We propose and study Collpasing Bandits, a new restless multi-armed bandit (RMAB) setting in which each arm follows a binary-state Markovian process with a special structure: when an arm is played, the state is fully observed, thus "collapsing" any uncertainty, but when an arm is passive, no observation is made, thus allowing uncertainty to evolve. The goal is to keep as many arms in the "good" state as possible by planning a limited budget of actions per round. Such Collapsing Bandits are natural models for many healthcare domains in which workers must simultaneously monitor patients and deliver interventions in a way that maximizes the health of their patient cohort. Our main contributions are as follows: (i) Building on the Whittle index technique for RMABs, we derive conditions under which the Collapsing Bandits problem is indexable. Our derivation hinges on novel conditions that characterize when the optimal policies may take the form of either "forward" or "reverse" threshold policies. (ii) We exploit the optimality of threshold policies to build fast algorithms for computing the Whittle index, including a closed-form. (iii) We evaluate our algorithm on several data distributions including data from a real-world healthcare task in which a worker must monitor and deliver interventions to maximize their patients' adherence to tuberculosis medication. Our algorithm achieves a 3-order-of-magnitude speedup compared to state-of-the-art RMAB techniques while achieving similar performance.
Australian National University（澳大利亚国立大学）；Data61/NICTA（Data61/国家信息与通信技术研究院）；University of Alberta（阿尔伯塔大学）
We study the problem of using causal models to improve the rate at which good interventions can be learned online in a stochastic environment. Our formalism combines multi-arm bandits and causal inference to model a novel type of bandit feedback that is not exploited by existing approaches. We propose a new algorithm that exploits the causal feedback and prove a bound on its simple regret that is strictly better (in all quantities) than algorithms that do not use the additional causal information.
Technion Israel Institute of Technology（以色列理工学院）；Indian Institute of Science（印度科学学院）；Adobe Research（Adobe研究院）
Learning good interventions in a causal graph can be modelled as a stochastic multi-armed bandit problem with side-information. First, we study this problem when interventions are more expensive than observations and a budget is specified. If there are no backdoor paths from an intervenable node to the reward node then we propose an algorithm to minimize simple regret that optimally trades-off observations and interventions based on the cost of intervention. We also propose an algorithm that accounts for the cost of interventions, utilizes causal side-information, and minimizes the expected cu…
NEC Corporation（日本电气公司）；Riken AIP（理化学研究所先进智能项目中心）；Tokyo Metropolitan University（东京都立大学）；Keio University（庆应义塾大学）；National Institute of Informatics（国立信息学研究所）
Bandit is a framework for designing sequential experiments. In each experiment, a learner selects an arm $A \in \mathcal{A}$ and obtains an observation corresponding to $A$. Theoretically, the tight regret lower-bound for the general bandit is polynomial with respect to the number of arms $|\mathcal{A}|$. This makes bandit incapable of handling an exponentially large number of arms, hence the bandit problem with side-information is often considered to overcome this lower bound. Recently, a bandit framework over a causal graph was introduced, where the structure of the causal graph is available…
Amazon（亚马逊）；University of Michigan（密歇根大学）；Radcliffe Institute, Harvard University（哈佛大学拉德克利夫研究所）
Increasing technological sophistication and widespread use of smartphones and wearable devices provide opportunities for innovative and highly personalized health interventions. A Just-In-Time Adaptive Intervention (JITAI) uses real-time data collection and communication capabilities of modern mobile devices to deliver interventions in real-time that are adapted to the in-the-moment needs of the user. The lack of methodological guidance in constructing data-based JITAIs remains a hurdle in advancing JITAI research despite the increasing popularity of JITAIs among clinical scientists. In this a…
Adobe Research（Adobe研究院）；Technion Israel Institute of Technology（以色列理工学院）
We study the problem of determining the best intervention in a Causal Bayesian Network (CBN) specified only by its causal graph. We model this as a stochastic multi-armed bandit (MAB) problem with side-information, where the interventions correspond to the arms of the bandit instance. First, we propose a simple regret minimization algorithm that takes as input a semi-Markovian causal graph with atomic interventions and possibly unobservable variables, and achieves $\tilde{O}(\sqrt{M/T})$ expected simple regret, where $M$ is dependent on the input CBN and could be very small compared to the num…
Harvard University（哈佛大学）；University of Southern California（南加利福尼亚大学）；Washington University in St. Louis（圣路易斯华盛顿大学）
Motivated by a broad class of mobile intervention problems, we propose and study restless multi-armed bandits (RMABs) with network effects. In our model, arms are partially recharging and connected through a graph, so that pulling one arm also improves the state of neighboring arms, significantly extending the previously studied setting of fully recharging bandits with no network effects. In mobile interventions, network effects may arise due to regular population movements (such as commuting between home and work). We show that network effects in RMABs induce strong reward coupling that is no…
Contextual bandits often provide simple and effective personalization in decision making problems, making them popular tools to deliver personalized interventions in mobile health as well as other health applications. However, when bandits are deployed in the context of a scientific study -- e.g. a clinical trial to test if a mobile health intervention is effective -- the aim is not only to personalize for an individual, but also to determine, with sufficient statistical power, whether or not the system's intervention is effective. It is essential to assess the effectiveness of the interventio…
Applications of machine learning in the non-profit and public sectors often feature an iterative workflow of data acquisition, prediction, and optimization of interventions. There are four major pain points that a machine learning pipeline must overcome in order to be actually useful in these settings: small data, data collected only under the default intervention, unmodeled objectives due to communication gap, and unforeseen consequences of the intervention. In this paper, we introduce bandit data-driven optimization, the first iterative prediction-prescription framework to address these pain…
School of Computer and Communication Sciences, EPFL（洛桑联邦理工学院计算机与通信科学学院）；Borealis AI（Borealis人工智能公司）；College of Management of Technology, EPFL（洛桑联邦理工学院技术管理学院）；Department of Computer Science, TUM（慕尼黑工业大学计算机科学系）
We consider the actor-critic contextual bandit for the mobile health (mHealth) intervention. State-of-the-art decision-making algorithms generally ignore the outliers in the dataset. In this paper, we propose a novel robust contextual bandit method for the mHealth. It can achieve the conflicting goal of reducing the influence of outliers while seeking for a similar solution compared with the state-of-the-art contextual bandit methods on the datasets without outliers. Such performance relies on two technologies: (1) the capped-$\ell_{2}$ norm; (2) a reliable method to set the thresholding hyper…
We study how to learn optimal interventions sequentially given causal information represented as a causal graph along with associated conditional distributions. Causal modeling is useful in real world problems like online advertisement where complex causal mechanisms underlie the relationship between interventions and outcomes. We propose two algorithms, causal upper confidence bound (C-UCB) and causal Thompson Sampling (C-TS), that enjoy improved cumulative regret bounds compared with algorithms that do not use causal information. We thus resolve an open problem posed by \cite{lattimore2016ca…
In light of the COVID-19 pandemic, it is an open challenge and critical practical problem to find a optimal way to dynamically prescribe the best policies that balance both the governmental resources and epidemic control in different countries and regions. To solve this multi-dimensional tradeoff of exploitation and exploration, we formulate this technical challenge as a contextual combinatorial bandit problem that jointly optimizes a multi-criteria reward function. Given the historical daily cases in a region and the past intervention plans in place, the agent should generate useful intervent…
In order to make good decision under uncertainty an agent must learn from observations. To do so, two of the most common frameworks are Contextual Bandits and Markov Decision Processes (MDPs). In this paper, we study whether there exist algorithms for the more general framework (MDP) which automatically provide the best performance bounds for the specific problem at hand without user intervention and without modifying the algorithm. In particular, it is found that a very minor variant of a recently proposed reinforcement learning algorithm for MDPs already matches the best possible regret boun…
In many public health settings, it is important for patients to adhere to health programs, such as taking medications and periodic health checks. Unfortunately, beneficiaries may gradually disengage from such programs, which is detrimental to their health. A concrete example of gradual disengagement has been observed by an organization that carries out a free automated call-based program for spreading preventive care information among pregnant women. Many women stop picking up calls after being enrolled for a few months. To avoid such disengagements, it is important to provide timely intervent…
Robert Bosch Centre for Data Science and Artificial Intelligence（罗伯特·博世数据科学与人工智能中心）；IIT Madras（印度理工学院马德拉斯分校）；Google Research（谷歌研究院）；Harvard University（哈佛大学）；ARMMAN
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 a…
Multi-armed bandit problems provide a framework to identify the optimal intervention over a sequence of repeated experiments. Without additional assumptions, minimax optimal performance (measured by cumulative regret) is well-understood. With access to additional observed variables that d-separate the intervention from the outcome (i.e., they are a d-separator), recent "causal bandit" algorithms provably incur less regret. However, in practice it is desirable to be agnostic to whether observed variables are a d-separator. Ideally, an algorithm should be adaptive; that is, perform nearly as wel…
Michael G. Foster School of Business, University of Washington（华盛顿大学迈克尔·G·福斯特商学院）；Kelley School of Business, Indiana University（印第安纳大学凯利商学院）
Online healthcare communities provide users with various healthcare interventions to promote healthy behavior and improve adherence. When faced with too many intervention choices, however, individuals may find it difficult to decide which option to take, especially when they lack the experience or knowledge to evaluate different options. The choice overload issue may negatively affect users' engagement in health management. In this study, we take a design-science perspective to propose a recommendation framework that helps users to select healthcare interventions. Taking into account that user…
Causal bandit is a nascent learning model where an agent sequentially experiments in a causal network of variables, in order to identify the reward-maximizing intervention. Despite the model's wide applicability, existing analytical results are largely restricted to a parallel bandit version where all variables are mutually independent. We introduce in this work the hierarchical causal bandit model as a viable path towards understanding general causal bandits with dependent variables. The core idea is to incorporate a contextual variable that captures the interaction among all variables with d…
Restless multi-armed bandits (RMAB) is a framework for allocating limited resources under uncertainty. It is an extremely useful model for monitoring beneficiaries and executing timely interventions to ensure maximum benefit in public health settings (e.g., ensuring patients take medicines in tuberculosis settings, ensuring pregnant mothers listen to automated calls about good pregnancy practices). Due to the limited resources, typically certain communities or regions are starved of interventions that can have follow-on effects. To avoid starvation in the executed interventions across individu…
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 …
The combinatorial pure exploration of causal bandits is the following online learning task: given a causal graph with unknown causal inference distributions, in each round we choose a subset of variables to intervene or do no intervention, and observe the random outcomes of all random variables, with the goal that using as few rounds as possible, we can output an intervention that gives the best (or almost best) expected outcome on the reward variable $Y$ with probability at least $1-δ$, where $δ$ is a given confidence level. We provide the first gap-dependent and fully adaptive pure explorati…
In causal bandit problems, the action set consists of interventions on variables of a causal graph. Several researchers have recently studied such bandit problems and pointed out their practical applications. However, all existing works rely on a restrictive and impractical assumption that the learner is given full knowledge of the causal graph structure upfront. In this paper, we develop novel causal bandit algorithms without knowing the causal graph. Our algorithms work well for causal trees, causal forests and a general class of causal graphs. The regret guarantees of our algorithms greatly…
Delivering treatment recommendations via pervasive electronic devices such as mobile phones has the potential to be a viable and scalable treatment medium for long-term health behavior management. But active experimentation of treatment options can be time-consuming, expensive and altogether unethical in some cases. There is a growing interest in methodological approaches that allow an experimenter to learn and evaluate the usefulness of a new treatment strategy before deployment. We present the first development of a treatment recommender system for emotion regulation using real-world histori…
This paper studies an instance of the multi-armed bandit (MAB) problem, specifically where several causal MABs operate chronologically in the same dynamical system. Practically the reward distribution of each bandit is governed by the same non-trivial dependence structure, which is a dynamic causal model. Dynamic because we allow for each causal MAB to depend on the preceding MAB and in doing so are able to transfer information between agents. Our contribution, the Chronological Causal Bandit (CCB), is useful in discrete decision-making settings where the causal effects are changing across tim…
This paper considers the actor-critic contextual bandit for the mobile health (mHealth) intervention. The state-of-the-art decision-making methods in mHealth generally assume that the noise in the dynamic system follows the Gaussian distribution. Those methods use the least-square-based algorithm to estimate the expected reward, which is prone to the existence of outliers. To deal with the issue of outliers, we propose a novel robust actor-critic contextual bandit method for the mHealth intervention. In the critic updating, the capped-$\ell_{2}$ norm is used to measure the approximation error,…
Using Adaptive Bandit Experiments to Increase and Investigate Engagement in Mental Health
University of Toronto（多伦多大学）；Northwestern University（西北大学）；Audacious Software；Mental Health America（美国心理健康组织）；Carleton College（卡尔顿学院）；University of Cambridge（剑桥大学）；Sapienza University of Rome（罗马大学）
Restless Multi-Armed Bandits (RMAB) is an apt model to represent decision-making problems in public health interventions (e.g., tuberculosis, maternal, and child care), anti-poaching planning, sensor monitoring, personalized recommendations and many more. Existing research in RMAB has contributed mechanisms and theoretical results to a wide variety of settings, where the focus is on maximizing expected value. In this paper, we are interested in ensuring that RMAB decision making is also fair to different arms while maximizing expected value. In the context of public health settings, this would…
We extend the classic multi-armed bandit (MAB) model to the setting of noncompliance, where the arm pull is a mere instrument and the treatment applied may differ from it, which gives rise to the instrument-armed bandit (IAB) problem. The IAB setting is relevant whenever the experimental units are human since free will, ethics, and the law may prohibit unrestricted or forced application of treatment. In particular, the setting is relevant in bandit models of dynamic clinical trials and other controlled trials on human interventions. Nonetheless, the setting has not been fully investigate in th…
Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Microsoft Research（微软研究院）
In combinatorial causal bandits (CCB), the learning agent chooses at most $K$ variables in each round to intervene, collects feedback from the observed variables, with the goal of minimizing expected regret on the target variable $Y$. We study under the context of binary generalized linear models (BGLMs) with a succinct parametric representation of the causal models. We present the algorithm BGLM-OFU for Markovian BGLMs (i.e. no hidden variables) based on the maximum likelihood estimation method, and show that it achieves $O(\sqrt{T}\log T)$ regret, where $T$ is the time horizon. For the speci…
University of Maryland（马里兰大学）；Tulane University（杜兰大学）
We propose a novel formulation of group fairness with biased feedback in the contextual multi-armed bandit (CMAB) setting. In the CMAB setting, a sequential decision maker must, at each time step, choose an arm to pull from a finite set of arms after observing some context for each of the potential arm pulls. In our model, arms are partitioned into two or more sensitive groups based on some protected feature(s) (e.g., age, race, or socio-economic status). Initial rewards received from pulling an arm may be distorted due to some unknown societal or measurement bias. We assume that in reality th…
Multi-Armed-Bandit frameworks have often been used by researchers to assess educational interventions, however, recent work has shown that it is more beneficial for a student to provide qualitative feedback through preference elicitation between different alternatives, making a dueling bandits framework more appropriate. In this paper, we explore the statistical quality of data under this framework by comparing traditional uniform sampling to a dueling bandit algorithm and find that dueling bandit algorithms perform well at cumulative regret minimisation, but lead to inflated Type-I error rate…
GSC-QEMit: A Telemetry-Driven Hierarchical Forecast-and-Bandit Framework for Adaptive Quantum Error Mitigation
1 Department of Software Engineering, Rochester Institute of Technology, Rochester, USA Emails；2 Institute for Quantum \& Information Sciences, Syracuse University, Syracuse, USA Emails
In online recommendation, customers arrive in a sequential and stochastic manner from an underlying distribution and the online decision model recommends a chosen item for each arriving individual based on some strategy. We study how to recommend an item at each step to maximize the expected reward while achieving user-side fairness for customers, i.e., customers who share similar profiles will receive a similar reward regardless of their sensitive attributes and items being recommended. By incorporating causal inference into bandits and adopting soft intervention to model the arm selection st…
Indian Institute of Science（印度科学院）；Adobe Research（Adobe研究院）
We study Markov Decision Processes (MDP) wherein states correspond to causal graphs that stochastically generate rewards. In this setup, the learner's goal is to identify atomic interventions that lead to high rewards by intervening on variables at each state. Generalizing the recent causal-bandit framework, the current work develops (simple) regret minimization guarantees for two-stage causal MDPs, with parallel causal graph at each state. We propose an algorithm that achieves an instance dependent regret bound. A key feature of our algorithm is that it utilizes convex optimization to address…
Criteo AI Lab（Criteo人工智能实验室）；Durham University（杜伦大学）
A common task for recommender systems is to build a pro le of the interests of a user from items in their browsing history and later to recommend items to the user from the same catalog. The users' behavior consists of two parts: the sequence of items that they viewed without intervention (the organic part) and the sequences of items recommended to them and their outcome (the bandit part). In this paper, we propose Bayesian Latent Organic Bandit model (BLOB), a probabilistic approach to combine the 'or-ganic' and 'bandit' signals in order to improve the estimation of recommendation quality. Th…
Power Constrained Nonstationary Bandits with Habituation and Recovery Dynamics
Department of Industrial and Systems Engineering, University of Wisconsin-Madison（工业与系统工程系，威斯康星大学麦迪逊分校）；College of Health Solutions, Arizona State University（健康解决方案学院，亚利桑那州立大学）
