arXiv subjects

Robert L. Bray

Publications and source records attributed to Robert L. Bray.

4 recordsLinked to original sources

arXiv2026

Training Neural Networks Embedded in Dynamic Discrete Choice Models

We develop the first general-purpose estimator for infinite-horizon dynamic discrete choice models whose estimation problem, after pre-computation, is unencumbered by large systems of linear equations -- either imposed as constraints, or embedded in the objective function. Our unnested fixed point (UFXP) and optimal unnested fixed point (OUFXP) estimators exploit a dual representation of Bellman's equation to separate the utility parameters from the dynamic programming fixed point. We establish the consistency and asymptotic normality of UFXP and OUFXP, as well as the efficiency of the latter. Our estimators enable researchers to model utility functions non-parametrically via flexible neural-network approximations.

econ.EM↗

arXiv2026

An $Ω(\log(N)/N)$ Lookahead is Sufficient to Bound Costs in the Overloaded Loss Network

I study the simplest model of revenue management with reusable resources: admission control of two customer classes into a loss queue. This model's long-run average collected reward has two natural upper bounds: the deterministic relaxation and the full-information offline problem. With these bounds, we can decompose the costs faced by the online decision maker into (i) the \emph{cost of variability}, given by the difference between the deterministic value and the offline value, and (ii) the \emph{cost of uncertainty}, given by the difference between the offline value and the online value. \cite{Xie2025} established that the sum of these two costs is $Θ(\log N)$, as the number of servers, $N$, goes to infinity. I show that we can entirely attribute this $Θ(\log N)$ rate to the cost of uncertainty, as the cost of variability remains $O(1)$ as $N \rightarrow \infty$. In other words, I show that anticipating future fluctuations is sufficient to bound operating costs -- smoothing out these fluctuations is unnecessary. In fact, I show that an $Ω(\log(N)/N)$ lookahead window is sufficient to bound operating costs.

econ.TH↗

arXiv2024

A Tutorial on Teaching Data Analytics with Generative AI

This tutorial addresses the challenge of incorporating large language models (LLMs), such as ChatGPT, in a data analytics class. It details several new in-class and out-of-class teaching techniques enabled by AI. For example, instructors can parallelize instruction by having students interact with different custom-made GPTs to learn different parts of an analysis and then teach each other what they learned from their AIs. For another example, instructors can turn problem sets into AI tutoring sessions, whereby a custom-made GPT guides a student through the problems, and the student uploads the chatlog for their homework submission. For a third example, you can assign different labs to each section of your class and have each section create AI assistants to help the other sections work through their labs. This tutorial advocates the programming in the English paradigm, in which students express the desired data transformations in prose and then use AI to generate the corresponding code. Students can wrangle data more effectively by programming in English than by manipulating in Excel. However, some students will program in English better than others, so you will still derive a robust grade distribution (at least with current LLMs).

cs.CY↗

arXiv2023

Logarithmic Regret in Multisecretary and Online Linear Programs with Continuous Valuations

I study how the shadow prices of a linear program that allocates an endowment of $nβ\in \mathbb{R}^{m}$ resources to $n$ customers behave as $n \rightarrow \infty$. I show the shadow prices (i) adhere to a concentration of measure, (ii) converge to a multivariate normal under central-limit-theorem scaling, and (iii) have a variance that decreases like $Θ(1/n)$. I use these results to prove that the expected regret in \cites{Li2019b} online linear program is $Θ(\log n)$, both when the customer variable distribution is known upfront and must be learned on the fly. I thus tighten \citeauthors{Li2019b} upper bound from $O(\log n \log \log n)$ to $O(\log n)$, and extend \cites{Lueker1995} $Ω(\log n)$ lower bound to the multi-dimensional setting. I illustrate my new techniques with a simple analysis of \cites{Arlotto2019} multisecretary problem.

cs.LG↗