The setting described is summarized in Box A.

The first and third equalities are straightforward. We restate a result extracted from the monograph by Luenberger [1969]. It relies on the dual functional φ, whose expression we recall below. Theorem 2 (stated as Theorem 1 in Section 8.6, page 224 in Luenberger, 1969) . " is required to apply the theorem.

A surge of applicants vying for a chance to be chosen for a voucher worth up to 2,000 for the California E-Bike Incentive Program triggered an error in the program's website, blocking everyone from applying. Officials say they've fixed the glitch for the next round of applications next week. The California E-Bike Incentive Program, launched by the California Air Resources Board, was established to help lower cost barriers to alternative methods of transportation such as e-bikes, with the goal of getting cars off the road and reduce greenhouse gas emissions. Eligible residents must be 18 years or older with an annual household income less than 300% of the Federal Poverty Level. The vouchers can be used toward the purchase of an electric bike.

In this paper, we create benchmarks and assess the effectiveness of error correction methods for Japanese vouchers in OCR (Optical Character Recognition) systems. It is essential for automation processing to correctly recognize scanned voucher text, such as the company name on invoices. However, perfect recognition is complex due to the noise, such as stamps. Therefore, it is crucial to correctly rectify erroneous OCR results. However, no publicly available OCR error correction benchmarks for Japanese exist, and methods have not been adequately researched. In this study, we measured text recognition accuracy by existing services on Japanese vouchers and developed a post-OCR correction benchmark. Then, we proposed simple baselines for error correction using language models and verified whether the proposed method could effectively correct these errors. In the experiments, the proposed error correction algorithm significantly improved overall recognition accuracy.

Problem definition: Traditionally, New York City's top 8 public schools have selected candidates solely based on their scores in the Specialized High School Admissions Test (SHSAT). These scores are known to be impacted by socioeconomic status of students and test preparation received in middle schools, leading to a massive filtering effect in the education pipeline. The classical mechanisms for assigning students to schools do not naturally address problems like school segregation and class diversity, which have worsened over the years. The scientific community, including policymakers, have reacted by incorporating group-specific quotas and proportionality constraints, with mixed results. The problem of finding effective and fair methods for broadening access to top-notch education is still unsolved. Methodology/results: We take an operations approach to the problem different from most established literature, with the goal of increasing opportunities for students with high economic needs. Using data from the Department of Education (DOE) in New York City, we show that there is a shift in the distribution of scores obtained by students that the DOE classifies as "disadvantaged" (following criteria mostly based on economic factors). We model this shift as a "bias" that results from an underestimation of the true potential of disadvantaged students. We analyze the impact this bias has on an assortative matching market. We show that centrally planned interventions can significantly reduce the impact of bias through scholarships or training, when they target the segment of disadvantaged students with average performance.

More than 5 million children under five years die from largely preventable or treatable medical conditions every year, with an overwhelmingly large proportion of deaths occurring in underdeveloped countries with low vaccination uptake. One of the United Nations' sustainable development goals (SDG 3) aims to end preventable deaths of newborns and children under five years of age. We focus on Nigeria, where the rate of infant mortality is appalling. In particular, low vaccination uptake in Nigeria is a major driver of more than 2,000 daily deaths of children under the age of five years. In this paper, we describe our collaboration with government partners in Nigeria to deploy ADVISER: AI-Driven Vaccination Intervention Optimiser. The framework, based on an integer linear program that seeks to maximize the cumulative probability of successful vaccination, is the first successful deployment of an AI-enabled toolchain for optimizing the allocation of health interventions in Nigeria. In this paper, we provide a background of the ADVISER framework and present results, lessons, and success stories of deploying ADVISER to more than 13,000 families in the state of Oyo, Nigeria.

We consider contextual bandit problems with knapsacks [CBwK], a problem where at each round, a scalar reward is obtained and vector-valued costs are suffered. The learner aims to maximize the cumulative rewards while ensuring that the cumulative costs are lower than some predetermined cost constraints. We assume that contexts come from a continuous set, that costs can be signed, and that the expected reward and cost functions, while unknown, may be uniformly estimated -- a typical assumption in the literature. In this setting, total cost constraints had so far to be at least of order $T^{3/4}$, where $T$ is the number of rounds, and were even typically assumed to depend linearly on $T$. We are however motivated to use CBwK to impose a fairness constraint of equalized average costs between groups: the budget associated with the corresponding cost constraints should be as close as possible to the natural deviations, of order $\sqrt{T}$. To that end, we introduce a dual strategy based on projected-gradient-descent updates, that is able to deal with total-cost constraints of the order of $\sqrt{T}$ up to poly-logarithmic terms. This strategy is more direct and simpler than existing strategies in the literature. It relies on a careful, adaptive, tuning of the step size.

In E-commerce, vouchers are important marketing tools to enhance users' engagement and boost sales and revenue. The likelihood that a user redeems a voucher is a key factor in voucher distribution decision. User-item Click-Through-Rate (CTR) models are often applied to predict the user-voucher redemption rate. However, the voucher scenario involves more complicated relations among users, items and vouchers. The users' historical behavior in a voucher collection activity reflects users' voucher usage patterns, which is nevertheless overlooked by the CTR-based solutions. In this paper, we propose a Deep Multi-behavior Graph Networks (DMBGN) to shed light on this field for the voucher redemption rate prediction. The complex structural user-voucher-item relationships are captured by a User-Behavior Voucher Graph (UVG). User behavior happening both before and after voucher collection is taken into consideration, and a high-level representation is extracted by Higher-order Graph Neural Networks. On top of a sequence of UVGs, an attention network is built which can help to learn users' long-term voucher redemption preference. Extensive experiments on three large-scale production datasets demonstrate the proposed DMBGN model is effective, with 10% to 16% relative AUC improvement over Deep Neural Networks (DNN), and 2% to 4% AUC improvement over Deep Interest Network (DIN). Source code and a sample dataset are made publicly available to facilitate future research.