Claudio Gentile

Robert Istvan Busa-Fekete, Heejin Choi, Travis Dick et al.

We consider the problem of Learning from Label Proportions (LLP), a weakly supervised classification setup where instances are grouped into "bags", and only the frequency of class labels at each bag is available. Albeit, the objective of the learner is to achieve low task loss at an individual instance level. Here we propose Easyllp: a flexible and simple-to-implement debiasing approach based on aggregate labels, which operates on arbitrary loss functions. Our technique allows us to accurately estimate the expected loss of an arbitrary model at an individual level. We showcase the flexibility of our approach by applying it to popular learning frameworks, like Empirical Risk Minimization (ERM) and Stochastic Gradient Descent (SGD) with provable guarantees on instance level performance. More concretely, we exhibit a variance reduction technique that makes the quality of LLP learning deteriorate only by a factor of k (k being bag size) in both ERM and SGD setups, as compared to full supervision. Finally, we validate our theoretical results on multiple datasets demonstrating our algorithm performs as well or better than previous LLP approaches in spite of its simplicity.

Sohan Rudra, Saksham Goel, Anirban Santara et al.

Object-goal navigation (Object-nav) entails searching, recognizing and navigating to a target object. Object-nav has been extensively studied by the Embodied-AI community, but most solutions are often restricted to considering static objects (e.g., television, fridge, etc.). We propose a modular framework for object-nav that is able to efficiently search indoor environments for not just static objects but also movable objects (e.g. fruits, glasses, phones, etc.) that frequently change their positions due to human intervention. Our contextual-bandit agent efficiently explores the environment by showing optimism in the face of uncertainty and learns a model of the likelihood of spotting different objects from each navigable location. The likelihoods are used as rewards in a weighted minimum latency solver to deduce a trajectory for the robot. We evaluate our algorithms in two simulated environments and a real-world setting, to demonstrate high sample efficiency and reliability.

Aldo Pacchiano, Christoph Dann, Claudio Gentile

We consider model selection for sequential decision making in stochastic environments with bandit feedback, where a meta-learner has at its disposal a pool of base learners, and decides on the fly which action to take based on the policies recommended by each base learner. Model selection is performed by regret balancing but, unlike the recent literature on this subject, we do not assume any prior knowledge about the base learners like candidate regret guarantees; instead, we uncover these quantities in a data-driven manner. The meta-learner is therefore able to leverage the realized regret incurred by each base learner for the learning environment at hand (as opposed to the expected regret), and single out the best such regret. We design two model selection algorithms operating with this more ambitious notion of regret and, besides proving model selection guarantees via regret balancing, we experimentally demonstrate the compelling practical benefits of dealing with actual regrets instead of candidate regret bounds.

Aldo Pacchiano, Christoph Dann, Claudio Gentile

We study the problem of model selection in bandit scenarios in the presence of nested policy classes, with the goal of obtaining simultaneous adversarial and stochastic ("best of both worlds") high-probability regret guarantees. Our approach requires that each base learner comes with a candidate regret bound that may or may not hold, while our meta algorithm plays each base learner according to a schedule that keeps the base learner's candidate regret bounds balanced until they are detected to violate their guarantees. We develop careful mis-specification tests specifically designed to blend the above model selection criterion with the ability to leverage the (potentially benign) nature of the environment. We recover the model selection guarantees of the CORRAL algorithm for adversarial environments, but with the additional benefit of achieving high probability regret bounds, specifically in the case of nested adversarial linear bandits. More importantly, our model selection results also hold simultaneously in stochastic environments under gap assumptions. These are the first theoretical results that achieve best of both world (stochastic and adversarial) guarantees while performing model selection in (linear) bandit scenarios.

Francesco Bonchi, Claudio Gentile, Francesco Paolo Nerini et al.

We present GERN, a novel scalable framework for training GNNs in node classification tasks, based on effective resistance, a standard tool in spectral graph theory. Our method progressively refines the GNN weights on a sequence of random spanning trees suitably transformed into path graphs which, despite their simplicity, are shown to retain essential topological and node information of the original input graph. The sparse nature of these path graphs substantially lightens the computational burden of GNN training. This not only enhances scalability but also improves accuracy in subsequent test phases, especially under small training set regimes, which are of great practical importance, as in many real-world scenarios labels may be hard to obtain. In these settings, our framework yields very good results as it effectively counters the training deterioration caused by overfitting when the training set is small. Our method also addresses common issues like over-squashing and over-smoothing while avoiding under-reaching phenomena. Although our framework is flexible and can be deployed in several types of GNNs, in this paper we focus on graph convolutional networks and carry out an extensive experimental investigation on a number of real-world graph benchmarks, where we achieve simultaneous improvement of training speed and test accuracy over a wide pool of representative baselines.

Alekh Agarwal, Claudio Gentile, Teodor V. Marinov

We study contextual bandit (CB) problems, where the user can sometimes respond with the best action in a given context. Such an interaction arises, for example, in text prediction or autocompletion settings, where a poor suggestion is simply ignored and the user enters the desired text instead. Crucially, this extra feedback is user-triggered on only a subset of the contexts. We develop a new framework to leverage such signals, while being robust to their biased nature. We also augment standard CB algorithms to leverage the signal, and show improved regret guarantees for the resulting algorithms under a variety of conditions on the helpfulness of and bias inherent in this feedback.

Stephen Pasteris, Fabio Vitale, Mark Herbster et al.

We investigate the problem of online collaborative filtering under no-repetition constraints, whereby users need to be served content in an online fashion and a given user cannot be recommended the same content item more than once. We start by designing and analyzing an algorithm that works under biclustering assumptions on the user-item preference matrix, and show that this algorithm exhibits an optimal regret guarantee, while being fully adaptive, in that it is oblivious to any prior knowledge about the sequence of users, the universe of items, as well as the biclustering parameters of the preference matrix. We then propose a more robust version of this algorithm which operates with general matrices. Also this algorithm is parameter free, and we prove regret guarantees that scale with the amount by which the preference matrix deviates from a biclustered structure. To our knowledge, these are the first results on online collaborative filtering that hold at this level of generality and adaptivity under no-repetition constraints. Finally, we complement our theoretical findings with simple experiments on real-world datasets aimed at both validating the theory and empirically comparing to standard baselines. This comparison shows the competitive advantage of our approach over these baselines.

Lorne Applebaum, Robert Busa-Fekete, August Y. Chen et al.

We address the problem of training conversion prediction models in advertising domains under privacy constraints, where direct links between ad clicks and conversions are unavailable. Motivated by privacy-preserving browser APIs and the deprecation of third-party cookies, we study a setting where the learner observes a sequence of clicks and a sequence of conversions, but can only link a conversion to a set of candidate clicks (an attribution set) rather than a unique source. We formalize this as learning from attribution sets generated by an oblivious adversary equipped with a prior distribution over the candidates. Despite the lack of explicit labels, we construct an unbiased estimator of the population loss from these coarse signals via a novel approach. Leveraging this estimator, we show that Empirical Risk Minimization achieves generalization guarantees that scale with the informativeness of the prior and is also robust against estimation errors in the prior, despite complex dependencies among attribution sets. Simple empirical evaluations on standard datasets suggest our unbiased approach significantly outperforms common industry heuristics, particularly in regimes where attribution sets are large or overlapping.

Robert Istvan Busa-Fekete, Julian Zimmert, Anne Xiangyi Zheng et al.

The quality of machine learning models depends heavily on their training data. Selecting high-quality, diverse training sets for large language models (LLMs) is a difficult task, due to the lack of cheap and reliable quality metrics. While querying existing LLMs for document quality is common, this is not scalable to the large number (billions) of documents used in training. Instead, practitioners often use classifiers trained on sparse quality signals. In this paper, we propose a text-embedding-based hierarchical clustering approach that adaptively selects the documents to be evaluated by the LLM to estimate cluster quality. We prove that our method is query efficient: under the assumption that the hierarchical clustering contains a subtree such that each leaf cluster in the tree is pure enough (i.e., it mostly contains either only good or only bad documents), with high probability, the method can correctly predict the quality of each document after querying a small number of documents. The number of such documents is proportional to the size of the smallest subtree with (almost) pure leaves, without the algorithm knowing this subtree in advance. Furthermore, in a comprehensive experimental study, we demonstrate the benefits of our algorithm compared to other classifier-based filtering methods.

Robert Busa-Fekete, Travis Dick, Claudio Gentile et al.

We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the goal is still to achieve small regret at the level of individual examples. We give results on the sample complexity of LLP under square loss, showing that our sample complexity is essentially optimal. From an algorithmic viewpoint, we rely on carefully designed variants of Empirical Risk Minimization, and Stochastic Gradient Descent algorithms, combined with ad hoc variance reduction techniques. On one hand, our theoretical results improve in important ways on the existing literature on LLP, specifically in the way the sample complexity depends on the bag size. On the other hand, we validate our algorithmic solutions on several datasets, demonstrating improved empirical performance (better accuracy for less samples) against recent baselines.

Alberto Caprara, Fabio Furini, Claudio Gentile et al.

We prove the \textbf{NP}-hardness, using Karp reductions, of some problems related to the correlation polytope and its corresponding cone, spanned by all of the $n\times n$ rank-one matrices over $\{0,1\}$. The problems are: membership, rank of the decomposition, and a ``relaxed rank'' obtained from relaxing the zero-norm expression for the rank to an $\ell_1$ norm. While membership and rank are natural problems for any matrix cone, the relaxed rank problem occurs in some signal processing and statistical applications.

Lorne Applebaum, Travis Dick, Claudio Gentile et al.

Motivated by problems in online advertising, we address the task of Learning from Label Proportions (LLP). In this partially-supervised setting, training data consists of groups of examples, termed bags, for which we only observe the average label value. The main goal, however, remains the design of a predictor for the labels of individual examples. We introduce a novel and versatile low-variance de-biasing methodology to learn from aggregate label information, significantly advancing the state of the art in LLP. Our approach exhibits remarkable flexibility, seamlessly accommodating a broad spectrum of practically relevant loss functions across both binary and multi-class classification settings. By carefully combining our estimators with standard techniques, we substantially improve sample complexity guarantees for a large class of losses of practical relevance. We also empirically validate the efficacy of our proposed approach across a diverse array of benchmark datasets, demonstrating compelling empirical advantages over standard baselines.

Róbert István Busa-Fekete, Travis Dick, Claudio Gentile et al.

We propose reconstruction advantage measures to audit label privatization mechanisms. A reconstruction advantage measure quantifies the increase in an attacker's ability to infer the true label of an unlabeled example when provided with a private version of the labels in a dataset (e.g., aggregate of labels from different users or noisy labels output by randomized response), compared to an attacker that only observes the feature vectors, but may have prior knowledge of the correlation between features and labels. We consider two such auditing measures: one additive, and one multiplicative. These incorporate previous approaches taken in the literature on empirical auditing and differential privacy. The measures allow us to place a variety of proposed privatization schemes -- some differentially private, some not -- on the same footing. We analyze these measures theoretically under a distributional model which encapsulates reasonable adversarial settings. We also quantify their behavior empirically on real and simulated prediction tasks. Across a range of experimental settings, we find that differentially private schemes dominate or match the privacy-utility tradeoff of more heuristic approaches.

Guanghui Wang, Zihao Hu, Claudio Gentile et al.

First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias, plays a critical role in understanding the generalization capabilities of optimization algorithms. Recent research has revealed that in separable binary classification tasks gradient-descent-based methods exhibit an implicit bias for the $\ell_2$-maximal margin classifier. Similarly, generic optimization methods, such as mirror descent and steepest descent, have been shown to converge to maximal margin classifiers defined by alternative geometries. While gradient-descent-based algorithms provably achieve fast implicit bias rates, corresponding rates in the literature for generic optimization methods are relatively slow. To address this limitation, we present a series of state-of-the-art implicit bias rates for mirror descent and steepest descent algorithms. Our primary technique involves transforming a generic optimization algorithm into an online optimization dynamic that solves a regularized bilinear game, providing a unified framework for analyzing the implicit bias of various optimization methods. Our accelerated rates are derived by leveraging the regret bounds of online learning algorithms within this game framework. We then show the flexibility of this framework by analyzing the implicit bias in adversarial training, and again obtain significantly improved convergence rates.

Claudio Gentile, Zhilei Wang, Tong Zhang

We consider a batch active learning scenario where the learner adaptively issues batches of points to a labeling oracle. Sampling labels in batches is highly desirable in practice due to the smaller number of interactive rounds with the labeling oracle (often human beings). However, batch active learning typically pays the price of a reduced adaptivity, leading to suboptimal results. In this paper we propose a solution which requires a careful trade off between the informativeness of the queried points and their diversity. We theoretically investigate batch active learning in the practically relevant scenario where the unlabeled pool of data is available beforehand ({\em pool-based} active learning). We analyze a novel stage-wise greedy algorithm and show that, as a function of the label complexity, the excess risk of this algorithm matches the known minimax rates in standard statistical learning settings. Our results also exhibit a mild dependence on the batch size. These are the first theoretical results that employ careful trade offs between informativeness and diversity to rigorously quantify the statistical performance of batch active learning in the pool-based scenario.

Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni et al.

We investigate a nonstochastic bandit setting in which the loss of an action is not immediately charged to the player, but rather spread over the subsequent rounds in an adversarial way. The instantaneous loss observed by the player at the end of each round is then a sum of many loss components of previously played actions. This setting encompasses as a special case the easier task of bandits with delayed feedback, a well-studied framework where the player observes the delayed losses individually. Our first contribution is a general reduction transforming a standard bandit algorithm into one that can operate in the harder setting: We bound the regret of the transformed algorithm in terms of the stability and regret of the original algorithm. Then, we show that the transformation of a suitably tuned FTRL with Tsallis entropy has a regret of order $\sqrt{(d+1)KT}$, where $d$ is the maximum delay, $K$ is the number of arms, and $T$ is the time horizon. Finally, we show that our results cannot be improved in general by exhibiting a matching (up to a log factor) lower bound on the regret of any algorithm operating in this setting.

Gui Citovsky, Giulia DeSalvo, Claudio Gentile et al.

The ability to train complex and highly effective models often requires an abundance of training data, which can easily become a bottleneck in cost, time, and computational resources. Batch active learning, which adaptively issues batched queries to a labeling oracle, is a common approach for addressing this problem. The practical benefits of batch sampling come with the downside of less adaptivity and the risk of sampling redundant examples within a batch -- a risk that grows with the batch size. In this work, we analyze an efficient active learning algorithm, which focuses on the large batch setting. In particular, we show that our sampling method, which combines notions of uncertainty and diversity, easily scales to batch sizes (100K-1M) several orders of magnitude larger than used in previous studies and provides significant improvements in model training efficiency compared to recent baselines. Finally, we provide an initial theoretical analysis, proving label complexity guarantees for a related sampling method, which we show is approximately equivalent to our sampling method in specific settings.

Dylan J. Foster, Claudio Gentile, Mehryar Mohri et al.

A major research direction in contextual bandits is to develop algorithms that are computationally efficient, yet support flexible, general-purpose function approximation. Algorithms based on modeling rewards have shown strong empirical performance, but typically require a well-specified model, and can fail when this assumption does not hold. Can we design algorithms that are efficient and flexible, yet degrade gracefully in the face of model misspecification? We introduce a new family of oracle-efficient algorithms for $\varepsilon$-misspecified contextual bandits that adapt to unknown model misspecification -- both for finite and infinite action settings. Given access to an online oracle for square loss regression, our algorithm attains optimal regret and -- in particular -- optimal dependence on the misspecification level, with no prior knowledge. Specializing to linear contextual bandits with infinite actions in $d$ dimensions, we obtain the first algorithm that achieves the optimal $O(d\sqrt{T} + \varepsilon\sqrt{d}T)$ regret bound for unknown misspecification level $\varepsilon$. On a conceptual level, our results are enabled by a new optimization-based perspective on the regression oracle reduction framework of Foster and Rakhlin, which we anticipate will find broader use.

Anirban Santara, Claudio Gentile, Gaurav Aggarwal et al.

Motivated by problems of learning to rank long item sequences, we introduce a variant of the cascading bandit model that considers flexible length sequences with varying rewards and losses. We formulate two generative models for this problem within the generalized linear setting, and design and analyze upper confidence algorithms for it. Our analysis delivers tight regret bounds which, when specialized to vanilla cascading bandits, results in sharper guarantees than previously available in the literature. We evaluate our algorithms on a number of real-world datasets, and show significantly improved empirical performance as compared to known cascading bandit baselines.

Pranjal Awasthi, Christoph Dann, Claudio Gentile et al.

We investigate the problem of active learning in the streaming setting in non-parametric regimes, where the labels are stochastically generated from a class of functions on which we make no assumptions whatsoever. We rely on recently proposed Neural Tangent Kernel (NTK) approximation tools to construct a suitable neural embedding that determines the feature space the algorithm operates on and the learned model computed atop. Since the shape of the label requesting threshold is tightly related to the complexity of the function to be learned, which is a-priori unknown, we also derive a version of the algorithm which is agnostic to any prior knowledge. This algorithm relies on a regret balancing scheme to solve the resulting online model selection problem, and is computationally efficient. We prove joint guarantees on the cumulative regret and number of requested labels which depend on the complexity of the labeling function at hand. In the linear case, these guarantees recover known minimax results of the generalization error as a function of the label complexity in a standard statistical learning setting.

Aldo Pacchiano, Christoph Dann, Claudio Gentile et al.

We propose a simple model selection approach for algorithms in stochastic bandit and reinforcement learning problems. As opposed to prior work that (implicitly) assumes knowledge of the optimal regret, we only require that each base algorithm comes with a candidate regret bound that may or may not hold during all rounds. In each round, our approach plays a base algorithm to keep the candidate regret bounds of all remaining base algorithms balanced, and eliminates algorithms that violate their candidate bound. We prove that the total regret of this approach is bounded by the best valid candidate regret bound times a multiplicative factor. This factor is reasonably small in several applications, including linear bandits and MDPs with nested function classes, linear bandits with unknown misspecification, and LinUCB applied to linear bandits with different confidence parameters. We further show that, under a suitable gap-assumption, this factor only scales with the number of base algorithms and not their complexity when the number of rounds is large enough. Finally, unlike recent efforts in model selection for linear stochastic bandits, our approach is versatile enough to also cover cases where the context information is generated by an adversarial environment, rather than a stochastic one.

Leonardo Cella, Claudio Gentile, Massimiliano Pontil

Motivated by a natural problem in online model selection with bandit information, we introduce and analyze a best arm identification problem in the rested bandit setting, wherein arm expected losses decrease with the number of times the arm has been played. The shape of the expected loss functions is similar across arms, and is assumed to be available up to unknown parameters that have to be learned on the fly. We define a novel notion of regret for this problem, where we compare to the policy that always plays the arm having the smallest expected loss at the end of the game. We analyze an arm elimination algorithm whose regret vanishes as the time horizon increases. The actual rate of convergence depends in a detailed way on the postulated functional form of the expected losses. Unlike known model selection efforts in the recent bandit literature, our algorithm exploits the specific structure of the problem to learn the unknown parameters of the expected loss function so as to identify the best arm as quickly as possible. We complement our analysis with a lower bound, indicating strengths and limitations of the proposed solution.

Corinna Cortes, Giulia DeSalvo, Claudio Gentile et al.

We present a new active learning algorithm that adaptively partitions the input space into a finite number of regions, and subsequently seeks a distinct predictor for each region, both phases actively requesting labels. We prove theoretical guarantees for both the generalization error and the label complexity of our algorithm, and analyze the number of regions defined by the algorithm under some mild assumptions. We also report the results of an extensive suite of experiments on several real-world datasets demonstrating substantial empirical benefits over existing single-region and non-adaptive region-based active learning baselines.

Fabio Vitale, Anand Rajagopalan, Claudio Gentile

We investigate active learning by pairwise similarity over the leaves of trees originating from hierarchical clustering procedures. In the realizable setting, we provide a full characterization of the number of queries needed to achieve perfect reconstruction of the tree cut. In the non-realizable setting, we rely on known important-sampling procedures to obtain regret and query complexity bounds. Our algorithms come with theoretical guarantees on the statistical error and, more importantly, lend themselves to linear-time implementations in the relevant parameters of the problem. We discuss such implementations, prove running time guarantees for them, and present preliminary experiments on real-world datasets showing the compelling practical performance of our algorithms as compared to both passive learning and simple active learning baselines.

Fabio Vitale, Nikos Parotsidis, Claudio Gentile

A reciprocal recommendation problem is one where the goal of learning is not just to predict a user's preference towards a passive item (e.g., a book), but to recommend the targeted user on one side another user from the other side such that a mutual interest between the two exists. The problem thus is sharply different from the more traditional items-to-users recommendation, since a good match requires meeting the preferences of both users. We initiate a rigorous theoretical investigation of the reciprocal recommendation task in a specific framework of sequential learning. We point out general limitations, formulate reasonable assumptions enabling effective learning and, under these assumptions, we design and analyze a computationally efficient algorithm that uncovers mutual likes at a pace comparable to those achieved by a clearvoyant algorithm knowing all user preferences in advance. Finally, we validate our algorithm against synthetic and real-world datasets, showing improved empirical performance over simple baselines.

Stephen Pasteris, Fabio Vitale, Claudio Gentile et al.

Pairwise clustering, in general, partitions a set of items via a known similarity function. In our treatment, clustering is modeled as a transductive prediction problem. Thus rather than beginning with a known similarity function, the function instead is hidden and the learner only receives a random sample consisting of a subset of the pairwise similarities. An additional set of pairwise side-information may be given to the learner, which then determines the inductive bias of our algorithms. We measure performance not based on the recovery of the hidden similarity function, but instead on how well we classify each item. We give tight bounds on the number of misclassifications. We provide two algorithms. The first algorithm SACA is a simple agglomerative clustering algorithm which runs in near linear time, and which serves as a baseline for our analyses. Whereas the second algorithm, RGCA, enables the incorporation of side-information which may lead to improved bounds at the cost of a longer running time.

Nicolò Cesa-Bianchi, Claudio Gentile, Gábor Lugosi et al.

Boltzmann exploration is a classic strategy for sequential decision-making under uncertainty, and is one of the most standard tools in Reinforcement Learning (RL). Despite its widespread use, there is virtually no theoretical understanding about the limitations or the actual benefits of this exploration scheme. Does it drive exploration in a meaningful way? Is it prone to misidentifying the optimal actions or spending too much time exploring the suboptimal ones? What is the right tuning for the learning rate? In this paper, we address several of these questions in the classic setup of stochastic multi-armed bandits. One of our main results is showing that the Boltzmann exploration strategy with any monotone learning-rate sequence will induce suboptimal behavior. As a remedy, we offer a simple non-monotone schedule that guarantees near-optimal performance, albeit only when given prior access to key problem parameters that are typically not available in practical situations (like the time horizon $T$ and the suboptimality gap $Δ$). More importantly, we propose a novel variant that uses different learning rates for different arms, and achieves a distribution-dependent regret bound of order $\frac{K\log^2 T}Δ$ and a distribution-independent bound of order $\sqrt{KT}\log K$ without requiring such prior knowledge. To demonstrate the flexibility of our technique, we also propose a variant that guarantees the same performance bounds even if the rewards are heavy-tailed.

Corinna Cortes, Giulia DeSalvo, Claudio Gentile et al.

We present an extensive study of the key problem of online learning where algorithms are allowed to abstain from making predictions. In the adversarial setting, we show how existing online algorithms and guarantees can be adapted to this problem. In the stochastic setting, we first point out a bias problem that limits the straightforward extension of algorithms such as UCB-N to time-varying feedback graphs, as needed in this context. Next, we give a new algorithm, UCB-GT, that exploits historical data and is adapted to time-varying feedback graphs. We show that this algorithm benefits from more favorable regret guarantees than a possible, but limited, extension of UCB-N. We further report the results of a series of experiments demonstrating that UCB-GT largely outperforms that extension of UCB-N, as well as more standard baselines.

Nicolò Cesa-Bianchi, Pierre Gaillard, Claudio Gentile et al.

We investigate contextual online learning with nonparametric (Lipschitz) comparison classes under different assumptions on losses and feedback information. For full information feedback and Lipschitz losses, we design the first explicit algorithm achieving the minimax regret rate (up to log factors). In a partial feedback model motivated by second-price auctions, we obtain algorithms for Lipschitz and semi-Lipschitz losses with regret bounds improving on the known bounds for standard bandit feedback. Our analysis combines novel results for contextual second-price auctions with a novel algorithmic approach based on chaining. When the context space is Euclidean, our chaining approach is efficient and delivers an even better regret bound.

Claudio Gentile, Shuai Li, Purushottam Kar et al.

We investigate a novel cluster-of-bandit algorithm CAB for collaborative recommendation tasks that implements the underlying feedback sharing mechanism by estimating the neighborhood of users in a context-dependent manner. CAB makes sharp departures from the state of the art by incorporating collaborative effects into inference as well as learning processes in a manner that seamlessly interleaving explore-exploit tradeoffs and collaborative steps. We prove regret bounds under various assumptions on the data, which exhibit a crisp dependence on the expected number of clusters over the users, a natural measure of the statistical difficulty of the learning task. Experiments on production and real-world datasets show that CAB offers significantly increased prediction performance against a representative pool of state-of-the-art methods.

Géraud Le Falher, Nicolò Cesa-Bianchi, Claudio Gentile et al.

In the problem of edge sign prediction, we are given a directed graph (representing a social network), and our task is to predict the binary labels of the edges (i.e., the positive or negative nature of the social relationships). Many successful heuristics for this problem are based on the troll-trust features, estimating at each node the fraction of outgoing and incoming positive/negative edges. We show that these heuristics can be understood, and rigorously analyzed, as approximators to the Bayes optimal classifier for a simple probabilistic model of the edge labels. We then show that the maximum likelihood estimator for this model approximately corresponds to the predictions of a Label Propagation algorithm run on a transformed version of the original social graph. Extensive experiments on a number of real-world datasets show that this algorithm is competitive against state-of-the-art classifiers in terms of both accuracy and scalability. Finally, we show that troll-trust features can also be used to derive online learning algorithms which have theoretical guarantees even when edges are adversarially labeled.

Shuai Li, Claudio Gentile, Alexandros Karatzoglou

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.

Nicolo' Cesa-Bianchi, Claudio Gentile, Yishay Mansour et al.

We study networks of communicating learning agents that cooperate to solve a common nonstochastic bandit problem. Agents use an underlying communication network to get messages about actions selected by other agents, and drop messages that took more than $d$ hops to arrive, where $d$ is a delay parameter. We introduce \textsc{Exp3-Coop}, a cooperative version of the {\sc Exp3} algorithm and prove that with $K$ actions and $N$ agents the average per-agent regret after $T$ rounds is at most of order $\sqrt{\bigl(d+1 + \tfrac{K}{N}α_{\le d}\bigr)(T\ln K)}$, where $α_{\le d}$ is the independence number of the $d$-th power of the connected communication graph $G$. We then show that for any connected graph, for $d=\sqrt{K}$ the regret bound is $K^{1/4}\sqrt{T}$, strictly better than the minimax regret $\sqrt{KT}$ for noncooperating agents. More informed choices of $d$ lead to bounds which are arbitrarily close to the full information minimax regret $\sqrt{T\ln K}$ when $G$ is dense. When $G$ has sparse components, we show that a variant of \textsc{Exp3-Coop}, allowing agents to choose their parameters according to their centrality in $G$, strictly improves the regret. Finally, as a by-product of our analysis, we provide the first characterization of the minimax regret for bandit learning with delay.

Shuai Li, Alexandros Karatzoglou, Claudio Gentile

Classical collaborative filtering, and content-based filtering methods try to learn a static recommendation model given training data. These approaches are far from ideal in highly dynamic recommendation domains such as news recommendation and computational advertisement, where the set of items and users is very fluid. In this work, we investigate an adaptive clustering technique for content recommendation based on exploration-exploitation strategies in contextual multi-armed bandit settings. Our algorithm takes into account the collaborative effects that arise due to the interaction of the users with the items, by dynamically grouping users based on the items under consideration and, at the same time, grouping items based on the similarity of the clusterings induced over the users. The resulting algorithm thus takes advantage of preference patterns in the data in a way akin to collaborative filtering methods. We provide an empirical analysis on medium-size real-world datasets, showing scalability and increased prediction performance (as measured by click-through rate) over state-of-the-art methods for clustering bandits. We also provide a regret analysis within a standard linear stochastic noise setting.

Noga Alon, Nicolò Cesa-Bianchi, Claudio Gentile et al.

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.

Claudio Gentile, Shuai Li, Giovanni Zappella

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.

Noga Alon, Nicolò Cesa-Bianchi, Claudio Gentile et al.

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.

Nicolò Cesa-Bianchi, Claudio Gentile, Giovanni Zappella

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.

Claudio Gentile, Mark Herbster, Stephen Pasteris

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.

Fabio Vitale, Nicolo Cesa-Bianchi, Claudio Gentile et al.

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.

Nicolo Cesa-Bianchi, Claudio Gentile, Fabio Vitale et al.

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.

Nicolo Cesa-Bianchi, Claudio Gentile, Fabio Vitale et al.

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.

Nicolo Cesa-Bianchi, Claudio Gentile, Fabio Vitale et al.

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|.

Claudio Gentile, Francesco Orabona

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.