We design and analyze a multi-level game-theoretic model of hierarchical policy interventions for epidemic control, such as those in response to the COVID-19 pandemic. Our model captures the potentially mismatched priorities among a hierarchy of policy-makers (e.g., federal, state, and local governments) with respect to two cost components that have opposite dependence on the policy strength—post-intervention infection rates and the socio-economic cost of policy implementation. Additionally, our model includes a crucial third factor in decisions: a cost of non-compliance with the policy-maker immediately above in the hierarchy, such as non-compliance of counties with state-level policies. We propose two novel algorithms for approximating solutions to such games. The first is based on best response dynamics (BRD) and exploits the tree structure of the game. The second combines quadratic integer programming (QIP), which enables us to collapse the two lowest levels of the game, with the best response dynamics. We experimentally characterize the scalability and equilibrium approximation quality of our two approaches against model parameters. Finally, we conduct experiments in simulations based on both synthetic and real-world data under various parameter configurations and analyze the resulting (approximate) equilibria to gain insight into the impact of decentralization on overall welfare (measured as the negative sum of costs) as well as emergent properties like social welfare, free-riding, and fairness in cost distribution among policy-makers.

We developed a common algorithmic solution addressing the problem of resource-constrained outreach encountered by social change organizations with different missions and operations: Breaking Ground -- an organization that helps individuals experiencing homelessness in New York transition to permanent housing and Leket -- the national food bank of Israel that rescues food from farms and elsewhere to feed the hungry. Specifically, we developed an estimation and optimization approach for partially-observed episodic restless bandits under $k$-step transitions. The results show that our Thompson sampling with Markov chain recovery (via Stein variational gradient descent) algorithm significantly outperforms baselines for the problems of both organizations. We carried out this work in a prospective manner with the express goal of devising a flexible-enough but also useful-enough solution that can help overcome a lack of sustainable impact in data science for social good.

Restless multi-arm bandits (RMABs) is a popular decision-theoretic framework that has been used to model real-world sequential decision making problems in public health, wildlife conservation, communication systems, and beyond. Deployed RMAB systems typically operate in two stages: the first predicts the unknown parameters defining the RMAB instance, and the second employs an optimization algorithm to solve the constructed RMAB instance. In this work we provide and analyze the results from a first-of-its-kind deployment of an RMAB system in public health domain, aimed at improving maternal and child health. Our analysis is focused towards understanding the relationship between prediction accuracy and overall performance of deployed RMAB systems. This is crucial for determining the value of investing in improving predictive accuracy towards improving the final system performance, and is useful for diagnosing, monitoring deployed RMAB systems. Using real-world data from our deployed RMAB system, we demonstrate that an improvement in overall prediction accuracy may even be accompanied by a degradation in the performance of RMAB system -- a broad investment of resources to improve overall prediction accuracy may not yield expected results. Following this, we develop decision-focused evaluation metrics to evaluate the predictive component and show that it is better at explaining (both empirically and theoretically) the overall performance of a deployed RMAB system.

Mobile Health Awareness programs in underserved communities often suffer from diminishing engagement over time and health workers have to make live service calls to encourage beneficiaries’ participation. Owing to health workers’ limited availability, we consider the optimization problem of scheduling live service calls in a Maternal and Child Health Awareness Program and model it using Restless Multi-Armed Bandits (RMAB). Since the parameters of the RMAB formulation are unknown, a model is learnt to first predict the parameters of the RMAB problem, which is subsequently solved using the Whittle Index algorithm. However, this Predict-then-Optimize framework maximises for the predictive accuracy rather than the quality of the final solution. Decision Focused Learning (DFL) solves this mismatch by integrating the optimization problem in the learning pipeline. Previous works have only shown the applicability of DFL in simulation setting. In collabo-ration with an NGO, we conduct a large-scale field study consisting of 9000 beneficiaries for 6 weeks and track key engagement metrics in a mobile health awareness program. To the best of our knowledge this is the first real-world study involving Decision Focused Learning. We demonstrate that beneficiaries in the DFL group expe-rience statistically significant reductions in cumulative engagement drop, while those in the Predict-then-Optimize group do not. This establishes the practicality of use of decision focused learning for real world problems. We also demonstrate that DFL learns a better decision boundary between the RMAB actions, and strategically predicts parameters for arms which contribute most to the final decision outcome.

We consider the task of evaluating policies of algorithmic resource allocation through randomized controlled trials (RCTs). Such policies are tasked with optimizing the utilization of limited intervention resources, with the goal of maximizing the benefits derived. Evaluation of such allocation policies through RCTs proves difficult, notwithstanding the scale of the trial, because the individuals’ outcomes are inextricably interlinked through resource constraints controlling the policy decisions. Our key contribution is to present a new estimator leveraging our proposed novel concept, that involves retrospective reshuffling of participants across experimental arms at the end of an RCT. We identify conditions under which such reassignments are permissible and can be leveraged to construct counterfactual trials, whose outcomes can be accurately ascertained, for free. We prove theoretically that such an estimator is more accurate than common estimators based on sample means -- we show that it returns an unbiased estimate and simultaneously reduces variance. We demonstrate the value of our approach through empirical experiments on synthetic, semisynthetic as well as real case study data and show improved estimation accuracy across the board.

This paper studies restless multi-armed bandit (RMAB) problems with unknown arm transition dynamics but with known correlated arm features. The goal is to learn a model to predict transition dynamics given features, where the Whittle index policy solves the RMAB problems using predicted transitions. However, prior works often learn the model by maximizing the predictive accuracy instead of final RMAB solution quality, causing a mismatch between training and evaluation objectives. To address this shortcoming, we propose a novel approach for decision-focused learning in RMAB that directly trains the predictive model to maximize the Whittle index solution quality. We present three key contributions: (i) we establish differentiability of the Whittle index policy to support decision-focused learning; (ii) we significantly improve the scalability of decision-focused learning approaches in sequential problems, specifically RMAB problems; (iii) we apply our algorithm to a previously collected dataset of maternal and child health to demonstrate its performance. Indeed, our algorithm is the first for decision-focused learning in RMAB that scales to real-world problem sizes.

Underserved communities face critical health challenges due to lack of access to timely and reliable information. Nongovernmental organizations are leveraging the widespread use of cellphones to combat these healthcare challenges and spread preventative awareness. The health workers at these organizations reach out individually to beneficiaries; however such programs still suffer from declining engagement. We have deployed SAHELI, a system to efficiently utilize the limited availability of health workers for improving maternal and child health in India. SAHELI uses the Restless Multiarmed Bandit (RMAB) framework to identify beneficiaries for outreach. It is the first deployed application for RMABs in public health, and is already in continuous use by our partner NGO, ARMMAN. We have already reached ~100K beneficiaries with SAHELI, and are on track to serve 1 million beneficiaries by the end of 2023. This scale and impact has been achieved through multiple innovations in the RMAB model and its development, in preparation of real world data, and in deployment practices; and through careful consideration of responsible AI practices. Specifically, in this paper, we describe our approach to learn from past data to improve the performance of SAHELI’s RMAB model, the real-world challenges faced during deployment and adoption of SAHELI, and the end-to-end pipeline.

We propose Streaming Bandits, a Restless Multi Armed Bandit (RMAB) framework in which heterogeneous arms may arrive and leave the system after staying on for a finite lifetime. Streaming Bandits naturally capture the health intervention planning problem, where health workers must manage the health outcomes of a patient cohort while new patients join and existing patients leave the cohort each day. Our contributions are as follows: (1) We derive conditions under which our problem satisfies indexability, a precondition that guarantees the existence and asymptotic optimality of the Whittle Index solution for RMABs. We establish the conditions using a polytime reduction of the Streaming Bandit setup to regular RMABs. (2) We further prove a phenomenon that we call index decay, whereby the Whittle index values are low for short residual lifetimes driving the intuition underpinning our algorithm. (3) We propose a novel and efficient algorithm to compute the index-based solution for Streaming Bandits. Unlike previous methods, our algorithm does not rely on solving the costly finite horizon problem on each arm of the RMAB, thereby lowering the computational complexity compared to existing methods. (4) Finally, we evaluate our approach via simulations run on realworld data sets from a tuberculosis patient monitoring task and an intervention planning task for improving maternal healthcare, in addition to other synthetic domains. Across the board, our algorithm achieves a 2-orders-of-magnitude speed-up over existing methods while maintaining the same solution quality.

From large-scale organizations to decentralized political systems, hierarchical strategic decision making is commonplace. We introduce a novel class of structured hierarchical games (SHGs) that formally capture such hierarchical strategic interactions. In an SHG, each player is a node in a tree, and strategic choices of players are sequenced from root to leaves, with root moving first, followed by its children, then followed by their children, and so on until the leaves. A player's utility in an SHG depends on its own decision, and on the choices of its parent and all the tree leaves. SHGs thus generalize simultaneous-move games, as well as Stackelberg games with many followers. We leverage the structure of both the sequence of player moves as well as payoff dependence to develop a gradient-based back propagation-style algorithm, which we call Differential Backward Induction (DBI), for approximating equilibria of SHGs. We provide a sufficient condition for convergence of DBI and demonstrate its efficacy in finding approximate equilibrium solutions to several SHG models of hierarchical policy-making problems.

The widespread availability of cell phones has enabled non-profits to deliver critical health information to their beneficiaries in a timely manner. This paper describes our work to assist non-profits that employ automated messaging programs to deliver timely preventive care information to beneficiaries (new and expecting mothers) during pregnancy and after delivery. Unfortunately, a key challenge in such information delivery programs is that a significant fraction of beneficiaries drop out of the program. Yet, non-profits often have limited health-worker resources (time) to place crucial service calls for live interaction with beneficiaries to prevent such engagement drops. To assist non-profits in optimizing this limited resource, we developed a Restless Multi-Armed Bandits (RMABs) system. One key technical contribution in this system is a novel clustering method of offline historical data to infer unknown RMAB parameters. Our second major contribution is evaluation of our RMAB system in collaboration with an NGO, via a real-world service quality improvement study. The study compared strategies for optimizing service calls to 23003 participants over a period of 7 weeks to reduce engagement drops. We show that the RMAB group provides statistically significant improvement over other comparison groups, reducing ~ 30% engagement drops. To the best of our knowledge, this is the first study demonstrating the utility of RMABs in real world public health settings. We are transitioning our RMAB system to the NGO for real-world use.

Community Health Workers (CHWs) form an important component of health-care systems globally, especially in low-resource settings. CHWs are often tasked with monitoring the health of and intervening on their patient cohort. Previous work has developed several classes of Restless Multi-Armed Bandits (RMABs) that are computationally tractable and indexable, a condition that guarantees asymptotic optimality, for solving such health monitoring and intervention problems (HMIPs). However, existing solutions to HMIPs fail to account for risk-sensitivity considerations of CHWs in the planning stage and may run the danger of ignoring some patients completely because they are deemed less valuable to intervene on. Additionally, these also rely on patients reporting their state of adherence accurately when intervened upon. Towards tackling these issues, our contributions in this paper are as follows: (1) We develop an RMAB solution to HMIPs that allows for reward functions that are monotone increasing, rather than linear, in the belief state and also supports a wider class of observations. (2) We prove theoretical guarantees on the asymptotic optimality of our algorithm for any arbitrary reward function. Additionally, we show that for the specific reward function considered in previous work, our theoretical conditions are stronger than the state-of-the-art guarantees. (3) We show the applicability of these new results for addressing the three issues pertaining to: risk-sensitive planning, equitable allocation and reliance on perfect observations as highlighted above. We evaluate these techniques on both simulated as well as real data from a prevalent CHW task of monitoring adherence of tuberculosis patients to their prescribed medication in Mumbai, India and show improved performance over the state-of-the-art. The simulation code is available at: https://github.com/AdityaMate/risk-aware-bandits.

Several scenarios involving public health interventions have a unifying underlying theme, that deals with the challenge of optimizing the limited intervention resources available. My dissertation casts this as a Restless Multi-Armed Bandit (RMAB) planning problem, identifying and addressing several new, fundamental questions in RMABs.

India has a maternal mortality ratio of 113 and child mortality ratio of 2830 per 100,000 live births. Lack of access to preventive care information is a major contributing factor for these deaths, especially in low resource households. We partner with ARMMAN, a non-profit based in India employing a call-based information program to disseminate health-related information to pregnant women and women with recent child deliveries. We analyze call records of over 300,000 women registered in the program created by ARMMAN and try to identify women who might not engage with these call programs that are proven to result in positive health outcomes. We built machine learning based models to predict the long term engagement pattern from call logs and beneficiaries' demographic information, and discuss the applicability of this method in the real world through a pilot validation. Through a pilot service quality improvement study, we show that using our model's predictions to make interventions boosts engagement metrics by 61.37%. We then formulate the intervention planning problem as restless multi-armed bandits (RMABs), and present preliminary results using this approach.

We present the design and analysis of a multi-level game-theoretic model of hierarchical policy-making, inspired by policy responses to the COVID-19 pandemic. Our model captures the potentially mismatched priorities among a hierarchy of policy-makers (e.g., federal, state, and local governments) with respect to two main cost components that have opposite dependence on the policy strength, such as post-intervention infection rates and the cost of policy implementation. Our model further includes a crucial third factor in decisions: a cost of non-compliance with the policy-maker immediately above in the hierarchy, such as non-compliance of state with federal policies. Our first contribution is a closed-form approximation of a recently published agent-based model to compute the number of infections for any implemented policy. Second, we present a novel equilibrium selection criterion that addresses common issues with equilibrium multiplicity in our setting. Third, we propose a hierarchical algorithm based on best response dynamics for computing an approximate equilibrium of the hierarchical policy-making game consistent with our solution concept. Finally, we present an empirical investigation of equilibrium policy strategies in this game in terms of the extent of free riding as well as fairness in the distribution of costs depending on game parameters such as the degree of centralization and disagreements about policy priorities among the agents.

We consider a system consisting of multiple sensors that send updates to a monitoring station via a shared communication channel. The focus is on designing scheduling policies to minimize the time-average of the weighted sum of the Age-of-Information of the sensors. We consider multiple channel models (i.i.d./Markov) and multiple information settings (CSI/delayed CSI/no CSI) and show that the scheduling problem is indexable for all settings considered. In addition, we compute the Whittle index in closed form for some of the settings. Via simulations, we show that Whittle Index based scheduling policies either outperform or match the performance of the best-known policy for all the settings studied.

Stackelberg security games are a critical tool for maximizing the utility of limited defense resources to protect important targets from an intelligent adversary. Motivated by green security, where the defender may only observe an adversary's response to defense on a limited set of targets, we study the problem of learning a defense that generalizes well to a new set of targets with novel feature values and combinations. Traditionally, this problem has been addressed via a two-stage approach where an adversary model is trained to maximize predictive accuracy without considering the defender's optimization problem. We develop an end-to-end game-focused approach, where the adversary model is trained to maximize a surrogate for the defender's expected utility. We show both in theory and experimental results that our game-focused approach achieves higher defender expected utility than the two-stage alternative when there is limited data.

During the network reconnaissance process, attackers scan the network to gather information before launching an attack. This is a good chance for defenders to use deception and disrupt the attacker’s learning process. In this paper, we present an exploratory experiment to test the effectiveness of a masking strategy (compared to a random masking strategy) to reduce the utility of attackers. A total of 30 human participants (in the role of attackers) are randomly assigned to one of the two experimental conditions: Optimal or Random (15 in each condition). Attackers appeared to be more successful in launching attacks in the optimal condition compared to the random condition but the total score of attackers was not different from the random masking strategy. Most importantly, we found a generalized tendency to act according to the certainty bias (or risk aversion). These observations will help to improve the current state-of-the-art masking algorithms of cyberdefense.

As the COVID-19 pandemic continues, formulating targeted policy interventions that are informed by differential SARS-CoV2 transmission dynamics will be of vital importance to national and regional governments. We develop an individual-level model for SARS-CoV2 transmission that accounts for location-dependent distributions of age, household structure, and comorbidities. We use these distributions together with age-stratified contact matrices to instantiate specific models for Hubei, China; Lombardy, Italy; and New York City, United States. Using data on reported deaths to obtain a posterior distribution over unknown parameters, we infer differences in the progression of the epidemic in the three locations. We also examine the role of transmission due to particular age groups on total infections and deaths. The effect of limiting contacts by a particular age group varies by location, indicating that strategies to reduce transmission should be tailored based on population-specific demography and social structure. These findings highlight the role of between-population variation in formulating policy interventions. Across the three populations though, we find that targeted "salutary sheltering" by 50% of a single age group may substantially curtail transmission when combined with the adoption of physical distancing measures by the rest of the population. Code may be found at https://github.com/bwilder0/covid_abm_release.

As the COVID-19 pandemic continues, formulating targeted policy interventions that are informed by differential SARS-CoV2 transmission dynamics will be of vital importance to national and regional governments. We develop an individual-level model for SARS-CoV2 transmission that accounts for location-dependent distributions of age, household structure, and comorbidities. We use these distributions together with age-stratified contact matrices to instantiate specific models for Hubei, China; Lombardy, Italy; and New York City, United States. Using data on reported deaths to obtain a posterior distribution over unknown parameters, we infer differences in the progression of the epidemic in the three locations. We also examine the role of transmission due to particular age groups on total infections and deaths. The effect of limiting contacts by a particular age group varies by location, indicating that strategies to reduce transmission should be tailored based on population-specific demography and social structure. These findings highlight the role of between-population variation in formulating policy interventions. Across the three populations though, we find that targeted “salutary sheltering" by 50% of a single age group may substantially curtail transmission when combined with the adoption of physical distancing measures by the rest of the population.