

COMING SOON

Session, Time and Place: Tutorial 3 | Monday, August 3rd | 14:00–16:00 | Room TBD.

Generative Models for Simulation and Decision-Making under
Distributional Shift

Abstract: Many simulation and data-driven decision problems begin with a nominal model estimated from historical data, while the system of interest may operate under shifted, context-dependent, partially observed, or stress-induced distributions. Modern generative models, including flow-based and score-based models, provide a useful mathematical framework for constructing such decision-relevant distributions.

This tutorial will introduce generative models from the viewpoint of simulation, stochastic modeling, and operations research. Rather than focusing only on synthetic data generation, we will view generative models as tools for representing, transforming, sampling from, and optimizing over probability distributions. The tutorial will cover transport maps, velocity fields, score fields, guided stochastic dynamics, and Wasserstein-space formulations. These ideas will be connected to scenario generation, posterior sampling, uncertainty quantification, robust decision-making, and distributionally robust optimization under distributional shift.

The tutorial is intended to be accessible to researchers in simulation, stochastic systems, machine learning, and operations research. The goal is to provide both a conceptual introduction and a mathematical roadmap for using generative models as simulation engines for decision-making under uncertainty.

Keywords: Generative models, simulation, sampling, distributional shift, decision-making

Session, Time and Place: Tutorial 1 | Monday, August 3rd | 8:00–10:00 | Room TBD.