Mobile Context-Aware Recommender Systems can be naturally modelled as an exploration exploitation trade-off (exr exp) problem, where the system has to choose between maximizing its expected rewards dealing with its current knowledge (exploitation) and learning more about the unknown user's preferences to improve its knowledge (exploration). This problem has been addressed by the reinforcement learning community but they do not consider the risk level of the current user's situation, where it may be dangerous to recommend items the user may not desire in her current situation if the risk level is high. We introduce in this paper an algorithm named R-UCB that considers the risk level of the user's situation to adaptively balance between exr and exp. The detailed analysis of the experimental results reveals several important discoveries in the exr exp behaviour.
In @cite_9 , assuming the expected reward of a document is linear, they perform recommendation based on contextual information about the users' documents. To maximize the total number of user's clicks, this work proposes the LINUCB algorithm which is computationally efficient if the expected rewards of documents are linear which is not always the case.
@cite_9
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We study contextual bandits with budget and time constraints, referred to as constrained contextual bandits.The time and budget constraints significantly complicate the exploration and exploitation tradeoff because they introduce complex coupling among contexts over time.Such coupling effects make it difficult to obtain oracle solutions that assume known statistics of bandits. To gain insight, we first study unit-cost systems with known context distribution. When the expected rewards are known, we develop an approximation of the oracle, referred to Adaptive-Linear-Programming (ALP), which achieves near-optimality and only requires the ordering of expected rewards. With these highly desirable features, we then combine ALP with the upper-confidence-bound (UCB) method in the general case where the expected rewards are unknown a priori . We show that the proposed UCB-ALP algorithm achieves logarithmic regret except for certain boundary cases. Further, we design algorithms and obtain similar regret analysis results for more general systems with unknown context distribution and heterogeneous costs. To the best of our knowledge, this is the first work that shows how to achieve logarithmic regret in constrained contextual bandits. Moreover, this work also sheds light on the study of computationally efficient algorithms for general constrained contextual bandits. We tackle the problem of online reward maximisation over a large finite set of actions described by their contexts. We focus on the case when the number of actions is too big to sample all of them even once. However we assume that we have access to the similarities between actions' contexts and that the expected reward is an arbitrary linear function of the contexts' images in the related reproducing kernel Hilbert space (RKHS). We propose KernelUCB, a kernelised UCB algorithm, and give a cumulative regret bound through a frequentist analysis. For contextual bandits, the related algorithm GP-UCB turns out to be a special case of our algorithm, and our finite-time analysis improves the regret bound of GP-UCB for the agnostic case, both in the terms of the kernel-dependent quantity and the RKHS norm of the reward function. Moreover, for the linear kernel, our regret bound matches the lower bound for contextual linear bandits. Algorithms for learning to rank Web documents usually assume a document's relevance is independent of other documents. This leads to learned ranking functions that produce rankings with redundant results. In contrast, user studies have shown that diversity at high ranks is often preferred. We present two online learning algorithms that directly learn a diverse ranking of documents based on users' clicking behavior. We show that these algorithms minimize abandonment, or alternatively, maximize the probability that a relevant document is found in the top k positions of a ranking. Moreover, one of our algorithms asymptotically achieves optimal worst-case performance even if users' interests change. We define a general framework for a large class of combinatorial multi-armed bandit (CMAB) problems, where simple arms with unknown distributions form super arms. In each round, a super arm is played and the outcomes of its related simple arms are observed, which helps the selection of super arms in future rounds. The reward of the super arm depends on the outcomes of played arms, and it only needs to satisfy two mild assumptions, which allow a large class of nonlinear reward instances. We assume the availability of an (α, β)-approximation oracle that takes the means of the distributions of arms and outputs a super arm that with probability β generates an β fraction of the optimal expected reward. The objective of a CMAB algorithm is to minimize (α, β)- approximation regret, which is the difference in total expected reward between the αbeta; fraction of expected reward when always playing the optimal super arm, and the expected reward of playing super arms according to the algorithm. We provide CUCB algorithm that achieves O(log n) regret, where n is the number of rounds played, and we further provide distribution-independent bounds for a large class of reward functions. Our regret analysis is tight in that it matches the bound for classical MAB problem up to a constant factor, and it significantly improves the regret bound in a recent paper on combinatorial bandits with linear rewards. We apply our CMAB framework to two new applications, probabilistic maximum coverage (PMC) for online advertising and social influence maximization for viral marketing, both having nonlinear reward structures. We define a general framework for a large class of combinatorial multi-armed bandit (CMAB) problems, where subsets of base arms with unknown distributions form super arms. In each round, a super arm is played and the base arms contained in the super arm are played and their outcomes are observed. We further consider the extension in which more base arms could be probabilistically triggered based on the outcomes of already triggered arms. The reward of the super arm depends on the outcomes of all played arms, and it only needs to satisfy two mild assumptions, which allow a large class of nonlinear reward instances. We assume the availability of an offline (α β)-approximation oracle that takes the means of the outcome distributions of arms and outputs a super arm that with probability β generates an α fraction of the optimal expected reward. The objective of an online learning algorithm for CMAB is to minimize (α β)-approximation regret, which is the difference in total expected reward between the αβ fraction of expected reward when always playing the optimal super arm, and the expected reward of playing super arms according to the algorithm. We provide CUCB algorithm that achieves O(log n) distribution-dependent regret, where n is the number of rounds played, and we further provide distribution-independent bounds for a large class of reward functions. Our regret analysis is tight in that it matches the bound of UCB1 algorithm (up to a constant factor) for the classical MAB problem, and it significantly improves the regret bound in an earlier paper on combinatorial bandits with linear rewards. We apply our CMAB framework to two new applications, probabilistic maximum coverage (PMC) for online advertising and social in uence maximization for viral marketing, both having nonlinear reward structures. In particular, application to social in uence maximization requires our extension on probabilistically triggered arms. 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 arrivals, which involves trading off the reward received from its own actions, the information learned from its own actions, the reward received from the actions requested of others and the cost paid for these actions-taking into account what it has learned about the value of assistance from each other learner. We develop distributed online learning algorithms and provide analytic bounds to compare the efficiency of these with algorithms with the complete knowledge (oracle) benchmark (in which the expected reward of every action in every context is known by every learner). Our estimates show that regret-the loss incurred by the algorithm-is sublinear in time. Our theoretical framework can be used in many practical applications including Big Data mining, event detection in surveillance sensor networks and distributed online recommendation systems. While numerous metrics for information retrieval are available in the case of binary relevance, there is only one commonly used metric for graded relevance, namely the Discounted Cumulative Gain (DCG). A drawback of DCG is its additive nature and the underlying independence assumption: a document in a given position has always the same gain and discount independently of the documents shown above it. Inspired by the "cascade" user model, we present a new editorial metric for graded relevance which overcomes this difficulty and implicitly discounts documents which are shown below very relevant documents. More precisely, this new metric is defined as the expected reciprocal length of time that the user will take to find a relevant document. This can be seen as an extension of the classical reciprocal rank to the graded relevance case and we call this metric Expected Reciprocal Rank (ERR). We conduct an extensive evaluation on the query logs of a commercial search engine and show that ERR correlates better with clicks metrics than other editorial metrics. Stochastic knapsack problems deal with selecting items with potentially random sizes and rewards so as to maximize the total reward while satisfying certain capacity constraints. A novel variant of this problem, where items are worthless unless collected in bundles, is introduced here. This setup is similar to the Groupon model, where a deal is off unless a minimum number of users sign up for it. Since the optimal algorithm to solve this problem is not practical, several adaptive greedy approaches with reasonable time and memory requirements are studied in detail - theoretically, as well as, experimentally. Worst case performance guarantees are provided for some of these greedy algorithms, while results of experimental evaluation demonstrate that they are much closer to optimal than what the theoretical bounds suggest. Applications include optimizing for online advertising pricing models where advertisers pay only when certain goals, in terms of clicks or conversions, are met. We perform extensive experiments for the situation where there are between two and five ads. For typical ad conversion rates, the greedy policy of selecting items having the highest individual expected reward obtains a value within 5 of optimal over 95 of the time for a wide selection of parameters. We consider the design and analysis of algorithms that learn from the consequences of their actions with the goal of maximizing their cumulative reward, when the consequence of a given action is felt immediately, and a linear function, which is unknown a priori, (approximately) relates a feature vector for each action state pair to the (expected) associated reward. We focus on two cases, one in which a continuous-valued reward is (approximately) given by applying the unknown linear function, and another in which the probability of receiving the larger of binary-valued rewards is obtained. For these cases we provide bounds on the per-trial regret for our algorithms that go to zero as the number of trials approaches infinity. We also provide lower bounds that show that the rate of convergence is nearly optimal. Traditionally, information retrieval systems aim to maximize thenumber of relevant documents returned to a user within some windowof the top. For that goal, the probability ranking principle, whichranks documents in decreasing order of probability of relevance, isprovably optimal. However, there are many scenarios in which thatranking does not optimize for the users information need. Oneexample is when the user would be satisfied with some limitednumber of relevant documents, rather than needing all relevantdocuments. We show that in such a scenario, an attempt to returnmany relevant documents can actually reduce the chances of findingany relevant documents. We consider a number of information retrieval metrics from theliterature, including the rank of the first relevant result, the no metric that penalizes a system only for retrieving no relevantresults near the top, and the diversity of retrieved results whenqueries have multiple interpretations. We observe that given aprobabilistic model of relevance, it is appropriate to rank so asto directly optimize these metrics in expectation. While doing somay be computationally intractable, we show that a simple greedyoptimization algorithm that approximately optimizes the givenobjectives produces rankings for TREC queries that outperform thestandard approach based on the probability ranking principle. In this paper, we propose a novel Deep Reinforcement Learning framework for news recommendation. Online personalized news recommendation is a highly challenging problem due to the dynamic nature of news features and user preferences. Although some online recommendation models have been proposed to address the dynamic nature of news recommendation, these methods have three major issues. First, they only try to model current reward (e.g., Click Through Rate). Second, very few work consider to use user feedback other than click no click labels (e.g., how frequent user returns) to help improve recommendation. Third, these methods tend to keep recommending similar news to users, which may cause users to get bored. Therefore, to address the aforementioned challenges, we propose a Deep Q-Learning based recommendation framework, which can model future reward explicitly. We further consider user return pattern as a supplement to click no click label in order to capture more user feedback information. In addition, an effective exploration strategy is incorporated to find new attractive news for users. Extensive experiments are conducted on the offline dataset and online production environment of Chinese Bing News and have shown the superior performance of our methods. Contextual bandits are widely used in Internet services from news recommendation to advertising, and to Web search. Generalized linear models (logistical regression in particular) have demonstrated stronger performance than linear models in many applications where rewards are binary. However, most theoretical analyses on contextual bandits so far are on linear bandits. In this work, we propose an upper confidence bound based algorithm for generalized linear contextual bandits, which achieves an @math regret over @math rounds with @math dimensional feature vectors. This regret matches the minimax lower bound, up to logarithmic terms, and improves on the best previous result by a @math factor, assuming the number of arms is fixed. A key component in our analysis is to establish a new, sharp finite-sample confidence bound for maximum-likelihood estimates in generalized linear models, which may be of independent interest. We also analyze a simpler upper confidence bound algorithm, which is useful in practice, and prove it to have optimal regret for certain cases. We describe an algorithm for learning in the presence of multiple criteria. Our technique generalizes previous approaches in that it can learn optimal policies for all linear preference assignments over the multiple reward criteria at once. The algorithm can be viewed as an extension to standard reinforcement learning for MDPs where instead of repeatedly backing up maximal expected rewards, we back up the set of expected rewards that are maximal for some set of linear preferences (given by a weight vector, w). We present the algorithm along with a proof of correctness showing that our solution gives the optimal policy for any linear preference function. The solution reduces to the standard value iteration algorithm for a specific weight vector, w. In this paper we present a new document representation model based on implicit user feedback obtained from search engine queries. The main objective of this model is to achieve better results in non-supervised tasks, such as clustering and labeling, through the incorporation of usage data obtained from search engine queries. This type of model allows us to discover the motivations of users when visiting a certain document. The terms used in queries can provide a better choice of features, from the user's point of view, for summarizing the Web pages that were clicked from these queries. In this work we extend and formalize as "query model" an existing but not very well known idea of "query view" for document representation. Furthermore, we create a novel model based on "frequent query patterns" called the "query-set model". Our evaluation shows that both "query-based" models outperform the vector-space model when used for clustering and labeling documents in a website. In our experiments, the query-set model reduces by more than 90 the number of features needed to represent a set of documents and improves by over 90 the quality of the results. We believe that this can be explained because our model chooses better features and provides more accurate labels according to the user's expectations. In the stochastic knapsack problem, we are given a knapsack of size B, and a set of jobs whose sizes and rewards are drawn from a known probability distribution. However, we know the actual size and reward only when the job completes. How should we schedule jobs to maximize the expected total reward? We know O(1)-approximations when we assume that (i) rewards and sizes are independent random variables, and (ii) we cannot prematurely cancel jobs. What can we say when either or both of these assumptions are changed? The stochastic knapsack problem is of interest in its own right, but techniques developed for it are applicable to other stochastic packing problems. Indeed, ideas for this problem have been useful for budgeted learning problems, where one is given several arms which evolve in a specified stochastic fashion with each pull, and the goal is to pull the arms a total of B times to maximize the reward obtained. Much recent work on this problem focus on the case when the evolution of the arms follows a martingale, i.e., when the expected reward from the future is the same as the reward at the current state. What can we say when the rewards do not form a martingale? In this paper, we give constant-factor approximation algorithms for the stochastic knapsack problem with correlations and or cancellations, and also for budgeted learning problems where the martingale condition is not satisfied. Indeed, we can show that previously proposed LP relaxations have large integrality gaps. We propose new time-indexed LP relaxations, and convert the fractional solutions into distributions over strategies, and then use the LP values and the time ordering information from these strategies to devise a randomized adaptive scheduling algorithm. We hope our LP formulation and decomposition methods may provide a new way to address other correlated bandit problems with more general contexts. 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 study how to find plans that maximize the expected total utility for a given MDP, a planning objective that is important for decision making in high-stakes domains. The optimal actions can now depend on the total reward that has been accumulated so far in addition to the current state. We extend our previous work on functional value iteration from one-switch utility functions to all utility functions that can be approximated with piecewise linear utility functions (with and without exponential tails) by using functional value iteration to find a plan that maximizes the expected total utility for the approximate utility function. Functional value iteration does not maintain a value for every state but a value function that maps the total reward that has been accumulated so far into a value. We describe how functional value iteration represents these value functions in finite form, how it performs dynamic programming by manipulating these representations and what kinds of approximation guarantees it is able to make. We also apply it to a probabilistic blocksworld problem, a standard test domain for decision-theoretic planners. An “Interestingness Modeler” uses deep neural networks to learn deep semantic models (DSM) of “interestingness.” The DSM, consisting of two branches of deep neural networks or their convolutional versions, identifies and predicts target documents that would interest users reading source documents. The learned model observes, identifies, and detects naturally occurring signals of interestingness in click transitions between source and target documents derived from web browser logs. Interestingness is modeled with deep neural networks that map source-target document pairs to feature vectors in a latent space, trained on document transitions in view of a “context” and optional “focus” of source and target documents. Network parameters are learned to minimize distances between source documents and their corresponding “interesting” targets in that space. The resulting interestingness model has applicable uses, including, but not limited to, contextual entity searches, automatic text highlighting, prefetching documents of likely interest, automated content recommendation, automated advertisement placement, etc. We consider learning query and document similarities from a click-through bipartite graph with metadata on the nodes. The metadata contains multiple types of features of queries and documents. We aim to leverage both the click-through bipartite graph and the features to learn query-document, document-document, and query-query similarities. The challenges include how to model and learn the similarity functions based on the graph data. We propose solving the problems in a principled way. Specifically, we use two different linear mappings to project the queries and documents in two different feature spaces into the same latent space, and take the dot product in the latent space as their similarity. Query-query and document-document similarities can also be naturally defined as dot products in the latent space. We formalize the learning of similarity functions as learning of the mappings that maximize the similarities of the observed query-document pairs on the enriched click-through bipartite graph. When queries and documents have multiple types of features, the similarity function is defined as a linear combination of multiple similarity functions, each based on one type of features. We further solve the learning problem by using a new technique called Multi-view Partial Least Squares (M-PLS). The advantages include the global optimum which can be obtained through Singular Value Decomposition (SVD) and the capability of finding high quality similar queries. We conducted large scale experiments on enterprise search data and web search data. The experimental results on relevance ranking and similar query finding demonstrate that the proposed method works significantly better than the baseline methods. Search engine click logs provide an invaluable source of relevance information but this information is biased because we ignore which documents from the result list the users have actually seen before and after they clicked. Otherwise, we could estimate document relevance by simple counting. In this paper, we propose a set of assumptions on user browsing behavior that allows the estimation of the probability that a document is seen, thereby providing an unbiased estimate of document relevance. To train, test and compare our model to the best alternatives described in the Literature, we gather a large set of real data and proceed to an extensive cross-validation experiment. Our solution outperforms very significantly all previous models. As a side effect, we gain insight into the browsing behavior of users and we can compare it to the conclusions of an eye-tracking experiments by [12]. In particular, our findings confirm that a user almost always see the document directly after a clicked document. They also explain why documents situated just after a very relevant document are clicked more often.