This paper considers a variant of the classical online learning problem with expert predictions. Our model’s differences and challenges are due to lacking any direct feedback on the loss each expert incurs at each time step $t$. We propose an approach that uses peer prediction and identify conditions where it succeeds. Our techniques revolve around a carefully designed peer score function $s()$ that scores experts’ predictions based on the peer consensus. We show a sufficient condition, that we call \emph{peer calibration}, under which standard online learning algorithms using loss feedback computed by the carefully crafted $s()$ have bounded regret with respect to the unrevealed ground truth values. We then demonstrate how suitable $s()$ functions can be derived for different assumptions and models.

We analyze algorithms for approximating a function [Formula: see text] mapping [Formula: see text] to [Formula: see text] using deep linear neural networks, that is, that learn a function [Formula: see text] parameterized by matrices [Formula: see text] and defined by [Formula: see text]. We focus on algorithms that learn through gradient descent on the population quadratic loss in the case that the distribution over the inputs is isotropic. We provide polynomial bounds on the number of iterations for gradient descent to approximate the least-squares matrix [Formula: see text], in the case where the initial hypothesis [Formula: see text] has excess loss bounded by a small enough constant. We also show that gradient descent fails to converge for [Formula: see text] whose distance from the identity is a larger constant, and we show that some forms of regularization toward the identity in each layer do not help. If [Formula: see text] is symmetric positive definite, we show that an algorithm that initializes [Formula: see text] learns an [Formula: see text]-approximation of [Formula: see text] using a number of updates polynomial in [Formula: see text], the condition number of [Formula: see text], and [Formula: see text]. In contrast, we show that if the least-squares matrix [Formula: see text] is symmetric and has a negative eigenvalue, then all members of a class of algorithms that perform gradient descent with identity initialization, and optionally regularize toward the identity in each layer, fail to converge. We analyze an algorithm for the case that [Formula: see text] satisfies [Formula: see text] for all [Formula: see text] but may not be symmetric. This algorithm uses two regularizers: one that maintains the invariant [Formula: see text] for all [Formula: see text] and the other that “balances” [Formula: see text] so that they have the same singular values.

The standard techniques for online learning of combinatorial objects perform multiplicative updates followed by projections into the convex hull of all the objects. However, this methodology can be expensive if the convex hull contains many facets. For example, the convex hull of $n$-symbol Huffman trees is known to have exponentially many facets. We get around this difficulty by exploiting extended formulations, which encode the polytope of combinatorial objects in a higher dimensional “extended” space with only polynomially many facets. We develop a general framework for converting extended formulations into efficient online algorithms with good relative loss bounds. We present applications of our framework to online learning of Huffman trees and permutations. The regret bounds of the resulting algorithms are within a factor of $\Ocal(\sqrt{\log(n)})$ of the state-of-the-art specialized algorithms for permutations, and depending on the loss regimes, improve on or match the state-of-the-art for Huffman trees. Our method is general and can be applied to other combinatorial objects.

We analyze dropout in deep networks with rectified linear units and the quadratic loss. Our results expose surprising differences between the behavior of dropout and more traditional regularizers like weight decay. For example, on some simple data sets dropout training produces negative weights even though the output is the sum of the inputs. This provides a counterpoint to the suggestion that dropout discourages co-adaptation of weights. We also show that the dropout penalty can grow exponentially in the depth of the network while the weight-decay penalty remains essentially linear, and that dropout is insensitive to various re-scalings of the input features, outputs, and network weights. This last insensitivity implies that there are no isolated local minima of the dropout training criterion. Our work uncovers new properties of dropout, extends our understanding of why dropout succeeds, and lays the foundation for further progress.

Monte-Carlo Tree Search (MCTS) grows a partial game tree and uses a large number of random simulations to approximate the values of the nodes. It has proven effective in games with such as Go and Hex where the large search space and difficulty of evaluating positions cause difficulties for standard methods. The best MCTS players use carefully hand-crafted rules to bias the random simulations. Obtaining good hand-crafting rules is a very difficult process, as even rules promoting better simulation play can result in a weaker MCTS system [12]. Our Hivemind system uses evolution strategies to automatically learn effective rules for biasing the random simulations. We have built a MCTS player using Hivemind for the game Hex. The Hivemind learned rules result in a 90% win rate against a baseline MCTS system, and significant improvement against the computer Hex world champion, MoHex.

The authors present BEAMER: a new spatially exploitative approach to learning object detectors which shows excellent results when applied to the task of detecting objects in greyscale aerial imagery in the presence of ambiguous and noisy data. There are four main contributions used to produce these results. First, they introduce a grammar-guided feature extraction system, enabling the exploration of a richer feature space while constraining the features to a useful subset. This is specified with a rule-based generative grammer crafted by a human expert. Second, they learn a classifier on this data using a newly proposed variant of AdaBoost which takes into account the spatially correlated nature of the data. Third, they perform another round of training to optimize the method of converting the pixel classifications generated by boosting into a high quality set of (x,y) locations. lastly, they carefully define three common problems in object detection and define two evaluation criteria that are tightly matched to these problems. Major strengths of this approach are: (1) a way of randomly searching a broad feature space, (2) its performance when evaluated on well-matched evaluation criteria, and (3) its use of the location prediction domain to learn object detectors as well as to generate detections that perform well on several tasks: object counting, tracking, and target detection. They demonstrate the efficacy of BEAMER with a comprehensive experimental evaluation on a challenging data set.

We analyze and compare the well-known gradient descent algorithm and the more recent exponentiated gradient algorithm for training a single neuron with an arbitrary transfer function. Both algorithms are easily generalized to larger neural networks, and the generalization of gradient descent is the standard backpropagation algorithm. In this paper we prove worst-case loss bounds for both algorithms in the single neuron case. Since local minima make it difficult to prove worst-case bounds for gradient-based algorithms, we must use a loss function that prevents the formation of spurious local minima. We define such a matching loss function for any strictly increasing differentiable transfer function and prove worst-case loss bounds for any such transfer function and its corresponding matching loss. For example, the matching loss for the identity function is the square loss and the matching loss for the logistic transfer function is the entropic loss. The different forms of the two algorithms' bounds indicates that exponentiated gradient outperforms gradient descent when the inputs contain a large number of irrelevant components. Simulations on synthetic data confirm these analytical results.

This paper presents a general information-theoretic approach for obtaining lower bounds on the number of examples needed to PAC learn in the presence of noise.This approach deals directly with the fundamental information quantities, avoiding a Bayesian analysis.The technique is applied to several different models, illustrating its generality and power.The resulting bounds add logarithmic factors to (or improve the constants in) previously known lower bounds.Pemlission to snake digital or hard copies of all or part of this work for personal or classroom use is gmnted without fee provided that copies are not nlade or distributed for profit or commercial advantage and that copies hear this notice and the full citation on the first page.To copy otherwise, to republish, to post on servers or to redistribute to lists, requuxs prior specific pcmlission and/or a fee.

We investigate the value of labels in a simple version of the standard on-line prediction model (the “experts ” setting). We present algorithms and adversary arguments defining tradeoffs between the number of mistakes made and the number of labels that the learner requests. One version of this question can be viewed as a family of games whose value is given by a complicated recurrence. Although our attempts to tind a closed form for this recurrence have been unsuccessful, we show how an algorithm can efficiently compute its value, enabling it to perform optimally. 1

We analyze algorithms that predict a binary value by combining the predictions of several prediction strategies, calledexperts. Our analysis is for worst-case situations, i.e., we make no assumptions about the way the sequence of bits to be predicted is generated. We measure the performance of the algorithm by the difference between the expected number of mistakes it makes on the bit sequence and the expected number of mistakes made by the best expert on this sequence, where the expectation is taken with respect to the randomization in the predictins. We show that the minimum achievable difference is on the order of the square root of the number of mistakes of the best expert, and we give efficient algorithms that achieve this. Our upper and lower bounds have matching leading constants in most cases. We then show how this leads to certain kinds of pattern recognition/learning algorithms with performance bounds that improve on the best results currently know in this context. We also compare our analysis to the case in which log loss is used instead of the expected number of mistakes.

Article Free Access Share on On Bayes methods for on-line Boolean prediction Authors: Nicolò Cesa-Bianchi DSI, University of Milan, Italy DSI, University of Milan, ItalyView Profile , David P. Helmbold University of California, Santa Cruz University of California, Santa CruzView Profile , Sandra Panizza DSI, University of Milan, Italy DSI, University of Milan, ItalyView Profile Authors Info & Claims COLT '96: Proceedings of the ninth annual conference on Computational learning theoryJanuary 1996 Pages 314–324https://doi.org/10.1145/238061.238162Published:01 January 1996Publication History 5citation237DownloadsMetricsTotal Citations5Total Downloads237Last 12 Months4Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

We address the problem of deciding when to spin down the disk of a mobile computer in order to extend battery life. Since one of the most critical resources in mobile computing environments is battery life, good energy conservation methods can dramatically increase the utility of mobile systems. We use a simple and efficient algorithm based on machine learning techniques that has excellent performance in practice. Our experimental results are based on traces collected from HP C2474s disks. Using this data, the algorithm outperforms several algorithms that are theoretically optimal in under various worst-case assumptions, as well as the best fixed time-out strategy. In particular, the algorithm reduces the power consumption of the disk to about half (depending on the disk's properties) of the energy consumed by a one minute fixed time-out. Since the algorithm adapts to usage patterns, it uses as little as 88% of the energy consumed by the best fixed time-out computed in retrospect. 1 In...

. Many algorithms for inferring a decision tree from data involve a two-phase process: First, a very large decision tree is grown which typically ends up "over-fitting" the data. To reduce over-fitting, in the second phase, the tree is pruned using one of a number of available methods. The final tree is then output and used for classification on test data. In this paper, we suggest an alternative approach to the pruning phase. Using a given unpruned decision tree, we present a new method of making predictions on test data, and we prove that our algorithm's performance will not be "much worse" (in a precise technical sense) than the predictions made by the best reasonably small pruning of the given decision tree. Thus, our procedure is guaranteed to be competitive (in terms of the quality of its predictions) with any pruning algorithm. We prove that our procedure is very efficient and highly robust. Our method can be viewed as a synthesis of two previously studied techniques. First, we ...

. We investigate the problem of estimating the proportion vector which maximizes the likelihood of a given sample for a mixture of given densities. We adapt a framework developed for supervised learning and give simple derivations for many of the standard iterative algorithms like gradient projection and EM. In this framework, the distance between the new and old proportion vectors is used as a penalty term. The square distance leads to the gradient projection update, and the relative entropy to a new update which we call the exponentiated gradient update (EGj ). Curiously, when a second order Taylor expansion of the relative entropy is used, we arrive at an update EMj which, for j = 1, gives the usual EM update. Experimentally, both the EMj-update and the EGj-update for j ? 1 outperform the EM algorithm and its variants. We also prove a polynomial bound on the rate of convergence of the EGj algorithm. 1. Introduction The problem of maximum-likelihood (ML) estimation of a mixture of de...

Article How to use expert advice Share on Authors: Nicolò Cesa-Bianchi View Profile , Yoav Freund View Profile , David P. Helmbold View Profile , David Haussler View Profile , Robert E. Schapire View Profile , Manfred K. Warmuth View Profile Authors Info & Claims STOC '93: Proceedings of the twenty-fifth annual ACM symposium on Theory of ComputingJune 1993 Pages 382–391https://doi.org/10.1145/167088.167198Online:01 June 1993Publication History 71citation406DownloadsMetricsTotal Citations71Total Downloads406Last 12 Months8Last 6 weeks3 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

One of the fundamental problems encountered when debugging a parallel program is determining the possible orders in which events could have occurred. Various problems, such as data races and intermittent deadlock, arise when there is insufficient synchronization between the tasks in a parallel program. A sequential trace of an execution can be misleading, as it implies additional event orderings, distorting the concurrent nature of the computation. Algorithms to generate, from the trace of an execution, those event orderings that can be relied on by the programmer are described. By its very nature, the information in an execution trace pertains only to that execution of the program, and may not generalize to other executions. This difficulty is mitigated by defining an inferred program based on the trace and original program, analyzing this inferred program, and showing how the inferred program relates to the original. The results of the algorithms can be used by other automated tools such as a data race detector or constraint checker.>

An algorithm is a weak learner if with some small probability it outputs a hypothesis with error slightly below 50%. This paper presents sufficient conditions for weak learning.

In the standard on-line model the learning algorithm tries to minimize the total number of mistakes made in a series of trials. On each trial the learner sees an instance, either accepts or rejects that instance, and then is told the appropriate response. The authors define a natural variant of this model ('apple tasting') where the learner gets feedback only when the instance is accepted. They use two transformations to relate the apple tasting model to an enhanced standard model where false acceptances are counted separately from false rejections. They present a strategy for trading between false acceptances and false rejections in the standard model. From one perspective this strategy is exactly optimal, including constants. They apply the results to obtain a good general purpose apple tasting algorithm as well as nearly optimal apple tasting algorithms for a variety of standard classes, such as conjunctions and disjunctions of n boolean variables. They also present and analyze a simpler transformation useful when the instances are drawn at random rather than selected by an adversary.>

The problem of learning an integer lattice of ${\bf Z}^k $ in an on-line fashion is considered. That is, the learning algorithm is given a sequence of k-tuples of integers and predicts for each tuple in the sequence whether it lies in a hidden target lattice of ${\bf Z}^k $. The goal of the algorithm is to minimize the number of prediction mistakes. An efficient learning algorithm with an absolute mistake bound of $k + \lfloor k\log (n\sqrt k ) \rfloor $ is given, where n is the maximum component of any tuple seen. It is shown that this bound is approximately a $\log \log n$ factor larger than the lower bound on the worst case number of mistakes given by the VC dimension of lattices that are restricted to $\{ - n, \cdots ,0, \cdots ,n \}^k $. This algorithm is used to learn rational lattices, cosets of lattices, an on-line word problem for abelian groups, and a subclass of the commutative regular languages. Furthermore, by adapting the results of [D. Helmbold, R. Sloan, and M. K. Warmuth, Machine Learning, 5 (1990), pp. 165–196], one can efficiently learn nested differences of each of the above classes (e.g., concepts of the form $c_1 - (c_2 - (c_3 - (c_4 - c_5 )))$, where each $c_i $ is the coset of a lattice).

A simple model of parallel computation which is capable of explaining speedups greater than n on n processors is presented. Necessary and sufficient conditions for these exceptional speedups are derived from the model. Several of the contradictory previous results relating to parallel speedup are resolved by using the model.>

We present a parallel algorithm for the two processor scheduling problem. This algorithm constructs an optimal schedule for unit execution time task systems with arbitrary precedence constraints using a polynomial number of processors and running in time polylog in the size of the input. Whereas previous parallel solutions for the problem made extensive use of randomization, our algorithm is completely deterministic and based on an interesting iteration technique. It is of independent relevance for two more reasons. It provides another example for the apparent difference in complexity between decision and search problems in the context of fast parallel computation, and it gives an $\mathcal{NC}$-algorithm for the matching problem in certain restricted cases.