Users of recommender systems often behave in a non-stationary fashion, due to their evolving preferences and tastes over time. In this work, we propose a practical approach for fast personalization to non-stationary users. The key idea is to frame this problem as a latent bandit, where the prototypical models of user behavior are learned offline and the latent state of the user is inferred online from its interactions with the models. We call this problem a non-stationary latent bandit. We propose Thompson sampling algorithms for regret minimization in non-stationary latent bandits, analyze them, and evaluate them on a real-world dataset. The main strength of our approach is that it can be combined with rich offline-learned models, which can be misspecified, and are subsequently fine-tuned online using posterior sampling. In this way, we naturally combine the strengths of offline and online learning.
Personalized recommendations for new users, also known as the cold-start problem, can be formulated as a contextual bandit problem. Existing contextual bandit algorithms generally rely on features alone to capture user variability. Such methods are inefficient in learning new users' interests. In this paper we propose Latent Contextual Bandits. We consider both the benefit of leveraging a set of learned latent user classes for new users, and how we can learn such latent classes from prior users. We show that our approach achieves a better regret bound than existing algorithms. We also demonstr…
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…
A latent bandit problem is one in which the learning agent knows the arm reward distributions conditioned on an unknown discrete latent state. The primary goal of the agent is to identify the latent state, after which it can act optimally. This setting is a natural midpoint between online and offline learning---complex models can be learned offline with the agent identifying latent state online---of practical relevance in, say, recommender systems. In this work, we propose general algorithms for this setting, based on both upper confidence bounds (UCBs) and Thompson sampling. Our methods are c…
Non-stationary bandits and online clustering of bandits lift the restrictive assumptions in contextual bandits and provide solutions to many important real-world scenarios. Though the essence in solving these two problems overlaps considerably, they have been studied independently. In this paper, we connect these two strands of bandit research under the notion of test of homogeneity, which seamlessly addresses change detection for non-stationary bandit and cluster identification for online clustering of bandit in a unified solution framework. Rigorous regret analysis and extensive empirical ev…
The multi-armed bandit problem has been extensively studied under the stationary assumption. However in reality, this assumption often does not hold because the distributions of rewards themselves may change over time. In this paper, we propose a change-detection (CD) based framework for multi-armed bandit problems under the piecewise-stationary setting, and study a class of change-detection based UCB (Upper Confidence Bound) policies, CD-UCB, that actively detects change points and restarts the UCB indices. We then develop CUSUM-UCB and PHT-UCB, that belong to the CD-UCB class and use cumulat…
We study the multi-armed bandit problem where the rewards are realizations of general non-stationary stochastic processes, a setting that generalizes many existing lines of work and analyses. In particular, we present a theoretical analysis and derive regret guarantees for rested bandits in which the reward distribution of each arm changes only when we pull that arm. Remarkably, our regret bounds are logarithmic in the number of rounds under several natural conditions. We introduce a new algorithm based on classical UCB ideas combined with the notion of weighted discrepancy, a useful tool for …
University of California, Davis（加利福尼亚大学戴维斯分校）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Classic contextual bandit algorithms for linear models, such as LinUCB, assume that the reward distribution for an arm is modeled by a stationary linear regression. When the linear regression model is non-stationary over time, the regret of LinUCB can scale linearly with time. In this paper, we propose a novel multiscale changepoint detection method for the non-stationary linear bandit problems, called Multiscale-LinUCB, which actively adapts to the changing environment. We also provide theoretical analysis of regret bound for Multiscale-LinUCB algorithm. Experimental results show that our pro…
This paper tackles the risk averse multi-armed bandits problem when incurred losses are non-stationary. The conditional value-at-risk (CVaR) is used as the objective function. Two estimation methods are proposed for this objective function in the presence of non-stationary losses, one relying on a weighted empirical distribution of losses and another on the dual representation of the CVaR. Such estimates can then be embedded into classic arm selection methods such as epsilon-greedy policies. Simulation experiments assess the performance of the arm selection algorithms based on the two novel es…
We propose an algorithm for non-stationary kernel bandits that does not require prior knowledge of the degree of non-stationarity. The algorithm follows randomized strategies obtained by solving optimization problems that balance exploration and exploitation. It adapts to non-stationarity by restarting when a change in the reward function is detected. Our algorithm enjoys a tighter dynamic regret bound than previous work on the non-stationary kernel bandit setting. Moreover, when applied to the non-stationary linear bandit setting by using a linear kernel, our algorithm is nearly minimax optim…
We study the bandit problem where arms are associated with stationary phi-mixing processes and where rewards are therefore dependent: the question that arises from this setting is that of recovering some independence by ignoring the value of some rewards. As we shall see, the bandit problem we tackle requires us to address the exploration/exploitation/independence trade-off. To do so, we provide a UCB strategy together with a general regret analysis for the case where the size of the independence blocks (the ignored rewards) is fixed and we go a step beyond by providing an algorithm that is ab…
We investigate the piecewise-stationary combinatorial semi-bandit problem. Compared to the original combinatorial semi-bandit problem, our setting assumes the reward distributions of base arms may change in a piecewise-stationary manner at unknown time steps. We propose an algorithm, \texttt{GLR-CUCB}, which incorporates an efficient combinatorial semi-bandit algorithm, \texttt{CUCB}, with an almost parameter-free change-point detector, the \emph{Generalized Likelihood Ratio Test} (GLRT). Our analysis shows that the regret of \texttt{GLR-CUCB} is upper bounded by $\mathcal{O}(\sqrt{NKT\log{T}}…
We study the problem of \emph{dynamic regret minimization} in $K$-armed Dueling Bandits under non-stationary or time varying preferences. This is an online learning setup where the agent chooses a pair of items at each round and observes only a relative binary `win-loss' feedback for this pair, sampled from an underlying preference matrix at that round. We first study the problem of static-regret minimization for adversarial preference sequences and design an efficient algorithm with $O(\sqrt{KT})$ high probability regret. We next use similar algorithmic ideas to propose an efficient and prova…
Non-stationarity appears in many online applications such as web search and advertising. In this paper, we study the online learning to rank problem in a non-stationary environment where user preferences change abruptly at an unknown moment in time. We consider the problem of identifying the K most attractive items and propose cascading non-stationary bandits, an online learning variant of the cascading model, where a user browses a ranked list from top to bottom and clicks on the first attractive item. We propose two algorithms for solving this non-stationary problem: CascadeDUCB and CascadeS…
We consider a Multi-Armed Bandit problem in which the rewards are non-stationary and are dependent on past actions and potentially on past contexts. At the heart of our method, we employ a recurrent neural network, which models these sequences. In order to balance between exploration and exploitation, we present an energy minimization term that prevents the neural network from becoming too confident in support of a certain action. This term provably limits the gap between the maximal and minimal probabilities assigned by the network. In a diverse set of experiments, we demonstrate that our met…
MARBLE: Multi-Armed Restless Bandits in Latent Markovian Environment
Department of Computer and Systems Sciences (DSV), Stockholm University（斯德哥尔摩大学计算机与系统科学系）；Inria Sophia Antipolis（法国国家信息与自动化研究所索菲亚·安蒂波利斯研究中心）；Smartprofile（Smartprofile公司）
Paderborn University（帕德博恩大学）；University of Munich（慕尼黑大学）
We study the non-stationary dueling bandits problem with $K$ arms, where the time horizon $T$ consists of $M$ stationary segments, each of which is associated with its own preference matrix. The learner repeatedly selects a pair of arms and observes a binary preference between them as feedback. To minimize the accumulated regret, the learner needs to pick the Condorcet winner of each stationary segment as often as possible, despite preference matrices and segment lengths being unknown. We propose the $\mathrm{Beat\, the\, Winner\, Reset}$ algorithm and prove a bound on its expected binary weak…
Center for Applied Intelligent Systems Research（应用智能系统研究中心）；Halmstad University（哈尔姆斯塔德大学）
In the latent bandit problem, the learner has access to reward distributions and -- for the non-stationary variant -- transition models of the environment. The reward distributions are conditioned on the arm and unknown latent states. The goal is to use the reward history to identify the latent state, allowing for the optimal choice of arms in the future. The latent bandit setting lends itself to many practical applications, such as recommender and decision support systems, where rich data allows the offline estimation of environment models with online learning remaining a critical component. …
University of Edinburgh（爱丁堡大学）；University College London（伦敦大学学院）；Nara Institute of Science and Technology（奈良先端科学技术大学院大学）
Active learning aims to reduce annotation cost by predicting which samples are useful for a human teacher to label. However it has become clear there is no best active learning algorithm. Inspired by various philosophies about what constitutes a good criteria, different algorithms perform well on different datasets. This has motivated research into ensembles of active learners that learn what constitutes a good criteria in a given scenario, typically via multi-armed bandit algorithms. Though algorithm ensembles can lead to better results, they overlook the fact that not only does algorithm eff…
Indian Institute of Technology, Madras（印度理工学院马德拉斯分校）
We consider the multi armed bandit problem in non-stationary environments. Based on the Bayesian method, we propose a variant of Thompson Sampling which can be used in both rested and restless bandit scenarios. Applying discounting to the parameters of prior distribution, we describe a way to systematically reduce the effect of past observations. Further, we derive the exact expression for the probability of picking sub-optimal arms. By increasing the exploitative value of Bayes' samples, we also provide an optimistic version of the algorithm. Extensive empirical analysis is conducted under va…
We consider minimisation of dynamic regret in non-stationary bandits with a slowly varying property. Namely, we assume that arms' rewards are stochastic and independent over time, but that the absolute difference between the expected rewards of any arm at any two consecutive time-steps is at most a drift limit $δ> 0$. For this setting that has not received enough attention in the past, we give a new algorithm which extends naturally the well-known Successive Elimination algorithm to the non-stationary bandit setting. We establish the first instance-dependent regret upper bound for slowly varyi…
Naveen Jindal School of Management, University of Texas at Dallas（德克萨斯大学达拉斯分校纳文·金达尔管理学院）
In this paper we study the non-stationary stochastic optimization question with bandit feedback and dynamic regret measures. The seminal work of Besbes et al. (2015) shows that, when aggregated function changes is known a priori, a simple re-starting algorithm attains the optimal dynamic regret. In this work, we designed a stochastic optimization algorithm with fixed step sizes, which combined together with the multi-scale sampling framework of Wei and Luo (2021) achieves the optimal dynamic regret in non-stationary stochastic optimization without requiring prior knowledge of function change b…
Non-Stationary Bandit Learning via Predictive Sampling
Jones Graduate School of Business, Rice University（里士满大学沃森商学院研究生院）；Stanford Graduate School of Business（斯坦福商学院）；Department of Management Science and Engineering, Department of Electrical Engineering, Stanford University（斯坦福大学管理科学与工程系、电气工程系）
Online recommender systems often face long delays in receiving feedback, especially when optimizing for some long-term metrics. While mitigating the effects of delays in learning is well-understood in stationary environments, the problem becomes much more challenging when the environment changes. In fact, if the timescale of the change is comparable to the delay, it is impossible to learn about the environment, since the available observations are already obsolete. However, the arising issues can be addressed if intermediate signals are available without delay, such that given those signals, t…
University of Southern California（南加州大学）；Microsoft Research, NYC（微软研究院（纽约））
Most contextual bandit algorithms minimize regret against the best fixed policy, a questionable benchmark for non-stationary environments that are ubiquitous in applications. In this work, we develop several efficient contextual bandit algorithms for non-stationary environments by equipping existing methods for i.i.d. problems with sophisticated statistical tests so as to dynamically adapt to a change in distribution. We analyze various standard notions of regret suited to non-stationary environments for these algorithms, including interval regret, switching regret, and dynamic regret. When co…
We consider a novel multi-armed bandit framework where the rewards obtained by pulling the arms are functions of a common latent random variable. The correlation between arms due to the common random source can be used to design a generalized upper-confidence-bound (UCB) algorithm that identifies certain arms as $non-competitive$, and avoids exploring them. As a result, we reduce a $K$-armed bandit problem to a $C+1$-armed problem, where $C+1$ includes the best arm and $C$ $competitive$ arms. Our regret analysis shows that the competitive arms need to be pulled $\mathcal{O}(\log T)$ times, whi…
The stochastic multi-armed bandit has provided a framework for studying decision-making in unknown environments. We propose a variant of the stochastic multi-armed bandit where the rewards are sampled from a stochastic linear dynamical system. The proposed strategy for this stochastic multi-armed bandit variant is to learn a model of the dynamical system while choosing the optimal action based on the learned model. Motivated by mathematical finance areas such as Intertemporal Capital Asset Pricing Model proposed by Merton and Stochastic Portfolio Theory proposed by Fernholz that both model ass…
Columbia University（哥伦比亚大学）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
We consider an online decision making setting known as contextual bandit problem, and propose an approach for improving contextual bandit performance by using an adaptive feature extraction (representation learning) based on online clustering. Our approach starts with an off-line pre-training on unlabeled history of contexts (which can be exploited by our approach, but not by the standard contextual bandit), followed by an online selection and adaptation of encoders. Specifically, given an input sample (context), the proposed approach selects the most appropriate encoding function to extract a…
University of Oslo（奥斯陆大学）；Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）
We study the problem of non-stationary dueling bandits and provide the first adaptive dynamic regret algorithm for this problem. The only two existing attempts in this line of work fall short across multiple dimensions, including pessimistic measures of non-stationary complexity and non-adaptive parameter tuning that requires knowledge of the number of preference changes. We develop an elimination-based rescheduling algorithm to overcome these shortcomings and show a near-optimal $\tilde{O}(\sqrt{S^{\texttt{CW}} T})$ dynamic regret bound, where $S^{\texttt{CW}}$ is the number of times the Cond…
We consider a non-stationary two-armed bandit framework and propose a change-detection based Thompson sampling (TS) algorithm, named TS with change-detection (TS-CD), to keep track of the dynamic environment. The non-stationarity is modeled using a Poisson arrival process, which changes the mean of the rewards on each arrival. The proposed strategy compares the empirical mean of the recent rewards of an arm with the estimate of the mean of the rewards from its history. It detects a change when the empirical mean deviates from the mean estimate by a value larger than a threshold. Then, we chara…
Indian Institute of Science（印度科学理工学院）；Inria Saclay – Île de France（法国国家信息与自动化研究所萨克雷-法兰西岛研究中心）
We study the task of maximizing rewards from recommending items (actions) to users sequentially interacting with a recommender system. Users are modeled as latent mixtures of C many representative user classes, where each class specifies a mean reward profile across actions. Both the user features (mixture distribution over classes) and the item features (mean reward vector per class) are unknown a priori. The user identity is the only contextual information available to the learner while interacting. This induces a low-rank structure on the matrix of expected rewards r a,b from recommending i…
Multi-armed bandit algorithms have become a reference solution for handling the explore/exploit dilemma in recommender systems, and many other important real-world problems, such as display advertisement. However, such algorithms usually assume a stationary reward distribution, which hardly holds in practice as users' preferences are dynamic. This inevitably costs a recommender system consistent suboptimal performance. In this paper, we consider the situation where the underlying distribution of reward remains unchanged over (possibly short) epochs and shifts at unknown time instants. In accor…
We introduce GLR-klUCB, a novel algorithm for the piecewise iid non-stationary bandit problem with bounded rewards. This algorithm combines an efficient bandit algorithm, kl-UCB, with an efficient, parameter-free, changepoint detector, the Bernoulli Generalized Likelihood Ratio Test, for which we provide new theoretical guarantees of independent interest. Unlike previous non-stationary bandit algorithms using a change-point detector, GLR-klUCB does not need to be calibrated based on prior knowledge on the arms' means. We prove that this algorithm can attain a $O(\sqrt{TA Υ_T\log(T)})$ regret i…
Otto-von-Guericke University of Magdeburg（马格德堡奥托·冯·格里克大学）；University of Warwick（华威大学）
In this paper, we study a non-stationary stochastic bandit problem, which generalizes the switching bandit problem. On top of the switching bandit problem (\textbf{Case a}), we are interested in three concrete examples: (\textbf{b}) the means of the arms are local polynomials, (\textbf{c}) the means of the arms are locally smooth, and (\textbf{d}) the gaps of the arms have a bounded number of inflexion points and where the highest arm mean cannot vary too much in a short range. These three settings are very different, but have in common the following: (i) the number of similarly-sized level se…
A survey is performed of various Multi-Armed Bandit (MAB) strategies in order to examine their performance in circumstances exhibiting non-stationary stochastic reward functions in conjunction with delayed feedback. We run several MAB simulations to simulate an online eCommerce platform for grocery pick up, optimizing for product availability. In this work, we evaluate several popular MAB strategies, such as $ε$-greedy, UCB1, and Thompson Sampling. We compare the respective performances of each MAB strategy in the context of regret minimization. We run the analysis in the scenario where the re…
Dynamic Regret for Non-Stationary Linear Bandits via Misspecification Reductions
Department of Mathematics, The Hong Kong University of Science and Technology（香港科技大学数学系）；Stern School of Business, New York University（纽约大学斯特恩商学院）；Department of IEDA, The Hong Kong University of Science and Technology（香港科技大学工业工程与决策分析系）
