Applications of machine learning inform human decision makers in a broad range of tasks. The resulting problem is usually formulated in terms of a single decision maker. We argue that it should rather be described as a two-player learning problem where one player is the machine and the other the human. While both players try to optimize the final decision, the setup is often characterized by (1) the presence of private information and (2) opacity, that is imperfect understanding between the decision makers. We prove that both properties can complicate decision making considerably. A lower bound quantifies the worst-case hardness of optimally advising a decision maker who is opaque or has access to private information. An upper bound shows that a simple coordination strategy is nearly minimax optimal. More efficient learning is possible under certain assumptions on the problem, for example that both players learn to take actions independently. Such assumptions are implicit in existing literature, for example in medical applications of machine learning, but have not been described or justified theoretically.
Peking University（北京大学）；Haihua Institute for Frontier Information Technology（海华前沿信息技术研究院）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）
We study locally differentially private (LDP) bandits learning in this paper. First, we propose simple black-box reduction frameworks that can solve a large family of context-free bandits learning problems with LDP guarantee. Based on our frameworks, we can improve previous best results for private bandits learning with one-point feedback, such as private Bandits Convex Optimization, and obtain the first result for Bandits Convex Optimization (BCO) with multi-point feedback under LDP. LDP guarantee and black-box nature make our frameworks more attractive in real applications compared with prev…
Yale University（耶鲁大学）；Rutgers, The State University of New Jersey（罗格斯大学（新泽西州立大学））；Bar-Ilan University（巴伊兰大学）
We study the best-arm identification problem in multi-armed bandits with stochastic, potentially private rewards, when the goal is to identify the arm with the highest quantile at a fixed, prescribed level. First, we propose a (non-private) successive elimination algorithm for strictly optimal best-arm identification, we show that our algorithm is $δ$-PAC and we characterize its sample complexity. Further, we provide a lower bound on the expected number of pulls, showing that the proposed algorithm is essentially optimal up to logarithmic factors. Both upper and lower complexity bounds depend …
Oregon State University（俄勒冈州立大学）；University of Virginia（弗吉尼亚大学）
Bandit algorithms have become a reference solution for interactive recommendation. However, as such algorithms directly interact with users for improved recommendations, serious privacy concerns have been raised regarding its practical use. In this work, we propose a differentially private linear contextual bandit algorithm, via a tree-based mechanism to add Laplace or Gaussian noise to model parameters. Our key insight is that as the model converges during online update, the global sensitivity of its parameters shrinks over time (thus named dynamic global sensitivity). Compared with existing …
We present differentially private algorithms for the stochastic Multi-Armed Bandit (MAB) problem. This is a problem for applications such as adaptive clinical trials, experiment design, and user-targeted advertising where private information is connected to individual rewards. Our major contribution is to show that there exist $(ε, δ)$ differentially private variants of Upper Confidence Bound algorithms which have optimal regret, $O(ε^{-1} + \log T)$. This is a significant improvement over previous results, which only achieve poly-log regret $O(ε^{-2} \log^{2} T)$, because of our use of a nove…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Wayne State University（韦恩州立大学）；Shandong University（山东大学）
We study private and robust multi-armed bandits (MABs), where the agent receives Huber's contaminated heavy-tailed rewards and meanwhile needs to ensure differential privacy. We first present its minimax lower bound, characterizing the information-theoretic limit of regret with respect to privacy budget, contamination level and heavy-tailedness. Then, we propose a meta-algorithm that builds on a private and robust mean estimation sub-routine \texttt{PRM} that essentially relies on reward truncation and the Laplace mechanism only. For two different heavy-tailed settings, we give specific scheme…
Google Research（谷歌研究院）；Tel Aviv University（特拉维夫大学）
We give an $(\varepsilon,δ)$-differentially private algorithm for the multi-armed bandit (MAB) problem in the shuffle model with a distribution-dependent regret of $O\left(\left(\sum_{a\in [k]:Δ_a>0}\frac{\log T}{Δ_a}\right)+\frac{k\sqrt{\log\frac{1}δ}\log T}{\varepsilon}\right)$, and a distribution-independent regret of $O\left(\sqrt{kT\log T}+\frac{k\sqrt{\log\frac{1}δ}\log T}{\varepsilon}\right)$, where $T$ is the number of rounds, $Δ_a$ is the suboptimality gap of the arm $a$, and $k$ is the total number of arms. Our upper bound almost matches the regret of the best known algorithms for th…
School of Statistics, Renmin University of China（中国人民大学统计学院）；School of Management, Fudan University（复旦大学管理学院）；Mendoza College of Business, University of Notre Dame（圣母大学门多萨商学院）；Center for Applied Statistics, School of Statistics, Renmin University of China（中国人民大学应用统计中心）；Department of Statistics, University of Warwick（华威大学统计系）
Vanilla Policy Optimization Is Both Optimal and Differentially Private for Stochastic Contextual Bandits
University of Illinois Chicago（伊利诺伊大学芝加哥分校）；Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）；Tel Aviv University（特拉维夫大学）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Google Research（谷歌研究院）
Boston University（波士顿大学）；Northeastern University（东北大学）；CNRS（法国国家科学研究中心）；Université de Paris（巴黎大学）
We design differentially private algorithms for the bandit convex optimization problem in the projection-free setting. This setting is important whenever the decision set has a complex geometry, and access to it is done efficiently only through a linear optimization oracle, hence Euclidean projections are unavailable (e.g. matroid polytope, submodular base polytope). This is the first differentially-private algorithm for projection-free bandit optimization, and in fact our bound of $\widetilde{O}(T^{3/4})$ matches the best known non-private projection-free algorithm (Garber-Kretzu, AISTATS `20…
Shandong University（山东大学）；KAUST（阿卜杜拉国王科技大学）；Nanjing University（南京大学）；East China Normal University（华东师范大学）
In this paper we investigate the problem of stochastic multi-armed bandits (MAB) in the (local) differential privacy (DP/LDP) model. Unlike previous results that assume bounded/sub-Gaussian reward distributions, we focus on the setting where each arm's reward distribution only has $(1+v)$-th moment with some $v\in (0, 1]$. In the first part, we study the problem in the central $ε$-DP model. We first provide a near-optimal result by developing a private and robust Upper Confidence Bound (UCB) algorithm. Then, we improve the result via a private and robust version of the Successive Elimination (…
Contextual bandits are online learners that, given an input, select an arm and receive a reward for that arm. They use the reward as a learning signal and aim to maximize the total reward over the inputs. Contextual bandits are commonly used to solve recommendation or ranking problems. This paper considers a learning setting in which multiple parties aim to train a contextual bandit together in a private way: the parties aim to maximize the total reward but do not want to share any of the relevant information they possess with the other parties. Specifically, multiple parties have access to (d…
Queen Mary University of London（伦敦玛丽女王大学）；Brave Software（勇敢软件公司）；Imperial College London（帝国理工学院）
Contextual bandit algorithms~(CBAs) often rely on personal data to provide recommendations. Centralized CBA agents utilize potentially sensitive data from recent interactions to provide personalization to end-users. Keeping the sensitive data locally, by running a local agent on the user's device, protects the user's privacy, however, the agent requires longer to produce useful recommendations, as it does not leverage feedback from other users. This paper proposes a technique we call Privacy-Preserving Bandits (P2B); a system that updates local agents by collecting feedback from other local ag…
The cooperative bandit problem is a multi-agent decision problem involving a group of agents that interact simultaneously with a multi-armed bandit, while communicating over a network with delays. The central idea in this problem is to design algorithms that can efficiently leverage communication to obtain improvements over acting in isolation. In this paper, we investigate the stochastic bandit problem under two settings - (a) when the agents wish to make their communication private with respect to the action sequence, and (b) when the agents can be byzantine, i.e., they provide (stochastical…
Boston University（波士顿大学）；Wayne State University（韦恩州立大学）
Differential privacy (DP) has been recently introduced to linear contextual bandits to formally address the privacy concerns in its associated personalized services to participating users (e.g., recommendations). Prior work largely focus on two trust models of DP: the central model, where a central server is responsible for protecting users sensitive data, and the (stronger) local model, where information needs to be protected directly on user side. However, there remains a fundamental gap in the utility achieved by learning algorithms under these two privacy models, e.g., $\tilde{O}(\sqrt{T})…
Virginia Tech（弗吉尼亚理工大学）；Wayne State University（韦恩州立大学）
In this paper, we study kernelized bandits with distributed biased feedback. This problem is motivated by several real-world applications (such as dynamic pricing, cellular network configuration, and policy making), where users from a large population contribute to the reward of the action chosen by a central entity, but it is difficult to collect feedback from all users. Instead, only biased feedback (due to user heterogeneity) from a subset of users may be available. In addition to such partial biased feedback, we are also faced with two practical challenges due to communication cost and com…
The Ohio State University（俄亥俄州立大学）；Iowa State University（爱荷华州立大学）
This paper investigates the problem of regret minimization for multi-armed bandit (MAB) problems with local differential privacy (LDP) guarantee. In stochastic bandit systems, the rewards may refer to the users' activities, which may involve private information and the users may not want the agent to know. However, in many cases, the agent needs to know these activities to provide better services such as recommendations and news feeds. To handle this dilemma, we adopt differential privacy and study the regret upper and lower bounds for MAB algorithms with a given LDP guarantee. In this paper, …
In this paper, we study the non-stationary online second price auction problem. We assume that the seller is selling the same type of items in $T$ rounds by the second price auction, and she can set the reserve price in each round. In each round, the bidders draw their private values from a joint distribution unknown to the seller. Then, the seller announced the reserve price in this round. Next, bidders with private values higher than the announced reserve price in that round will report their values to the seller as their bids. The bidder with the highest bid larger than the reserved price w…
Microsoft Research Silicon Valley（微软研究院硅谷分院）；Cornell University（康奈尔大学）；Facebook（脸书）
We consider a multi-round auction setting motivated by pay-per-click auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. Initially, neither the auctioneer nor the advertisers have any information about the likelihood of clicks on the advertisements. The auctioneer's goal is to design a (dominant strategies) truthful mechanism that (approximately) maximizes the social welfare. If the advertisers bid their true private …
We study the contextual linear bandit problem, a version of the standard stochastic multi-armed bandit (MAB) problem where a learner sequentially selects actions to maximize a reward which depends also on a user provided per-round context. Though the context is chosen arbitrarily or adversarially, the reward is assumed to be a stochastic function of a feature vector that encodes the context and selected action. Our goal is to devise private learners for the contextual linear bandit problem. We first show that using the standard definition of differential privacy results in linear regret. So in…
I study a game of strategic exploration with private payoffs and public actions in a Bayesian bandit setting. In particular, I look at cascade equilibria, in which agents switch over time from the risky action to the riskless action only when they become sufficiently pessimistic. I show that these equilibria exist under some conditions and establish their salient properties. Individual exploration in these equilibria can be more or less than the single-agent level depending on whether the agents start out with a common prior or not, but the most optimistic agent always underexplores. I also sh…
For sponsored search auctions, we consider contextual multi-armed bandit problem in the presence of strategic agents. In this setting, at each round, an advertising platform (center) runs an auction to select the best-suited ads relevant to the query posted by the user. It is in the best interest of the center to select an ad that has a high expected value (i.e., probability of getting a click $\times$ value it derives from a click of the ad). The probability of getting a click (CTR) is unknown to the center and depends on the user's profile (context) posting the query. Further, the value deri…
University of Virginia（弗吉尼亚大学）；University of Colorado, Boulder（科罗拉多大学博尔德分校）
We study the problem of incentivizing exploration for myopic users in linear bandits, where the users tend to exploit arm with the highest predicted reward instead of exploring. In order to maximize the long-term reward, the system offers compensation to incentivize the users to pull the exploratory arms, with the goal of balancing the trade-off among exploitation, exploration and compensation. We consider a new and practically motivated setting where the context features observed by the user are more informative than those used by the system, e.g., features based on users' private information…
Chalmers University of Technology（查尔姆斯理工大学）；University of Lille（里尔大学）；Harvard University（哈佛大学）
In this paper, we improve the previously best known regret bound to achieve $ε$-differential privacy in oblivious adversarial bandits from $\mathcal{O}{(T^{2/3}/ε)}$ to $\mathcal{O}{(\sqrt{T} \ln T /ε)}$. This is achieved by combining a Laplace Mechanism with EXP3. We show that though EXP3 is already differentially private, it leaks a linear amount of information in $T$. However, we can improve this privacy by relying on its intrinsic exponential mechanism for selecting actions. This allows us to reach $\mathcal{O}{(\sqrt{\ln T})}$-DP, with a regret of $\mathcal{O}{(T^{2/3})}$ that holds again…
The widespread proliferation of data-driven decision-making has ushered in a recent interest in the design of privacy-preserving algorithms. In this paper, we consider the ubiquitous problem of gaussian process (GP) bandit optimization from the lens of privacy-preserving statistics. We propose a solution for differentially private GP bandit optimization that combines a uniform kernel approximator with random perturbations, providing a generic framework to create differentially-private (DP) Gaussian process bandit algorithms. For two specific DP settings - joint and local differential privacy, …
City University of Hong Kong（香港城市大学）；City University of Hong Kong Shenzhen Research Institute（香港城市大学深圳研究院）
Communication bottleneck and data privacy are two critical concerns in federated multi-armed bandit (MAB) problems, such as situations in decision-making and recommendations of connected vehicles via wireless. In this paper, we design the privacy-preserving communication-efficient algorithm in such problems and study the interactions among privacy, communication and learning performance in terms of the regret. To be specific, we design privacy-preserving learning algorithms and communication protocols and derive the learning regret when networked private agents are performing online bandit lea…
Media Lab（媒体实验室）；Institute for Data, Systems and Society（数据、系统与社会研究所）；Massachusetts Institute of Technology（麻省理工学院）
The rapid proliferation of decentralized learning systems mandates the need for differentially-private cooperative learning. In this paper, we study this in context of the contextual linear bandit: we consider a collection of agents cooperating to solve a common contextual bandit, while ensuring that their communication remains private. For this problem, we devise \textsc{FedUCB}, a multiagent private algorithm for both centralized and decentralized (peer-to-peer) federated learning. We provide a rigorous technical analysis of its utility in terms of regret, improving several results in cooper…
Peking University（北京大学）；Microsoft Research Asia（微软亚洲研究院）
In this paper, we study Combinatorial Semi-Bandits (CSB) that is an extension of classic Multi-Armed Bandits (MAB) under Differential Privacy (DP) and stronger Local Differential Privacy (LDP) setting. Since the server receives more information from users in CSB, it usually causes additional dependence on the dimension of data, which is a notorious side-effect for privacy preserving learning. However for CSB under two common smoothness assumptions \cite{kveton2015tight,chen2016combinatorial}, we show it is possible to remove this side-effect. In detail, for $B_{\infty}$-bounded smooth CSB unde…
We extend the model of Multi-armed Bandit with unit switching cost to incorporate a metric between the actions. We consider the case where the metric over the actions can be modeled by a complete binary tree, and the distance between two leaves is the size of the subtree of their least common ancestor, which abstracts the case that the actions are points on the continuous interval $[0,1]$ and the switching cost is their distance. In this setting, we give a new algorithm that establishes a regret of $\widetilde{O}(\sqrt{kT} + T/k)$, where $k$ is the number of actions and $T$ is the time horizon…
In this paper, we propose differentially private algorithms for the problem of stochastic linear bandits in the central, local and shuffled models. In the central model, we achieve almost the same regret as the optimal non-private algorithms, which means we get privacy for free. In particular, we achieve a regret of $\tilde{O}(\sqrt{T}+\frac{1}ε)$ matching the known lower bound for private linear bandits, while the best previously known algorithm achieves $\tilde{O}(\frac{1}ε\sqrt{T})$. In the local case, we achieve a regret of $\tilde{O}(\frac{1}ε{\sqrt{T}})$ which matches the non-private reg…
We study the problem of multi-armed bandits with $ε$-global Differential Privacy (DP). First, we prove the minimax and problem-dependent regret lower bounds for stochastic and linear bandits that quantify the hardness of bandits with $ε$-global DP. These bounds suggest the existence of two hardness regimes depending on the privacy budget $ε$. In the high-privacy regime (small $ε$), the hardness depends on a coupled effect of privacy and partial information about the reward distributions. In the low-privacy regime (large $ε$), bandits with $ε$-global DP are not harder than the bandits without p…
Consider a requester who wishes to crowdsource a series of identical binary labeling tasks to a pool of workers so as to achieve an assured accuracy for each task, in a cost optimal way. The workers are heterogeneous with unknown but fixed qualities and their costs are private. The problem is to select for each task an optimal subset of workers so that the outcome obtained from the selected workers guarantees a target accuracy level. The problem is a challenging one even in a non strategic setting since the accuracy of aggregated label depends on unknown qualities. We develop a novel multi-arm…
