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Jacob Goldin

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3 papers

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NeurIPS Conference 2025 Conference Paper

Near-Exponential Savings for Population Mean Estimation with Active Learning

Julian Morimoto
Jacob Goldin
Daniel Ho

We study the problem of efficiently estimating the mean of a $k$-class random variable, $Y$, using a limited number of labels, $N$, in settings where the analyst has access to auxiliary information (i. e. : covariates) $X$ that may be informative about $Y$. We propose an active learning algorithm ("PartiBandits") to estimate $\mathbb{E}[Y]$. The algorithm yields an estimate, $\widehat{\mu}_{\text{PB}}$, such that $\left( \widehat{\mu}_{\text{PB}} - \mathbb{E}[Y]\right)^2$ is $\tilde{\mathcal{O}}\left( \frac{\nu + \exp(c \cdot (-N/\log(N))) }{N} \right)$, where $c > 0$ is a constant and $\nu$ is the risk of the Bayes-optimal classifier. PartiBandits is essentially a two-stage algorithm. In the first stage, it learns a partition of the unlabeled data that shrinks the average conditional variance of $Y$. In the second stage it uses a UCB-style subroutine ("WarmStart-UCB") to request labels from each stratum round-by-round. Both the main algorithm's and the subroutine's convergence rates are minimax optimal in classical settings. PartiBandits bridges the UCB and disagreement-based approaches to active learning despite these two approaches being designed to tackle very different tasks. We illustrate our methods through simulation using nationwide electronic health records. Our methods can be implemented using the \textbf{PartiBandits} package in R.

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AAAI Conference 2023 Conference Paper

Entropy Regularization for Population Estimation

Ben Chugg
Peter Henderson
Jacob Goldin
Daniel E. Ho

Entropy regularization is known to improve exploration in sequential decision-making problems. We show that this same mechanism can also lead to nearly unbiased and lower-variance estimates of the mean reward in the optimize-and-estimate structured bandit setting. Mean reward estimation (i.e., population estimation) tasks have recently been shown to be essential for public policy settings where legal constraints often require precise estimates of population metrics. We show that leveraging entropy and KL divergence can yield a better trade-off between reward and estimator variance than existing baselines, all while remaining nearly unbiased. These properties of entropy regularization illustrate an exciting potential for bringing together the optimal exploration and estimation literature.

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AAAI Conference 2023 Conference Paper

Integrating Reward Maximization and Population Estimation: Sequential Decision-Making for Internal Revenue Service Audit Selection

Peter Henderson
Ben Chugg
Brandon Anderson
Kristen Altenburger
Alex Turk
John Guyton
Jacob Goldin
Daniel E. Ho

We introduce a new setting, optimize-and-estimate structured bandits. Here, a policy must select a batch of arms, each characterized by its own context, that would allow it to both maximize reward and maintain an accurate (ideally unbiased) population estimate of the reward. This setting is inherent to many public and private sector applications and often requires handling delayed feedback, small data, and distribution shifts. We demonstrate its importance on real data from the United States Internal Revenue Service (IRS). The IRS performs yearly audits of the tax base. Two of its most important objectives are to identify suspected misreporting and to estimate the "tax gap" -- the global difference between the amount paid and true amount owed. Based on a unique collaboration with the IRS, we cast these two processes as a unified optimize-and-estimate structured bandit. We analyze optimize-and-estimate approaches to the IRS problem and propose a novel mechanism for unbiased population estimation that achieves rewards comparable to baseline approaches. This approach has the potential to improve audit efficacy, while maintaining policy-relevant estimates of the tax gap. This has important social consequences given that the current tax gap is estimated at nearly half a trillion dollars. We suggest that this problem setting is fertile ground for further research and we highlight its interesting challenges. The results of this and related research are currently being incorporated into the continual improvement of the IRS audit selection methods.

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