Data mining algorithms are increasingly used in automated decision making across all walks of daily life. Unfortunately, as reported in several studies these algorithms inject bias from data and environment leading to inequitable and unfair solutions. To mitigate bias in machine learning, different formalizations of fairness have been proposed that can be categorized into group fairness and individual fairness. Group fairness requires that different groups should be treated similarly which might be unfair to some individuals within a group. On the other hand, individual fairness requires that similar individuals be treated similarly. However, individual fairness remains understudied due to its reliance on problem-specific similarity metrics. We propose a metric-free individual fairness and a cooperative contextual bandits (CCB) algorithm. The CCB algorithm utilizes fairness as a reward and attempts to maximize it. The advantage of treating fairness as a reward is that the fairness criterion does not need to be differentiable. The proposed algorithm is tested on multiple real-world benchmark datasets. The results show the effectiveness of the proposed algorithm at mitigating bias and at achieving both individual and group fairness.
Harvard University（哈佛大学）；University of Lille（里尔大学）；Chalmers University of Technology（查尔姆斯理工大学）
We study fairness within the stochastic, \emph{multi-armed bandit} (MAB) decision making framework. We adapt the fairness framework of "treating similar individuals similarly" to this setting. Here, an `individual' corresponds to an arm and two arms are `similar' if they have a similar quality distribution. First, we adopt a {\em smoothness constraint} that if two arms have a similar quality distribution then the probability of selecting each arm should be similar. In addition, we define the {\em fairness regret}, which corresponds to the degree to which an algorithm is not calibrated, where p…
We study fairness in linear bandit problems. Starting from the notion of meritocratic fairness introduced in Joseph et al. [2016], we carry out a more refined analysis of a more general problem, achieving better performance guarantees with fewer modelling assumptions on the number and structure of available choices as well as the number selected. We also analyze the previously-unstudied question of fairness in infinite linear bandit problems, obtaining instance-dependent regret upper bounds as well as lower bounds demonstrating that this instance-dependence is necessary. The result is a framew…
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…
Contextual bandit algorithms have become widely used for recommendation in online systems (e.g. marketplaces, music streaming, news), where they now wield substantial influence on which items get exposed to the users. This raises questions of fairness to the items -- and to the sellers, artists, and writers that benefit from this exposure. We argue that the conventional bandit formulation can lead to an undesirable and unfair winner-takes-all allocation of exposure. To remedy this problem, we propose a new bandit objective that guarantees merit-based fairness of exposure to the items while opt…
University of Arkansas（阿肯色大学）；Penn State University（宾夕法尼亚州立大学）；Worcester Polytechnic Institute（伍斯特理工学院）
Personalized recommendation based on multi-arm bandit (MAB) algorithms has shown to lead to high utility and efficiency as it can dynamically adapt the recommendation strategy based on feedback. However, unfairness could incur in personalized recommendation. In this paper, we study how to achieve user-side fairness in personalized recommendation. We formulate our fair personalized recommendation as a modified contextual bandit and focus on achieving fairness on the individual whom is being recommended an item as opposed to achieving fairness on the items that are being recommended. We introduc…
University California San Diego（加州大学圣地亚哥分校）；Shanghai Jiao Tong University（上海交通大学）；Nanjing University of Posts and Telecommunications（南京邮电大学）
We study the problem of stochastic bandits with adversarial corruptions in the cooperative multi-agent setting, where $V$ agents interact with a common $K$-armed bandit problem, and each pair of agents can communicate with each other to expedite the learning process. In the problem, the rewards are independently sampled from distributions across all agents and rounds, but they may be corrupted by an adversary. Our goal is to minimize both the overall regret and communication cost across all agents. We first show that an additive term of corruption is unavoidable for any algorithm in this probl…
We introduce a framework for decentralized online learning for multi-armed bandits (MAB) with multiple cooperative players. The reward obtained by the players in each round depends on the actions taken by all the players. It's a team setting, and the objective is common. Information asymmetry is what makes the problem interesting and challenging. We consider three types of information asymmetry: action information asymmetry when the actions of the players can't be observed but the rewards received are common; reward information asymmetry when the actions of the other players are observable but…
Considerable research effort has been guided towards algorithmic fairness but there is still no major breakthrough. In practice, an exhaustive search over all possible techniques and hyperparameters is needed to find optimal fairness-accuracy trade-offs. Hence, coupled with the lack of tools for ML practitioners, real-world adoption of bias reduction methods is still scarce. To address this, we present Fairband, a bandit-based fairness-aware hyperparameter optimization (HO) algorithm. Fairband is conceptually simple, resource-efficient, easy to implement, and agnostic to both the objective met…
We study an interesting variant of the stochastic multi-armed bandit problem, called the Fair-SMAB problem, where each arm is required to be pulled for at least a given fraction of the total available rounds. We investigate the interplay between learning and fairness in terms of a pre-specified vector denoting the fractions of guaranteed pulls. We define a fairness-aware regret, called r-Regret, that takes into account the above fairness constraints and naturally extends the conventional notion of regret. Our primary contribution is characterizing a class of Fair-SMAB algorithms by two paramet…
University of Victoria（维多利亚大学）；Southeast University（东南大学）；Harbin Institute of Technology（哈尔滨工业大学）
We study the combinatorial sleeping multi-armed semi-bandit problem with long-term fairness constraints~(CSMAB-F). To address the problem, we adopt Thompson Sampling~(TS) to maximize the total rewards and use virtual queue techniques to handle the fairness constraints, and design an algorithm called \emph{TS with beta priors and Bernoulli likelihoods for CSMAB-F~(TSCSF-B)}. Further, we prove TSCSF-B can satisfy the fairness constraints, and the time-averaged regret is upper bounded by $\frac{N}{2η} + O\left(\frac{\sqrt{mNT\ln T}}{T}\right)$, where $N$ is the total number of arms, $m$ is the ma…
Media Lab and Institute for Data, Systems and Society, Massachusetts Institute of Technology（麻省理工学院媒体实验室与数据、系统与社会研究所）
We study the heavy-tailed stochastic bandit problem in the cooperative multi-agent setting, where a group of agents interact with a common bandit problem, while communicating on a network with delays. Existing algorithms for the stochastic bandit in this setting utilize confidence intervals arising from an averaging-based communication protocol known as~\textit{running consensus}, that does not lend itself to robust estimation for heavy-tailed settings. We propose \textsc{MP-UCB}, a decentralized multi-agent algorithm for the cooperative stochastic bandit that incorporates robust estimation wi…
We study an interesting variant of the stochastic multi-armed bandit problem, called the Fair-SMAB problem, where each arm is required to be pulled for at least a given fraction of the total available rounds. We investigate the interplay between learning and fairness in terms of a pre-specified vector denoting the fractions of guaranteed pulls. We define a fairness-aware regret, called $r$-Regret, that takes into account the above fairness constraints and naturally extends the conventional notion of regret. Our primary contribution is characterizing a class of Fair-SMAB algorithms by two param…
The multi-armed bandits' framework is the most common platform to study strategies for sequential decision-making problems. Recently, the notion of fairness has attracted a lot of attention in the machine learning community. One can impose the fairness condition that at any given point of time, even during the learning phase, a poorly performing candidate should not be preferred over a better candidate. This fairness constraint is known to be one of the most stringent and has been studied in the stochastic multi-armed bandits' framework in a stationary setting for which regret bounds have been…
In cooperative bandits, a framework that captures essential features of collective sequential decision making, agents can minimize group regret, and thereby improve performance, by leveraging shared information. However, sharing information can be costly, which motivates developing policies that minimize group regret while also reducing the number of messages communicated by agents. Existing cooperative bandit algorithms obtain optimal performance when agents share information with their neighbors at \textit{every time step}, i.e., full communication. This requires $Θ(T)$ number of messages, w…
We introduce the study of fairness in multi-armed bandit problems. Our fairness definition can be interpreted as demanding that given a pool of applicants (say, for college admission or mortgages), a worse applicant is never favored over a better one, despite a learning algorithm's uncertainty over the true payoffs. We prove results of two types. First, in the important special case of the classic stochastic bandits problem (i.e., in which there are no contexts), we provide a provably fair algorithm based on "chained" confidence intervals, and provide a cumulative regret bound with a cubic dep…
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…
Princeton University（普林斯顿大学）；Massachusetts Institute of Technology（麻省理工学院）
The cooperative bandit problem is increasingly becoming relevant due to its applications in large-scale decision-making. However, most research for this problem focuses exclusively on the setting with perfect communication, whereas in most real-world distributed settings, communication is often over stochastic networks, with arbitrary corruptions and delays. In this paper, we study cooperative bandit learning under three typical real-world communication scenarios, namely, (a) message-passing over stochastic time-varying networks, (b) instantaneous reward-sharing over a network with random dela…
Cooperative multi-agent decision making involves a group of agents cooperatively solving learning problems while communicating over a network with delays. In this paper, we consider the kernelised contextual bandit problem, where the reward obtained by an agent is an arbitrary linear function of the contexts' images in the related reproducing kernel Hilbert space (RKHS), and a group of agents must cooperate to collectively solve their unique decision problems. For this problem, we propose \textsc{Coop-KernelUCB}, an algorithm that provides near-optimal bounds on the per-agent regret, and is bo…
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…
Recent advances in wireless radio frequency (RF) energy harvesting allows sensor nodes to increase their lifespan by remotely charging their batteries. The amount of energy harvested by the nodes varies depending on their ambient environment, and proximity to the source. The lifespan of the sensor network depends on the minimum amount of energy a node can harvest in the network. It is thus important to learn the least amount of energy harvested by nodes so that the source can transmit on a frequency band that maximizes this amount. We model this learning problem as a novel stochastic Maximin M…
Fair Distributed Cooperative Bandit Learning on Networks for Intelligent Internet of Things Systems (Technical Report)
School of Electronics and Communication Engineering, Sun Yat-sen University（中山大学电子与通信工程学院）；China Academy of Electronics and Information Technology（中国电子科技集团公司电子科学研究院）
Microsoft Research（微软研究院）；University of California, Berkeley（加州大学伯克利分校）
We study the problem of information sharing and cooperation in Multi-Player Multi-Armed bandits. We propose the first algorithm that achieves logarithmic regret for this problem when the collision reward is unknown. Our results are based on two innovations. First, we show that a simple modification to a successive elimination strategy can be used to allow the players to estimate their suboptimality gaps, up to constant factors, in the absence of collisions. Second, we leverage the first result to design a communication protocol that successfully uses the small reward of collisions to coordinat…
Indian Institute of Science（印度科学学院）；Indian Institute of Technology, Kharagpur（印度理工学院克勒格布尔分校）
We extend the notion of regret with a welfarist perspective. Focussing on the classic multi-armed bandit (MAB) framework, the current work quantifies the performance of bandit algorithms by applying a fundamental welfare function, namely the Nash social welfare (NSW) function. This corresponds to equating algorithm's performance to the geometric mean of its expected rewards and leads us to the study of Nash regret, defined as the difference between the -- a priori unknown -- optimal mean (among the arms) and the algorithm's performance. Since NSW is known to satisfy fairness axioms, our approa…
Microsoft Research（微软研究院）；UBC（不列颠哥伦比亚大学）；Stanford University（斯坦福大学）
We consider the cooperative multi-player version of the stochastic multi-armed bandit problem. We study the regime where the players cannot communicate but have access to shared randomness. In prior work by the first two authors, a strategy for this regime was constructed for two players and three arms, with regret $\tilde{O}(\sqrt{T})$, and with no collisions at all between the players (with very high probability). In this paper we show that these properties (near-optimal regret and no collisions at all) are achievable for any number of players and arms. At a high level, the previous strategy…
We study an important variant of the stochastic multi-armed bandit (MAB) problem, which takes penalization into consideration. Instead of directly maximizing cumulative expected reward, we need to balance between the total reward and fairness level. In this paper, we present some new insights in MAB and formulate the problem in the penalization framework, where rigorous penalized regret can be well defined and more sophisticated regret analysis is possible. Under such a framework, we propose a hard-threshold UCB-like algorithm, which enjoys many merits including asymptotic fairness, nearly opt…
We study a decentralized cooperative stochastic multi-armed bandit problem with $K$ arms on a network of $N$ agents. In our model, the reward distribution of each arm is the same for each agent and rewards are drawn independently across agents and time steps. In each round, each agent chooses an arm to play and subsequently sends a message to her neighbors. The goal is to minimize the overall regret of the entire network. We design a fully decentralized algorithm that uses an accelerated consensus procedure to compute (delayed) estimates of the average of rewards obtained by all the agents for…
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…
Simultaneously Achieving Group Exposure Fairness and Within-Group Meritocracy in Stochastic Bandits
Indian Institute of Technology Ropar（印度理工学院罗帕尔分校）；Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校）；International Institute of Information Technology, Hyderabad（国际信息技术学院海得拉巴分校）
Tel Aviv University（特拉维夫大学）；Google Research（谷歌研究院）
We study agents communicating over an underlying network by exchanging messages, in order to optimize their individual regret in a common nonstochastic multi-armed bandit problem. We derive regret minimization algorithms that guarantee for each agent $v$ an individual expected regret of $\widetilde{O}\left(\sqrt{\left(1+\frac{K}{\left|\mathcal{N}\left(v\right)\right|}\right)T}\right)$, where $T$ is the number of time steps, $K$ is the number of actions and $\mathcal{N}\left(v\right)$ is the set of neighbors of agent $v$ in the communication graph. We present algorithms both for the case that t…
Making an informed decision -- for example, when choosing a career or housing -- requires knowledge about the available options. Such knowledge is generally acquired through costly trial and error, but this learning process can be disrupted by competition. In this work, we study how competition affects the long-term outcomes of individuals as they learn. We build on a line of work that models this setting as a two-sided matching market with bandit learners. A recent result in this area states that it is impossible to simultaneously guarantee two natural desiderata: stability and low optimal re…
In this paper we propose a novel framework for decentralized, online learning by many learners. At each moment of time, an instance characterized by a certain context may arrive to each learner; based on the context, the learner can select one of its own actions (which gives a reward and provides information) or request assistance from another learner. In the latter case, the requester pays a cost and receives the reward but the provider learns the information. In our framework, learners are modeled as cooperative contextual bandits. Each learner seeks to maximize the expected reward from its …
Temple University（天普大学）；Iowa State University（爱荷华州立大学）
The multi-armed bandit (MAB) model has been widely adopted for studying many practical optimization problems (network resource allocation, ad placement, crowdsourcing, etc.) with unknown parameters. The goal of the player here is to maximize the cumulative reward in the face of uncertainty. However, the basic MAB model neglects several important factors of the system in many real-world applications, where multiple arms can be simultaneously played and an arm could sometimes be "sleeping". Besides, ensuring fairness is also a key design concern in practice. To that end, we propose a new Combina…
Pure Exploration in Asynchronous Federated Bandits
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Yale University（耶鲁大学）；Oregon State University（俄勒冈州立大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
