Online Learning and Online Convex Optimization

Shalev‐Shwartz, Shai

doi:10.1561/9781601985477

Cited by 526 publications

(641 citation statements)

References 34 publications

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“…In what follows, we may then derive the corresponding bound on the maximum deviation simply using (4).…”

Section: Bounds On the Maximum Estimation Deviationsmentioning

confidence: 99%

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Generic Bounds On The Maximum Deviations In Sequential Prediction: An Information-Theoretic Analysis

Fang

Zhu

2019

2019 IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP)

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In this paper, we derive generic bounds on the maximum deviations in prediction errors for sequential prediction via an information-theoretic approach. The fundamental bounds are shown to depend only on the conditional entropy of the data point to be predicted given the previous data points. In the asymptotic case, the bounds are achieved if and only if the prediction error is white and uniformly distributed.

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“…In what follows, we may then derive the corresponding bound on the maximum deviation simply using (4).…”

Section: Bounds On the Maximum Estimation Deviationsmentioning

confidence: 99%

“…Sequential prediction (or sequence prediction) [1][2][3][4][5] has been an important component of sequential learning. In this paper, we will utilize information theory to analyze the fundamental performance bounds of sequential prediction.…”

Section: Introductionmentioning

confidence: 99%

Generic Bounds On The Maximum Deviations In Sequential Prediction: An Information-Theoretic Analysis

Fang

Zhu

2019

2019 IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP)

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“…Subscript t at the cost function (2) reminds us its dependence on the request r t that is generated at t. Since these events may vary according to a non-stationary process, we will use the concept of regret from online convex optimization [22].…”

Section: Problem Formulationmentioning

confidence: 99%

“…This assumption reflects that, in practice, caches are populated before the requests are issued. Since by Lemma 1 f t (y) are convex, our problem falls in the Online Convex Optimization framework [22]. The performance metric of an algorithm in this line of work is the regret: the difference between costs incurred by the algorithm and the best static configuration in hindsight.…”

Section: Problem Formulationmentioning

confidence: 99%

Learning to Cooperate in D2D Caching Networks

Paschos

Destounis

Iosifidis

2019

2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

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We consider a wireless device-to-device (D2D) cooperative network where memory-endowed nodes store and exchange content. Each node generates random file requests following an unknown and possibly arbitrary spatio-temporal process, and a base station (BS) delivers any file that is not found at its neighbors' cache, at the expense of higher cost. We design an online learning algorithm which minimizes the aggregate delivery cost by assisting each node to decide which files to cache and which files to fetch from the BS and other devices. Our policy relies on the online gradient descent algorithm, is amenable to distributed execution, and achieves asymptotically optimal performance for any request pattern, without prior information.

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“…be a sequence generalized by the update rule (1) in the case where only part labels of instances are revealed and e t be the gap as defined in (3). Then, for any f ∈  and any stepsize > 0, we have…”

Section: Estimated Gradient For Online Learning With Sparse Labelsmentioning

confidence: 99%

Online learning with sparse labels

Zou

Liang

2018

Concurrency and Computation

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Summary In this paper, we consider an online learning scenario where the instances arrive sequentially with partly revealed labels. We assume that the labels of instances are revealed randomly according to some distribution, eg, Bernoulli distribution. Three specific algorithms based on different inspirations are developed. The first one performs the idea of Estimated gradient for which a strict high‐probability regret guarantee in scale of Õfalse(Tfalse/pfalse) can be derived, when the distributing parameter p is revealed. An empirical version is also developed for cases where the learner has to learn the parameter p when it is not revealed. Experiments on several benchmark data sets show the feasibility of the proposed method. To further improve the performance, two kinds of aggressive algorithms are presented. The first one is based on the idea of instances recalling, which tries to get the full use of the labeled instances. The second one is based on the idea of labels learning, and it tries to learn the labels for unlabeled instances. In particular, it includes the step of online co‐learning, which aims to learn the labels, and the step of weighted voting, which aims to make the final decision. Empirical results confirm the positive effects of the two aggressive algorithms.

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Online Learning and Online Convex Optimization

Cited by 526 publications

References 34 publications

Generic Bounds On The Maximum Deviations In Sequential Prediction: An Information-Theoretic Analysis

Generic Bounds On The Maximum Deviations In Sequential Prediction: An Information-Theoretic Analysis

Learning to Cooperate in D2D Caching Networks

Online learning with sparse labels

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