arXiv subjects

Claudio Gentile

Publications and source records attributed to Claudio Gentile.

50 records · Page 3Linked to original sources

arXiv2016

Graph Clustering Bandits for Recommendation

We investigate an efficient context-dependent clustering technique for recommender systems based on exploration-exploitation strategies through multi-armed bandits over multiple users. Our algorithm dynamically groups users based on their observed behavioral similarity during a sequence of logged activities. In doing so, the algorithm reacts to the currently served user by shaping clusters around him/her but, at the same time, it explores the generation of clusters over users which are not currently engaged. We motivate the effectiveness of this clustering policy, and provide an extensive empirical analysis on real-world datasets, showing scalability and improved prediction performance over state-of-the-art methods for sequential clustering of users in multi-armed bandit scenarios.

stat.ML↗

arXiv2014

Nonstochastic Multi-Armed Bandits with Graph-Structured Feedback

We present and study a partial-information model of online learning, where a decision maker repeatedly chooses from a finite set of actions, and observes some subset of the associated losses. This naturally models several situations where the losses of different actions are related, and knowing the loss of one action provides information on the loss of other actions. Moreover, it generalizes and interpolates between the well studied full-information setting (where all losses are revealed) and the bandit setting (where only the loss of the action chosen by the player is revealed). We provide several algorithms addressing different variants of our setting, and provide tight regret bounds depending on combinatorial properties of the information feedback structure.

cs.LG↗

arXiv2014

Online Clustering of Bandits

We introduce a novel algorithmic approach to content recommendation based on adaptive clustering of exploration-exploitation ("bandit") strategies. We provide a sharp regret analysis of this algorithm in a standard stochastic noise setting, demonstrate its scalability properties, and prove its effectiveness on a number of artificial and real-world datasets. Our experiments show a significant increase in prediction performance over state-of-the-art methods for bandit problems.

cs.LG↗

arXiv2013

A Gang of Bandits

Multi-armed bandit problems are receiving a great deal of attention because they adequately formalize the exploration-exploitation trade-offs arising in several industrially relevant applications, such as online advertisement and, more generally, recommendation systems. In many cases, however, these applications have a strong social component, whose integration in the bandit algorithm could lead to a dramatic performance increase. For instance, we may want to serve content to a group of users by taking advantage of an underlying network of social relationships among them. In this paper, we introduce novel algorithmic approaches to the solution of such networked bandit problems. More specifically, we design and analyze a global strategy which allocates a bandit algorithm to each network node (user) and allows it to "share" signals (contexts and payoffs) with the neghboring nodes. We then derive two more scalable variants of this strategy based on different ways of clustering the graph nodes. We experimentally compare the algorithm and its variants to state-of-the-art methods for contextual bandits that do not use the relational information. Our experiments, carried out on synthetic and real-world datasets, show a marked increase in prediction performance obtained by exploiting the network structure.

cs.LG↗

arXiv2013

From Bandits to Experts: A Tale of Domination and Independence

We consider the partial observability model for multi-armed bandits, introduced by Mannor and Shamir. Our main result is a characterization of regret in the directed observability model in terms of the dominating and independence numbers of the observability graph. We also show that in the undirected case, the learner can achieve optimal regret without even accessing the observability graph before selecting an action. Both results are shown using variants of the Exp3 algorithm operating on the observability graph in a time-efficient manner.

cs.LG↗

arXiv2013

Online Similarity Prediction of Networked Data from Known and Unknown Graphs

We consider online similarity prediction problems over networked data. We begin by relating this task to the more standard class prediction problem, showing that, given an arbitrary algorithm for class prediction, we can construct an algorithm for similarity prediction with "nearly" the same mistake bound, and vice versa. After noticing that this general construction is computationally infeasible, we target our study to {\em feasible} similarity prediction algorithms on networked data. We initially assume that the network structure is {\em known} to the learner. Here we observe that Matrix Winnow \cite{w07} has a near-optimal mistake guarantee, at the price of cubic prediction time per round. This motivates our effort for an efficient implementation of a Perceptron algorithm with a weaker mistake guarantee but with only poly-logarithmic prediction time. Our focus then turns to the challenging case of networks whose structure is initially {\em unknown} to the learner. In this novel setting, where the network structure is only incrementally revealed, we obtain a mistake-bounded algorithm with a quadratic prediction time per round.

cs.LG↗

arXiv2013

A Linear Time Active Learning Algorithm for Link Classification -- Full Version --

We present very efficient active learning algorithms for link classification in signed networks. Our algorithms are motivated by a stochastic model in which edge labels are obtained through perturbations of a initial sign assignment consistent with a two-clustering of the nodes. We provide a theoretical analysis within this model, showing that we can achieve an optimal (to whithin a constant factor) number of mistakes on any graph G = (V,E) such that |E| = Ω(|V|^{3/2}) by querying O(|V|^{3/2}) edge labels. More generally, we show an algorithm that achieves optimality to within a factor of O(k) by querying at most order of |V| + (|V|/k)^{3/2} edge labels. The running time of this algorithm is at most of order |E| + |V|\log|V|.

cs.LG↗

arXiv2013

A Correlation Clustering Approach to Link Classification in Signed Networks -- Full Version --

Motivated by social balance theory, we develop a theory of link classification in signed networks using the correlation clustering index as measure of label regularity. We derive learning bounds in terms of correlation clustering within three fundamental transductive learning settings: online, batch and active. Our main algorithmic contribution is in the active setting, where we introduce a new family of efficient link classifiers based on covering the input graph with small circuits. These are the first active algorithms for link classification with mistake bounds that hold for arbitrary signed networks.

cs.LG↗

arXiv2013

See the Tree Through the Lines: The Shazoo Algorithm -- Full Version --

Predicting the nodes of a given graph is a fascinating theoretical problem with applications in several domains. Since graph sparsification via spanning trees retains enough information while making the task much easier, trees are an important special case of this problem. Although it is known how to predict the nodes of an unweighted tree in a nearly optimal way, in the weighted case a fully satisfactory algorithm is not available yet. We fill this hole and introduce an efficient node predictor, Shazoo, which is nearly optimal on any weighted tree. Moreover, we show that Shazoo can be viewed as a common nontrivial generalization of both previous approaches for unweighted trees and weighted lines. Experiments on real-world datasets confirm that Shazoo performs well in that it fully exploits the structure of the input tree, and gets very close to (and sometimes better than) less scalable energy minimization methods.

cs.LG↗

arXiv2013

Active Learning on Trees and Graphs

We investigate the problem of active learning on a given tree whose nodes are assigned binary labels in an adversarial way. Inspired by recent results by Guillory and Bilmes, we characterize (up to constant factors) the optimal placement of queries so to minimize the mistakes made on the non-queried nodes. Our query selection algorithm is extremely efficient, and the optimal number of mistakes on the non-queried nodes is achieved by a simple and efficient mincut classifier. Through a simple modification of the query selection algorithm we also show optimality (up to constant factors) with respect to the trade-off between number of queries and number of mistakes on non-queried nodes. By using spanning trees, our algorithms can be efficiently applied to general graphs, although the problem of finding optimal and efficient active learning algorithms for general graphs remains open. Towards this end, we provide a lower bound on the number of mistakes made on arbitrary graphs by any active learning algorithm using a number of queries which is up to a constant fraction of the graph size.

cs.LG↗

arXiv2013

On Multilabel Classification and Ranking with Partial Feedback

We present a novel multilabel/ranking algorithm working in partial information settings. The algorithm is based on 2nd-order descent methods, and relies on upper-confidence bounds to trade-off exploration and exploitation. We analyze this algorithm in a partial adversarial setting, where covariates can be adversarial, but multilabel probabilities are ruled by (generalized) linear models. We show O(T^{1/2} log T) regret bounds, which improve in several ways on the existing results. We test the effectiveness of our upper-confidence scheme by contrasting against full-information baselines on real-world multilabel datasets, often obtaining comparable performance.

cs.LG↗

arXiv2012

Random Spanning Trees and the Prediction of Weighted Graphs

We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be characterized (up to logarithmic factors) by the cutsize of a random spanning tree of the graph. The cutsize is induced by the unknown adversarial labeling of the graph nodes. In deriving our characterization, we obtain a simple randomized algorithm achieving in expectation the optimal mistake bound on any polynomially connected weighted graph. Our algorithm draws a random spanning tree of the original graph and then predicts the nodes of this tree in constant expected amortized time and linear space. Experiments on real-world datasets show that our method compares well to both global (Perceptron) and local (label propagation) methods, while being generally faster in practice.

cs.LG↗

arXiv2011

Bandits with an Edge

We consider a bandit problem over a graph where the rewards are not directly observed. Instead, the decision maker can compare two nodes and receive (stochastic) information pertaining to the difference in their value. The graph structure describes the set of possible comparisons. Consequently, comparing between two nodes that are relatively far requires estimating the difference between every pair of nodes on the path between them. We analyze this problem from the perspective of sample complexity: How many queries are needed to find an approximately optimal node with probability more than $1-δ$ in the PAC setup? We show that the topology of the graph plays a crucial in defining the sample complexity: graphs with a low diameter have a much better sample complexity.

cs.LG↗

arXiv2011

A Maximal Large Deviation Inequality for Sub-Gaussian Variables

In this short note we prove a maximal concentration lemma for sub-Gaussian random variables stating that for independent sub-Gaussian random variables we have \[P<(\max_{1\le i\le N}S_{i}>ε>) \le\exp<(-\frac{1}{N^2}\sum_{i=1}^{N}\frac{ε^{2}}{2σ_{i}^{2}}>), \] where $S_i$ is the sum of $i$ zero mean independent sub-Gaussian random variables and $σ_i$ is the variance of the $i$th random variable.

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