arXiv subjects

Robert E. Schapire

Publications and source records attributed to Robert E. Schapire.

34 records · Page 2Linked to original sources

arXiv2015

Achieving All with No Parameters: Adaptive NormalHedge

We study the classic online learning problem of predicting with expert advice, and propose a truly parameter-free and adaptive algorithm that achieves several objectives simultaneously without using any prior information. The main component of this work is an improved version of the NormalHedge.DT algorithm (Luo and Schapire, 2014), called AdaNormalHedge. On one hand, this new algorithm ensures small regret when the competitor has small loss and almost constant regret when the losses are stochastic. On the other hand, the algorithm is able to compete with any convex combination of the experts simultaneously, with a regret in terms of the relative entropy of the prior and the competitor. This resolves an open problem proposed by Chaudhuri et al. (2009) and Chernov and Vovk (2010). Moreover, we extend the results to the sleeping expert setting and provide two applications to illustrate the power of AdaNormalHedge: 1) competing with time-varying unknown competitors and 2) predicting almost as well as the best pruning tree. Our results on these applications significantly improve previous work from different aspects, and a special case of the first application resolves another open problem proposed by Warmuth and Koolen (2014) on whether one can simultaneously achieve optimal shifting regret for both adversarial and stochastic losses.

cs.LG↗

arXiv2014

A Drifting-Games Analysis for Online Learning and Applications to Boosting

We provide a general mechanism to design online learning algorithms based on a minimax analysis within a drifting-games framework. Different online learning settings (Hedge, multi-armed bandit problems and online convex optimization) are studied by converting into various kinds of drifting games. The original minimax analysis for drifting games is then used and generalized by applying a series of relaxations, starting from choosing a convex surrogate of the 0-1 loss function. With different choices of surrogates, we not only recover existing algorithms, but also propose new algorithms that are totally parameter-free and enjoy other useful properties. Moreover, our drifting-games framework naturally allows us to study high probability bounds without resorting to any concentration results, and also a generalized notion of regret that measures how good the algorithm is compared to all but the top small fraction of candidates. Finally, we translate our new Hedge algorithm into a new adaptive boosting algorithm that is computationally faster as shown in experiments, since it ignores a large number of examples on each round.

cs.LG↗

arXiv2014

Taming the Monster: A Fast and Simple Algorithm for Contextual Bandits

We present a new algorithm for the contextual bandit learning problem, where the learner repeatedly takes one of $K$ actions in response to the observed context, and observes the reward only for that chosen action. Our method assumes access to an oracle for solving fully supervised cost-sensitive classification problems and achieves the statistically optimal regret guarantee with only $\tilde{O}(\sqrt{KT/\log N})$ oracle calls across all $T$ rounds, where $N$ is the number of policies in the policy class we compete against. By doing so, we obtain the most practical contextual bandit learning algorithm amongst approaches that work for general policy classes. We further conduct a proof-of-concept experiment which demonstrates the excellent computational and prediction performance of (an online variant of) our algorithm relative to several baselines.

cs.LG↗

arXiv2013

Towards Minimax Online Learning with Unknown Time Horizon

We consider online learning when the time horizon is unknown. We apply a minimax analysis, beginning with the fixed horizon case, and then moving on to two unknown-horizon settings, one that assumes the horizon is chosen randomly according to some known distribution, and the other which allows the adversary full control over the horizon. For the random horizon setting with restricted losses, we derive a fully optimal minimax algorithm. And for the adversarial horizon setting, we prove a nontrivial lower bound which shows that the adversary obtains strictly more power than when the horizon is fixed and known. Based on the minimax solution of the random horizon setting, we then propose a new adaptive algorithm which "pretends" that the horizon is drawn from a distribution from a special family, but no matter how the actual horizon is chosen, the worst-case regret is of the optimal rate. Furthermore, our algorithm can be combined and applied in many ways, for instance, to online convex optimization, follow the perturbed leader, exponential weights algorithm and first order bounds. Experiments show that our algorithm outperforms many other existing algorithms in an online linear optimization setting.

cs.LG↗

arXiv2012

Advances in Boosting (Invited Talk)

Boosting is a general method of generating many simple classification rules and combining them into a single, highly accurate rule. In this talk, I will review the AdaBoost boosting algorithm and some of its underlying theory, and then look at how this theory has helped us to face some of the challenges of applying AdaBoost in two domains: In the first of these, we used boosting for predicting and modeling the uncertainty of prices in complicated, interacting auctions. The second application was to the classification of caller utterances in a telephone spoken-dialogue system where we faced two challenges: the need to incorporate prior knowledge to compensate for initially insufficient data; and a later need to filter the large stream of unlabeled examples being collected to select the ones whose labels are likely to be most informative.

cs.LG↗

arXiv2012

A Bayesian Boosting Model

We offer a novel view of AdaBoost in a statistical setting. We propose a Bayesian model for binary classification in which label noise is modeled hierarchically. Using variational inference to optimize a dynamic evidence lower bound, we derive a new boosting-like algorithm called VIBoost. We show its close connections to AdaBoost and give experimental results from four datasets.

stat.ML↗

arXiv2012

Imitation Learning with a Value-Based Prior

The goal of imitation learning is for an apprentice to learn how to behave in a stochastic environment by observing a mentor demonstrating the correct behavior. Accurate prior knowledge about the correct behavior can reduce the need for demonstrations from the mentor. We present a novel approach to encoding prior knowledge about the correct behavior, where we assume that this prior knowledge takes the form of a Markov Decision Process (MDP) that is used by the apprentice as a rough and imperfect model of the mentor's behavior. Specifically, taking a Bayesian approach, we treat the value of a policy in this modeling MDP as the log prior probability of the policy. In other words, we assume a priori that the mentor's behavior is likely to be a high value policy in the modeling MDP, though quite possibly different from the optimal policy. We describe an efficient algorithm that, given a modeling MDP and a set of demonstrations by a mentor, provably converges to a stationary point of the log posterior of the mentor's policy, where the posterior is computed with respect to the "value based" prior. We also present empirical evidence that this prior does in fact speed learning of the mentor's policy, and is an improvement in our experiments over similar previous methods.

cs.LG↗

arXiv2012

Combining Spatial and Telemetric Features for Learning Animal Movement Models

We introduce a new graphical model for tracking radio-tagged animals and learning their movement patterns. The model provides a principled way to combine radio telemetry data with an arbitrary set of userdefined, spatial features. We describe an efficient stochastic gradient algorithm for fitting model parameters to data and demonstrate its effectiveness via asymptotic analysis and synthetic experiments. We also apply our model to real datasets, and show that it outperforms the most popular radio telemetry software package used in ecology. We conclude that integration of different data sources under a single statistical framework, coupled with appropriate parameter and state estimation procedures, produces both accurate location estimates and an interpretable statistical model of animal movement.

cs.LG↗

arXiv2012

Contextual Bandit Learning with Predictable Rewards

Contextual bandit learning is a reinforcement learning problem where the learner repeatedly receives a set of features (context), takes an action and receives a reward based on the action and context. We consider this problem under a realizability assumption: there exists a function in a (known) function class, always capable of predicting the expected reward, given the action and context. Under this assumption, we show three things. We present a new algorithm---Regressor Elimination--- with a regret similar to the agnostic setting (i.e. in the absence of realizability assumption). We prove a new lower bound showing no algorithm can achieve superior performance in the worst case even with the realizability assumption. However, we do show that for any set of policies (mapping contexts to actions), there is a distribution over rewards (given context) such that our new algorithm has constant regret unlike the previous approaches.

cs.LG↗

arXiv2012

A Contextual-Bandit Approach to Personalized News Article Recommendation

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.

cs.LG↗

arXiv2011

Contextual Bandit Algorithms with Supervised Learning Guarantees

We address the problem of learning in an online, bandit setting where the learner must repeatedly select among $K$ actions, but only receives partial feedback based on its choices. We establish two new facts: First, using a new algorithm called Exp4.P, we show that it is possible to compete with the best in a set of $N$ experts with probability $1-δ$ while incurring regret at most $O(\sqrt{KT\ln(N/δ)})$ over $T$ time steps. The new algorithm is tested empirically in a large-scale, real-world dataset. Second, we give a new algorithm called VE that competes with a possibly infinite set of policies of VC-dimension $d$ while incurring regret at most $O(\sqrt{T(d\ln(T) + \ln (1/δ))})$ with probability $1-δ$. These guarantees improve on those of all previous algorithms, whether in a stochastic or adversarial environment, and bring us closer to providing supervised learning type guarantees for the contextual bandit setting.

cs.LG↗

arXiv2011

A theory of multiclass boosting

Boosting combines weak classifiers to form highly accurate predictors. Although the case of binary classification is well understood, in the multiclass setting, the "correct" requirements on the weak classifier, or the notion of the most efficient boosting algorithms are missing. In this paper, we create a broad and general framework, within which we make precise and identify the optimal requirements on the weak-classifier, as well as design the most effective, in a certain sense, boosting algorithms that assume such requirements.

stat.ML↗

arXiv2011

The Rate of Convergence of AdaBoost

The AdaBoost algorithm was designed to combine many "weak" hypotheses that perform slightly better than random guessing into a "strong" hypothesis that has very low error. We study the rate at which AdaBoost iteratively converges to the minimum of the "exponential loss." Unlike previous work, our proofs do not require a weak-learning assumption, nor do they require that minimizers of the exponential loss are finite. Our first result shows that at iteration $t$, the exponential loss of AdaBoost's computed parameter vector will be at most $ε$ more than that of any parameter vector of $\ell_1$-norm bounded by $B$ in a number of rounds that is at most a polynomial in $B$ and $1/ε$. We also provide lower bounds showing that a polynomial dependence on these parameters is necessary. Our second result is that within $C/ε$ iterations, AdaBoost achieves a value of the exponential loss that is at most $ε$ more than the best possible value, where $C$ depends on the dataset. We show that this dependence of the rate on $ε$ is optimal up to constant factors, i.e., at least $Ω(1/ε)$ rounds are necessary to achieve within $ε$ of the optimal exponential loss.

math.OC↗

arXiv2008

Analysis of boosting algorithms using the smooth margin function

We introduce a useful tool for analyzing boosting algorithms called the ``smooth margin function,'' a differentiable approximation of the usual margin for boosting algorithms. We present two boosting algorithms based on this smooth margin, ``coordinate ascent boosting'' and ``approximate coordinate ascent boosting,'' which are similar to Freund and Schapire's AdaBoost algorithm and Breiman's arc-gv algorithm. We give convergence rates to the maximum margin solution for both of our algorithms and for arc-gv. We then study AdaBoost's convergence properties using the smooth margin function. We precisely bound the margin attained by AdaBoost when the edges of the weak classifiers fall within a specified range. This shows that a previous bound proved by Rätsch and Warmuth is exactly tight. Furthermore, we use the smooth margin to capture explicit properties of AdaBoost in cases where cyclic behavior occurs.

stat.ML↗

arXiv2007

Faster solutions of the inverse pairwise Ising problem

Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes. Finding these models requires us to solve an inverse problem: given experimentally measured expectation values, what are the parameters of the underlying Hamiltonian? This problem sits at the intersection of statistical physics and machine learning, and we suggest that more efficient solutions are possible by merging ideas from the two fields. We use a combination of recent coordinate descent algorithms with an adaptation of the histogram Monte Carlo method, and implement these techniques to take advantage of the sparseness found in data on real neurons. The resulting algorithm learns the parameters of an Ising model describing a network of forty neurons within a few minutes. This opens the possibility of analyzing much larger data sets now emerging, and thus testing hypotheses about the collective behaviors of these networks.

q-bio.QM↗

arXiv2004

Generalization bounds for averaged classifiers

We study a simple learning algorithm for binary classification. Instead of predicting with the best hypothesis in the hypothesis class, that is, the hypothesis that minimizes the training error, our algorithm predicts with a weighted average of all hypotheses, weighted exponentially with respect to their training error. We show that the prediction of this algorithm is much more stable than the prediction of an algorithm that predicts with the best hypothesis. By allowing the algorithm to abstain from predicting on some examples, we show that the predictions it makes when it does not abstain are very reliable. Finally, we show that the probability that the algorithm abstains is comparable to the generalization error of the best hypothesis in the class.

math.ST↗