In this paper, we propose and study opportunistic contextual bandits - a special case of contextual bandits where the exploration cost varies under different environmental conditions, such as network load or return variation in recommendations. When the exploration cost is low, so is the actual regret of pulling a sub-optimal arm (e.g., trying a suboptimal recommendation). Therefore, intuitively, we could explore more when the exploration cost is relatively low and exploit more when the exploration cost is relatively high. Inspired by this intuition, for opportunistic contextual bandits with Linear payoffs, we propose an Adaptive Upper-Confidence-Bound algorithm (AdaLinUCB) to adaptively balance the exploration-exploitation trade-off for opportunistic learning. We prove that AdaLinUCB achieves O((log T)^2) problem-dependent regret upper bound, which has a smaller coefficient than that of the traditional LinUCB algorithm. Moreover, based on both synthetic and real-world dataset, we show that AdaLinUCB significantly outperforms other contextual bandit algorithms, under large exploration cost fluctuations.
Most existing approaches in Mobile Context-Aware Recommender Systems focus on recommending relevant items to users taking into account contextual information, such as time, location, or social aspects. However, none of them has considered the problem of user's content evolution. We introduce in this paper an algorithm that tackles this dynamicity. It is based on dynamic exploration exploitation and can adaptively balance the two aspects by deciding which user's situation is most relevant for exploration or exploitation. Within a deliberately designed offline simulation framework we conduct evaluations with real online event log data. The experimental results demonstrate that our algorithm outperforms surveyed algorithms. We show how a standard tool from statistics --- namely confidence bounds --- can be used to elegantly deal with situations which exhibit an exploitation-exploration trade-off. Our technique for designing and analyzing algorithms for such situations is general and can be applied when an algorithm has to make exploitation-versus-exploration decisions based on uncertain information provided by a random process. We apply our technique to two models with such an exploitation-exploration trade-off. For the adversarial bandit problem with shifting our new algorithm suffers only O((ST)1 2) regret with high probability over T trials with S shifts. Such a regret bound was previously known only in expectation. The second model we consider is associative reinforcement learning with linear value functions. For this model our technique improves the regret from O(T3 4) to O(T1 2). We consider a non-Bayesian infinite horizon version of the multi-armed bandit problem with the objective of designing simple policies whose regret increases sldwly with time. In their seminal work on this problem, Lai and Robbins had obtained a O(logn) lower bound on the regret with a constant that depends on the KullbackLeibler number. They also constructed policies for some specific families of probability distributions (including exponential families) that achieved the lower bound. In this paper we construct index policies that depend on the rewards from each arm only through their sample mean. These policies are computationally much simpler and are also applicable much more generally. They achieve a O(logn) regret with a constant that is also based on the Kullback-Leibler number. This constant turns out to be optimal for one-parameter exponential families; however, in general it is derived from the optimal one via a 'contraction' principle. Our results rely entirely on a few key lemmas from the theory of large deviations. Thompson sampling is one of oldest heuristic to address the exploration exploitation trade-off, but it is surprisingly unpopular in the literature. We present here some empirical results using Thompson sampling on simulated and real data, and show that it is highly competitive. And since this heuristic is very easy to implement, we argue that it should be part of the standard baselines to compare against. We improve the theoretical analysis and empirical performance of algorithms for the stochastic multi-armed bandit problem and the linear stochastic multi-armed bandit problem. In particular, we show that a simple modification of Auer's UCB algorithm (Auer, 2002) achieves with high probability constant regret. More importantly, we modify and, consequently, improve the analysis of the algorithm for the for linear stochastic bandit problem studied by Auer (2002), (2008), Rusmevichientong and Tsitsiklis (2010), (2010). Our modification improves the regret bound by a logarithmic factor, though experiments show a vast improvement. In both cases, the improvement stems from the construction of smaller confidence sets. For their construction we use a novel tail inequality for vector-valued martingales.  Contextual bandit algorithms provide principled online learning solutions to find optimal trade-offs between exploration and exploitation with companion side-information. They have been extensively used in many important practical scenarios, such as display advertising and content recommendation. A common practice estimates the unknown bandit parameters pertaining to each user independently. This unfortunately ignores dependency among users and thus leads to suboptimal solutions, especially for the applications that have strong social components. In this paper, we develop a collaborative contextual bandit algorithm, in which the adjacency graph among users is leveraged to share context and payoffs among neighboring users while online updating. We rigorously prove an improved upper regret bound of the proposed collaborative bandit algorithm comparing to conventional independent bandit algorithms. Extensive experiments on both synthetic and three large-scale real-world datasets verified the improvement of our proposed algorithm against several state-of-the-art contextual bandit algorithms. Contextual bandit algorithms provide principled online learning solutions to find optimal trade-offs between exploration and exploitation with companion side-information. Most contextual bandit algorithms simply assume the learner would have access to the entire set of features, which govern the generation of payoffs from a user to an item. However, in practice it is challenging to exhaust all relevant features ahead of time, and oftentimes due to privacy or sampling constraints many factors are unobservable to the algorithm. Failing to model such hidden factors leads a system to make constantly suboptimal predictions. In this paper, we propose to learn the hidden features for contextual bandit algorithms. Hidden features are explicitly introduced in our reward generation assumption, in addition to the observable contextual features. A scalable bandit algorithm is achieved via coordinate descent, in which closed form solutions exist at each iteration for both hidden features and bandit parameters. Most importantly, we rigorously prove that the developed contextual bandit algorithm achieves a sublinear upper regret bound with high probability, and a linear regret is inevitable if one fails to model such hidden features. Extensive experimentation on both simulations and large-scale real-world datasets verified the advantages of the proposed algorithm compared with several state-of-the-art contextual bandit algorithms and existing ad-hoc combinations between bandit algorithms and matrix factorization methods. Contextual bandit algorithms have become popular for online recommendation systems such as Digg, Yahoo! Buzz, and news recommendation in general. Offline evaluation of the effectiveness of new algorithms in these applications is critical for protecting online user experiences but very challenging due to their "partial-label" nature. Common practice is to create a simulator which simulates the online environment for the problem at hand and then run an algorithm against this simulator. However, creating simulator itself is often difficult and modeling bias is usually unavoidably introduced. In this paper, we introduce a replay methodology for contextual bandit algorithm evaluation. Different from simulator-based approaches, our method is completely data-driven and very easy to adapt to different applications. More importantly, our method can provide provably unbiased evaluations. Our empirical results on a large-scale news article recommendation dataset collected from Yahoo! Front Page conform well with our theoretical results. Furthermore, comparisons between our offline replay and online bucket evaluation of several contextual bandit algorithms show accuracy and effectiveness of our offline evaluation method. Personalized web services strive to adapt their services (advertisements, news articles, etc.) to individual users by making use of both content and user information. Despite a few recent advances, this problem remains challenging for at least two reasons. First, web service is featured with dynamically changing pools of content, rendering traditional collaborative filtering methods inapplicable. Second, the scale of most web services of practical interest calls for solutions that are both fast in learning and computation. In this work, we model personalized recommendation of news articles as a contextual bandit problem, a principled approach in which a learning algorithm sequentially selects articles to serve users based on contextual information about the users and articles, while simultaneously adapting its article-selection strategy based on user-click feedback to maximize total user clicks. The contributions of this work are three-fold. First, we propose a new, general contextual bandit algorithm that is computationally efficient and well motivated from learning theory. Second, we argue that any bandit algorithm can be reliably evaluated offline using previously recorded random traffic. Finally, using this offline evaluation method, we successfully applied our new algorithm to a Yahoo! Front Page Today Module dataset containing over 33 million events. Results showed a 12.5 click lift compared to a standard context-free bandit algorithm, and the advantage becomes even greater when data gets more scarce. We present Epoch-Greedy, an algorithm for multi-armed bandits with observable side information. Epoch-Greedy has the following properties: No knowledge of a time horizon @math is necessary. The regret incurred by Epoch-Greedy is controlled by a sample complexity bound for a hypothesis class. The regret scales as @math or better (sometimes, much better). Here @math is the complexity term in a sample complexity bound for standard supervised learning. We consider structured multi-armed bandit problems based on the Generalized Linear Model (GLM) framework of statistics. For these bandits, we propose a new algorithm, called GLM-UCB. We derive finite time, high probability bounds on the regret of the algorithm, extending previous analyses developed for the linear bandits to the non-linear case. The analysis highlights a key difficulty in generalizing linear bandit algorithms to the non-linear case, which is solved in GLM-UCB by focusing on the reward space rather than on the parameter space. Moreover, as the actual effectiveness of current parameterized bandit algorithms is often poor in practice, we provide a tuning method based on asymptotic arguments, which leads to significantly better practical performance. We present two numerical experiments on real-world data that illustrate the potential of the GLM-UCB approach. Reinforcement learning policies face the exploration versus exploitation dilemma, i.e. the search for a balance between exploring the environment to find profitable actions while taking the empirically best action as often as possible. A popular measure of a policy's success in addressing this dilemma is the regret, that is the loss due to the fact that the globally optimal policy is not followed all the times. One of the simplest examples of the exploration exploitation dilemma is the multi-armed bandit problem. Lai and Robbins were the first ones to show that the regret for this problem has to grow at least logarithmically in the number of plays. Since then, policies which asymptotically achieve this regret have been devised by Lai and Robbins and many others. In this work we show that the optimal logarithmic regret is also achievable uniformly over time, with simple and efficient policies, and for all reward distributions with bounded support. In this paper we study the contextual bandit problem (also known as the multi-armed bandit problem with expert advice) for linear payoff functions. For T rounds, K actions, and d dimensional feature vectors, we prove an O (√ Td ln(KT ln(T ) δ) ) regret bound that holds with probability 1− δ for the simplest known (both conceptually and computationally) efficient upper confidence bound algorithm for this problem. We also prove a lower bound of Ω( √ Td) for this setting, matching the upper bound up to logarithmic factors.