A Relative Exponential Weighing Algorithm for Adversarial Utility-based Dueling Bandits

We study the K-armed dueling bandit problem which is a variation of the classical Multi-Armed Bandit (MAB) problem in which the learner receives only relative feedback about the selected pairs of arms. We propose a new algorithm called Relative Exponential-weight algorithm for Exploration and Exploitation (REX3) to handle the adversarial utility-based formulation of this problem. This algorithm is a non-trivial extension of the Exponential-weight algorithm for Exploration and Exploitation (EXP3) algorithm. We prove a finite time expected regret upper bound of order O(sqrt(K ln(K)T)) for this algorithm and a general lower bound of order omega(sqrt(KT)). At the end, we provide experimental results using real data from information retrieval applications

Relative Upper Confidence Bound for the K-Armed Dueling Bandit Problem

This paper proposes a new method for the K-armed dueling bandit problem, a variation on the regular K-armed bandit problem that offers only relative feedback about pairs of arms. Our approach extends the Upper Confidence Bound algorithm to the relative setting by using estimates of the pairwise probabilities to select a promising arm and applying Upper Confidence Bound with the winner as a benchmark. We prove a finite-time regret bound of order O(log t). In addition, our empirical results using real data from an information retrieval application show that it greatly outperforms the state of the art.Comment: 13 pages, 6 figure

Regret Bounds and Regimes of Optimality for User-User and Item-Item Collaborative Filtering

We consider an online model for recommendation systems, with each user being recommended an item at each time-step and providing 'like' or 'dislike' feedback. Each user may be recommended a given item at most once. A latent variable model specifies the user preferences: both users and items are clustered into types. All users of a given type have identical preferences for the items, and similarly, items of a given type are either all liked or all disliked by a given user. We assume that the matrix encoding the preferences of each user type for each item type is randomly generated; in this way, the model captures structure in both the item and user spaces, the amount of structure depending on the number of each of the types. The measure of performance of the recommendation system is the expected number of disliked recommendations per user, defined as expected regret. We propose two algorithms inspired by user-user and item-item collaborative filtering (CF), modified to explicitly make exploratory recommendations, and prove performance guarantees in terms of their expected regret. For two regimes of model parameters, with structure only in item space or only in user space, we prove information-theoretic lower bounds on regret that match our upper bounds up to logarithmic factors. Our analysis elucidates system operating regimes in which existing CF algorithms are nearly optimal.Comment: 51 page

A quadratic lower bound for Rocchio’s similarity-based relevance feedback algorithm with a fixed query updating factor

Rocchio’s similarity-based relevance feedback algorithm, one of the most important query reformation methods in information retrieval, is essentially an adaptive supervised learning algorithm from examples. In practice, Rocchio’s algorithm often uses a fixed query updating factor. When this is the case, we strengthen the linear Ω(n) lower bound obtained by Chen and Zhu (Inf. Retr. 5:61–86, 2002) and prove that Rocchio’s algorithm makes Ω(k(n−k)) mistakes in searching for a collection of documents represented by a monotone disjunction of k relevant features over the n-dimensional binary vector space {0,1}n, when the inner product similarity measure is used. A quadratic lower bound is obtained when k is linearly proportional to n. We also prove an O(k(n−k)3) upper bound for Rocchio’s algorithm with the inner product similarity measure in searching for such a collection of documents with a constant query updating factor and a zero classification threshold