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.

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.

We provide practical, efficient, and nonparametric methods for auditing the fairness of deployed classification and regression models. Whereas previous work relies on a fixed-sample size, our methods are sequential and allow for the continuous monitoring of incoming data, making them highly amenable to tracking the fairness of real-world systems. We also allow the data to be collected by a probabilistic policy as opposed to sampled uniformly from the population. This enables auditing to be conducted on data gathered for another purpose. Moreover, this policy may change over time and different policies may be used on different subpopulations. Finally, our methods can handle distribution shift resulting from either changes to the model or changes in the underlying population. Our approach is based on recent progress in anytime-valid inference and game-theoretic statistics---the ``testing by betting'' framework in particular. These connections ensure that our methods are interpretable, fast, and easy to implement. We demonstrate the efficacy of our approach on three benchmark fairness datasets.

We present a unified framework for deriving PAC-Bayesian generalization bounds. Unlike most previous literature on this topic, our bounds are anytime-valid (i.e., time-uniform), meaning that they hold at all stopping times, not only for a fixed sample size. Our approach combines four tools in the following order: (a) nonnegative supermartingales or reverse submartingales, (b) the method of mixtures, (c) the Donsker-Varadhan formula (or other convex duality principles), and (d) Ville's inequality. Our main result is a PAC-Bayes theorem which holds for a wide class of discrete stochastic processes. We show how this result implies time-uniform versions of well-known classical PAC-Bayes bounds, such as those of Seeger, McAllester, Maurer, and Catoni, in addition to many recent bounds. We also present several novel bounds. Our framework also enables us to relax traditional assumptions; in particular, we consider nonstationary loss functions and non-iid data. In sum, we unify the derivation of past bounds and ease the search for future bounds: one may simply check if our supermartingale or submartingale conditions are met and, if so, be guaranteed a (time-uniform) PAC-Bayes bound.

This paper introduces a new, highly consequential setting for the use of computer vision for environmental sustainability. Concentrated Animal Feeding Operations (CAFOs) (aka intensive livestock farms or "factory farms") produce significant manure and pollution. Dumping manure in the winter months poses significant environmental risks and violates environmental law in many states. Yet the federal Environmental Protection Agency (EPA) and state agencies have relied primarily on self-reporting to monitor such instances of "land application." Our paper makes four contributions. First, we introduce the environmental, policy, and agricultural setting of CAFOs and land application. Second, we provide a new dataset of high-cadence (daily to weekly) 3m/pixel satellite imagery from 2018-20 for 330 CAFOs in Wisconsin with hand labeled instances of land application (n=57,697). Third, we develop an object detection model to predict land application and a system to perform inference in near real-time. We show that this system effectively appears to detect land application (PR AUC = 0.93) and we uncover several outlier facilities which appear to apply regularly and excessively. Last, we estimate the population prevalence of land application events in Winter 2021/22. We show that the prevalence of land application is much higher than what is self-reported by facilities. The system can be used by environmental regulators and interest groups, one of which piloted field visits based on this system this past winter. Overall, our application demonstrates the potential for AI-based computer vision systems to solve major problems in environmental compliance with near-daily imagery.

We classify the functions f:ℕ^d → ℕ that are stably computable by leaderless, output-oblivious discrete (stochastic) Chemical Reaction Networks (CRNs). CRNs that compute such functions are systems of reactions over species that include d designated input species, whose initial counts represent an input x ∈ ℕ^d, and one output species whose eventual count represents f(x). Chen et al. showed that the class of functions computable by CRNs is precisely the semilinear functions. In output-oblivious CRNs, the output species is never a reactant. Output-oblivious CRNs are easily composable since a downstream CRN can consume the output of an upstream CRN without affecting its correctness. Severson et al. showed that output-oblivious CRNs compute exactly the subclass of semilinear functions that are eventually the minimum of quilt-affine functions, i.e., affine functions with different intercepts in each of finitely many congruence classes. They call such functions the output-oblivious functions. A leaderless CRN can compute only superadditive functions, and so a leaderless output-oblivious CRN can compute only superadditive, output-oblivious functions. In this work we show that a function f:ℕ^d → ℕ is stably computable by a leaderless, output-oblivious CRN if and only if it is superadditive and output-oblivious.

We introduce Stochastic Probing with Prices (SPP),$a$variant of the Stochastic Probing (SP) model in which we must pay a price to probe an element. A SPP problem involves two set systems ($\mathcal{N},\mathcal{I}_{\mathrm{i}\mathrm{n}}$) and ($\mathcal{N},\mathcal{I}_{\mathrm{o}\mathrm{u}\mathrm{t}}$) where each$e\in \mathcal{N}$is active with probability$p_{e}$. To discover whether an element$e$is active, it must be probed by paying the price$\Delta_{\mathrm{e}}$. If an element is probed and is active, then it is irrevocably added to the solution. Moreover, at all times, the set of probed elements must lie in$\mathcal{I}_{\text{out}}$, and the solution (the set of probed and active elements) must lie in$\mathcal{I}_{\text{in}}$. The goal is to maximize a submodular set function$f$minus the cost of the probes. We give a bicriteria approximation algorithm to the online version of this problem, in which the elements are shown to the algorithm in a possibly adversarial order. Our results translate to state-of-the-art approximations for the traditional (online) stochastic probing problem.

We classify the functions $f:\mathbb{N}^2 \rightarrow \mathbb{N}$ which are stably computable by output-oblivious Stochastic Chemical Reaction Networks (CRNs), i.e., systems of reactions in which output species are never reactants. While it is known that precisely the semilinear functions are stably computable by CRNs, such CRNs sometimes rely on initially producing too many output species and then consuming the excess in order to reach a correct stable state. These CRNs may be difficult to integrate into larger systems: if the output of a CRN $\mathcal{C}$ becomes the input to a downstream CRN $\mathcal{C}'$, then $\mathcal{C}'$ could inadvertently consume too many outputs before $\mathcal{C}$ stabilizes. If, on the other hand, $\mathcal{C}$ is output-oblivious then $\mathcal{C}'$ may consume $\mathcal{C}$'s output as soon as it is available. In this work we prove that a semilinear function $f:\mathbb{N}^2 \rightarrow \mathbb{N}$ is stably computable by an output-oblivious CRN with a leader if and only if it is both increasing and either grid-affine (intuitively, its domains are congruence classes), or the minimum of a finite set of fissure functions (intuitively, functions behaving like the min function).