We present an extensive study of the key problem of online learning where algorithms are allowed to abstain from making predictions. In the adversarial setting, we show how existing online algorithms and guarantees can be adapted to this problem. In the stochastic setting, we first point out a bias problem that limits the straightforward extension of algorithms such as UCB-N to time-varying feedback graphs, as needed in this context. Next, we give a new algorithm, UCB-GT, that exploits historical data and is adapted to time-varying feedback graphs. We show that this algorithm benefits from more favorable regret guarantees than a possible, but limited, extension of UCB-N. We further report the results of a series of experiments demonstrating that UCB-GT largely outperforms that extension of UCB-N, as well as more standard baselines.
Tsinghua University（清华大学）；The Chinese University of Hong Kong（香港中文大学）
We study the online restless bandit problem, where the state of each arm evolves according to a Markov chain, and the reward of pulling an arm depends on both the pulled arm and the current state of the corresponding Markov chain. In this paper, we propose Restless-UCB, a learning policy that follows the explore-then-commit framework. In Restless-UCB, we present a novel method to construct offline instances, which only requires $O(N)$ time-complexity ($N$ is the number of arms) and is exponentially better than the complexity of existing learning policy. We also prove that Restless-UCB achieves…
In the setting of sequential prediction of individual $\{0, 1\}$-sequences with expert advice, we show that by allowing the learner to abstain from the prediction by paying a cost marginally smaller than $\frac 12$ (say, $0.49$), it is possible to achieve expected regret bounds that are independent of the time horizon $T$. We exactly characterize the dependence on the abstention cost $c$ and the number of experts $N$ by providing matching upper and lower bounds of order $\frac{\log N}{1-2c}$, which is to be contrasted with the best possible rate of $\sqrt{T\log N}$ that is available without th…
This paper studies classification with an abstention option in the online setting. In this setting, examples arrive sequentially, the learner is given a hypothesis class $\mathcal H$, and the goal of the learner is to either predict a label on each example or abstain, while ensuring that it does not make more than a pre-specified number of mistakes when it does predict a label. Previous work on this problem has left open two main challenges. First, not much is known about the optimality of algorithms, and in particular, about what an optimal algorithmic strategy is for any individual hypothesi…
University Paris-Saclay（巴黎-萨克雷大学）；UVSQ（凡尔赛大学）；Criteo（科睿拓）；Tampere University（坦佩雷大学）
In this paper, the method UCB-RS, which resorts to recommendation system (RS) for enhancing the upper-confidence bound algorithm UCB, is presented. The proposed method is used for dealing with non-stationary and large-state spaces multi-armed bandit problems. The proposed method has been targeted to the problem of the product recommendation in the online advertising. Through extensive testing with RecoGym, an OpenAI Gym-based reinforcement learning environment for the product recommendation in online advertising, the proposed method outperforms the widespread reinforcement learning schemes suc…
Edge Computing (EC) offers a superior user experience by positioning cloud resources in close proximity to end users. The challenge of allocating edge resources efficiently while maximizing profit for the EC platform remains a sophisticated problem, especially with the added complexity of the online arrival of resource requests. To address this challenge, we propose to cast the problem as a multi-armed bandit problem and develop two novel online pricing mechanisms, the Kullback-Leibler Upper Confidence Bound (KL-UCB) algorithm and the Min-Max Optimal algorithm, for heterogeneous edge resource …
A fundamental challenge in contextual bandits is to develop flexible, general-purpose algorithms with computational requirements no worse than classical supervised learning tasks such as classification and regression. Algorithms based on regression have shown promising empirical success, but theoretical guarantees have remained elusive except in special cases. We provide the first universal and optimal reduction from contextual bandits to online regression. We show how to transform any oracle for online regression with a given value function class into an algorithm for contextual bandits with …
Product ranking is the core problem for revenue-maximizing online retailers. To design proper product ranking algorithms, various consumer choice models are proposed to characterize the consumers' behaviors when they are provided with a list of products. However, existing works assume that each consumer purchases at most one product or will keep viewing the product list after purchasing a product, which does not agree with the common practice in real scenarios. In this paper, we assume that each consumer can purchase multiple products at will. To model consumers' willingness to view and purcha…
Netflix（奈飞）；Stanford University（斯坦福大学）；NYU Stern School of Business（纽约大学斯特恩商学院）
During online decision making in Multi-Armed Bandits (MAB), one needs to conduct inference on the true mean reward of each arm based on data collected so far at each step. However, since the arms are adaptively selected--thereby yielding non-iid data--conducting inference accurately is not straightforward. In particular, sample averaging, which is used in the family of UCB and Thompson sampling (TS) algorithms, does not provide a good choice as it suffers from bias and a lack of good statistical properties (e.g. asymptotic normality). Our thesis in this paper is that more sophisticated inferen…
Columbia University（哥伦比亚大学）；Fudan University（复旦大学）
We propose a cumulative oversampling (CO) method for online learning. Our key idea is to sample parameter estimations from the updated belief space once in each round (similar to Thompson Sampling), and utilize the cumulative samples up to the current round to construct optimistic parameter estimations that asymptotically concentrate around the true parameters as tighter upper confidence bounds compared to the ones constructed with standard UCB methods. We apply CO to a novel budgeted variant of the Influence Maximization (IM) semi-bandits with linear generalization of edge weights, whose offl…
University of Toronto（多伦多大学）；The Chinese University of Hong Kong（香港中文大学）
It has been recently shown in the literature that the sample averages from online learning experiments are biased when used to estimate the mean reward. To correct the bias, off-policy evaluation methods, including importance sampling and doubly robust estimators, typically calculate the conditional propensity score, which is ill-defined for non-randomized policies such as UCB. This paper provides a procedure to debias the samples using bootstrap, which doesn't require the knowledge of the reward distribution and can be applied to any adaptive policies. Numerical experiments demonstrate the ef…
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…
Asymptotically and Minimax Optimal Regret Bounds for Multi-Armed Bandits with Abstention
Institute of Operations Research and Analytics（运营研究与分析研究所）；National University of Singapore（新加坡国立大学）；Department of Electrical and Computer Engineering（电子与计算机工程系）；Department of Mathematics（数学系）
We consider the classical multi-armed bandit problem with Markovian rewards. When played an arm changes its state in a Markovian fashion while it remains frozen when not played. The player receives a state-dependent reward each time it plays an arm. The number of states and the state transition probabilities of an arm are unknown to the player. The player's objective is to maximize its long-term total reward by learning the best arm over time. We show that under certain conditions on the state transition probabilities of the arms, a sample mean based index policy achieves logarithmic regret un…
A UCB Bandit Algorithm for General ML-Based Estimators
School of Mathematics, University of Minnesota—Twin Cities（明尼苏达大学 Twin Cities 分校数学系）；Department of Computer Science, City University of Hong Kong（香港城市大学计算机科学系）
We develop algorithms with low regret for learning episodic Markov decision processes based on kernel approximation techniques. The algorithms are based on both the Upper Confidence Bound (UCB) as well as Posterior or Thompson Sampling (PSRL) philosophies, and work in the general setting of continuous state and action spaces when the true unknown transition dynamics are assumed to have smoothness induced by an appropriate Reproducing Kernel Hilbert Space (RKHS).
Multi-armed bandit (MAB) is a class of online learning problems where a learning agent aims to maximize its expected cumulative reward while repeatedly selecting to pull arms with unknown reward distributions. We consider a scenario where the reward distributions may change in a piecewise-stationary fashion at unknown time steps. We show that by incorporating a simple change-detection component with classic UCB algorithms to detect and adapt to changes, our so-called M-UCB algorithm can achieve nearly optimal regret bound on the order of $O(\sqrt{MKT\log T})$, where $T$ is the number of time s…
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…
Department of ECE（ECE系）；The Ohio State University（俄亥俄州立大学）；Alibaba, USA（阿里巴巴（美国））
Motivated by the increasing concern about privacy in nowadays data-intensive online learning systems, we consider a black-box optimization in the nonparametric Gaussian process setting with local differential privacy (LDP) guarantee. Specifically, the rewards from each user are further corrupted to protect privacy and the learner only has access to the corrupted rewards to minimize the regret. We first derive the regret lower bounds for any LDP mechanism and any learning algorithm. Then, we present three almost optimal algorithms based on the GP-UCB framework and Laplace DP mechanism. In this …
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…
Optimizing Digital Therapeutic Interventions: Online Learning under Endogenous Adherence
Department of Industrial and Systems Engineering, University of Wisconsin-Madison（威斯康星大学麦迪逊分校工业与系统工程系）；College of Health Solutions, Arizona State University（亚利桑那州立大学健康解决方案学院）
In this paper we investigate the problem of measuring end-to-end Incentive Compatibility (IC) regret given black-box access to an auction mechanism. Our goal is to 1) compute an estimate for IC regret in an auction, 2) provide a measure of certainty around the estimate of IC regret, and 3) minimize the time it takes to arrive at an accurate estimate. We consider two main problems, with different informational assumptions: In the \emph{advertiser problem} the goal is to measure IC regret for some known valuation $v$, while in the more general \emph{demand-side platform (DSP) problem} we wish to…
Adversarial Attacks on Online Learning to Rank with Click Feedback
California Institute of Technology（加州理工学院）；Southeast University（东南大学）；The Chinese University of Hong Kong（香港中文大学）；Shanghai Jiao Tong University（上海交通大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
Upper Confidence Bound (UCB) method is arguably the most celebrated one used in online decision making with partial information feedback. Existing techniques for constructing confidence bounds are typically built upon various concentration inequalities, which thus lead to over-exploration. In this paper, we propose a non-parametric and data-dependent UCB algorithm based on the multiplier bootstrap. To improve its finite sample performance, we further incorporate second-order correction into the above construction. In theory, we derive both problem-dependent and problem-independent regret bound…
This paper is in the field of stochastic Multi-Armed Bandits (MABs), i.e., those sequential selection techniques able to learn online using only the feedback given by the chosen option (a.k.a. arm). We study a particular case of the rested and restless bandits in which the arms' expected payoff is monotonically non-decreasing. This characteristic allows designing specifically crafted algorithms that exploit the regularity of the payoffs to provide tight regret bounds. We design an algorithm for the rested case (R-ed-UCB) and one for the restless case (R-less-UCB), providing a regret bound depe…
Singapore University of Technology and Design（新加坡科技设计大学）；Nanjing University of Posts and Telecommunications（南京邮电大学）
By exploiting the computing power and local data of distributed clients, federated learning (FL) features ubiquitous properties such as reduction of communication overhead and preserving data privacy. In each communication round of FL, the clients update local models based on their own data and upload their local updates via wireless channels. However, latency caused by hundreds to thousands of communication rounds remains a bottleneck in FL. To minimize the training latency, this work provides a multi-armed bandit-based framework for online client scheduling (CS) in FL without knowing wireles…
This work studies the question of Representation Learning in RL: how can we learn a compact low-dimensional representation such that on top of the representation we can perform RL procedures such as exploration and exploitation, in a sample efficient manner. We focus on the low-rank Markov Decision Processes (MDPs) where the transition dynamics correspond to a low-rank transition matrix. Unlike prior works that assume the representation is known (e.g., linear MDPs), here we need to learn the representation for the low-rank MDP. We study both the online RL and offline RL settings. For the onlin…
University of California San Diego（加州大学圣地亚哥分校）；University of Arizona（亚利桑那大学）；Facebook AI Research（脸书人工智能研究院）
We study the problem of online multi-task learning where the tasks are performed within similar but not necessarily identical multi-armed bandit environments. In particular, we study how a learner can improve its overall performance across multiple related tasks through robust transfer of knowledge. While an upper confidence bound (UCB)-based algorithm has recently been shown to achieve nearly-optimal performance guarantees in a setting where all tasks are solved concurrently, it remains unclear whether Thompson sampling (TS) algorithms, which have superior empirical performance in general, sh…
Online learning with delayed feedback has received increasing attention recently due to its several applications in distributed, web-based learning problems. In this paper we provide a systematic study of the topic, and analyze the effect of delay on the regret of online learning algorithms. Somewhat surprisingly, it turns out that delay increases the regret in a multiplicative way in adversarial problems, and in an additive way in stochastic problems. We give meta-algorithms that transform, in a black-box fashion, algorithms developed for the non-delayed case into ones that can handle the pre…
MediaTek Research（联发科研究）；National University of Singapore（新加坡国立大学）；University of California, San Diego（加州大学圣地亚哥分校）
Confidence intervals are a crucial building block in the analysis of various online learning problems. The analysis of kernel based bandit and reinforcement learning problems utilize confidence intervals applicable to the elements of a reproducing kernel Hilbert space (RKHS). However, the existing confidence bounds do not appear to be tight, resulting in suboptimal regret bounds. In fact, the existing regret bounds for several kernelized bandit algorithms (e.g., GP-UCB, GP-TS, and their variants) may fail to even be sublinear. It is unclear whether the suboptimal regret bound is a fundamental …
Adobe Research（Adobe研究院）；Czech Technical University（捷克技术大学）；DeepMind；University of Alberta（阿尔伯塔大学）
Online learning to rank is a core problem in information retrieval and machine learning. Many provably efficient algorithms have been recently proposed for this problem in specific click models. The click model is a model of how the user interacts with a list of documents. Though these results are significant, their impact on practice is limited, because all proposed algorithms are designed for specific click models and lack convergence guarantees in other models. In this work, we propose BatchRank, the first online learning to rank algorithm for a broad class of click models. The class encomp…
The Chinese University of Hong Kong（香港中文大学）；Tencent（腾讯）；Chongqing University（重庆大学）
A fundamental question for companies with large amount of logged data is: How to use such logged data together with incoming streaming data to make good decisions? Many companies currently make decisions via online A/B tests, but wrong decisions during testing hurt users' experiences and cause irreversible damage. A typical alternative is offline causal inference, which analyzes logged data alone to make decisions. However, these decisions are not adaptive to the new incoming data, and so a wrong decision will continuously hurt users' experiences. To overcome the aforementioned limitations, we…
