Pub Date : 2019-07-23DOI: 10.1609/AAAI.V34I04.5986
Vishakha Patil, Ganesh Ghalme, V. Nair, Y. Narahari
We study an interesting variant of the stochastic multi-armed bandit problem, called the Fair-SMAB problem, where each arm is required to be pulled for at least a given fraction of the total available rounds. We investigate the interplay between learning and fairness in terms of a pre-specified vector denoting the fractions of guaranteed pulls. We define a fairness-aware regret, called $r$-Regret, that takes into account the above fairness constraints and naturally extends the conventional notion of regret. Our primary contribution is characterizing a class of Fair-SMAB algorithms by two parameters: the unfairness tolerance and the learning algorithm used as a black-box. We provide a fairness guarantee for this class that holds uniformly over time irrespective of the choice of the learning algorithm. In particular, when the learning algorithm is UCB1, we show that our algorithm achieves $O(ln T)$ $r$-Regret. Finally, we evaluate the cost of fairness in terms of the conventional notion of regret.
{"title":"Achieving Fairness in the Stochastic Multi-armed Bandit Problem","authors":"Vishakha Patil, Ganesh Ghalme, V. Nair, Y. Narahari","doi":"10.1609/AAAI.V34I04.5986","DOIUrl":"https://doi.org/10.1609/AAAI.V34I04.5986","url":null,"abstract":"We study an interesting variant of the stochastic multi-armed bandit problem, called the Fair-SMAB problem, where each arm is required to be pulled for at least a given fraction of the total available rounds. We investigate the interplay between learning and fairness in terms of a pre-specified vector denoting the fractions of guaranteed pulls. We define a fairness-aware regret, called $r$-Regret, that takes into account the above fairness constraints and naturally extends the conventional notion of regret. Our primary contribution is characterizing a class of Fair-SMAB algorithms by two parameters: the unfairness tolerance and the learning algorithm used as a black-box. We provide a fairness guarantee for this class that holds uniformly over time irrespective of the choice of the learning algorithm. In particular, when the learning algorithm is UCB1, we show that our algorithm achieves $O(ln T)$ $r$-Regret. Finally, we evaluate the cost of fairness in terms of the conventional notion of regret.","PeriodicalId":14794,"journal":{"name":"J. Mach. Learn. Res.","volume":"15 1","pages":"174:1-174:31"},"PeriodicalIF":0.0,"publicationDate":"2019-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75610082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-02-21DOI: 10.3929/ETHZ-B-000414972
Pragnya Alatur, K. Levy, Andreas Krause
We consider a setting where multiple players sequentially choose among a common set of actions (arms). Motivated by a cognitive radio networks application, we assume that players incur a loss upon colliding, and that communication between players is not possible. Existing approaches assume that the system is stationary. Yet this assumption is often violated in practice, e.g., due to signal strength fluctuations. In this work, we design the first Multi-player Bandit algorithm that provably works in arbitrarily changing environments, where the losses of the arms may even be chosen by an adversary. This resolves an open problem posed by Rosenski, Shamir, and Szlak (2016).
{"title":"Multi-Player Bandits: The Adversarial Case","authors":"Pragnya Alatur, K. Levy, Andreas Krause","doi":"10.3929/ETHZ-B-000414972","DOIUrl":"https://doi.org/10.3929/ETHZ-B-000414972","url":null,"abstract":"We consider a setting where multiple players sequentially choose among a common set of actions (arms). Motivated by a cognitive radio networks application, we assume that players incur a loss upon colliding, and that communication between players is not possible. Existing approaches assume that the system is stationary. Yet this assumption is often violated in practice, e.g., due to signal strength fluctuations. In this work, we design the first Multi-player Bandit algorithm that provably works in arbitrarily changing environments, where the losses of the arms may even be chosen by an adversary. This resolves an open problem posed by Rosenski, Shamir, and Szlak (2016).","PeriodicalId":14794,"journal":{"name":"J. Mach. Learn. Res.","volume":"515 1","pages":"77:1-77:23"},"PeriodicalIF":0.0,"publicationDate":"2019-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77094807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies the rates of convergence for learning distributions implicitly with the adversarial framework and Generative Adversarial Networks (GAN), which subsume Wasserstein, Sobolev, MMD GAN, and Generalized/Simulated Method of Moments (GMM/SMM) as special cases. We study a wide range of parametric and nonparametric target distributions, under a host of objective evaluation metrics. We investigate how to obtain a good statistical guarantee for GANs through the lens of regularization. On the nonparametric end, we derive the optimal minimax rates for distribution estimation under the adversarial framework. On the parametric end, we establish a theory for general neural network classes (including deep leaky ReLU networks), that characterizes the interplay on the choice of generator and discriminator pair. We discover and isolate a new notion of regularization, called the generator-discriminator-pair regularization, that sheds light on the advantage of GANs compared to classical parametric and nonparametric approaches for explicit distribution estimation. We develop novel oracle inequalities as the main technical tools for analyzing GANs, which is of independent interest.
{"title":"How Well Generative Adversarial Networks Learn Distributions","authors":"Tengyuan Liang","doi":"10.2139/ssrn.3714011","DOIUrl":"https://doi.org/10.2139/ssrn.3714011","url":null,"abstract":"This paper studies the rates of convergence for learning distributions implicitly with the adversarial framework and Generative Adversarial Networks (GAN), which subsume Wasserstein, Sobolev, MMD GAN, and Generalized/Simulated Method of Moments (GMM/SMM) as special cases. We study a wide range of parametric and nonparametric target distributions, under a host of objective evaluation metrics. We investigate how to obtain a good statistical guarantee for GANs through the lens of regularization. On the nonparametric end, we derive the optimal minimax rates for distribution estimation under the adversarial framework. On the parametric end, we establish a theory for general neural network classes (including deep leaky ReLU networks), that characterizes the interplay on the choice of generator and discriminator pair. We discover and isolate a new notion of regularization, called the generator-discriminator-pair regularization, that sheds light on the advantage of GANs compared to classical parametric and nonparametric approaches for explicit distribution estimation. We develop novel oracle inequalities as the main technical tools for analyzing GANs, which is of independent interest.","PeriodicalId":14794,"journal":{"name":"J. Mach. Learn. Res.","volume":"103 1","pages":"228:1-228:41"},"PeriodicalIF":0.0,"publicationDate":"2018-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80303668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Scikit-multiflow is a multi-output/multi-label and stream data mining framework for the Python programming language. Conceived to serve as a platform to encourage democratization of stream learning research, it provides multiple state of the art methods for stream learning, stream generators and evaluators. scikit-multiflow builds upon popular open source frameworks including scikit-learn, MOA and MEKA. Development follows the FOSS principles and quality is enforced by complying with PEP8 guidelines and using continuous integration and automatic testing. The source code is publicly available at this https URL.
{"title":"Scikit-Multiflow: A Multi-output Streaming Framework","authors":"Jacob Montiel, J. Read, A. Bifet, T. Abdessalem","doi":"10.5555/3291125.3309634","DOIUrl":"https://doi.org/10.5555/3291125.3309634","url":null,"abstract":"Scikit-multiflow is a multi-output/multi-label and stream data mining framework for the Python programming language. Conceived to serve as a platform to encourage democratization of stream learning research, it provides multiple state of the art methods for stream learning, stream generators and evaluators. scikit-multiflow builds upon popular open source frameworks including scikit-learn, MOA and MEKA. Development follows the FOSS principles and quality is enforced by complying with PEP8 guidelines and using continuous integration and automatic testing. The source code is publicly available at this https URL.","PeriodicalId":14794,"journal":{"name":"J. Mach. Learn. Res.","volume":"31 3","pages":"72:1-72:5"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91446714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-04-15DOI: 10.3929/ETHZ-B-000344707
S. Becker, Patrick Cheridito, Arnulf Jentzen
In this paper we develop a deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples. As such, it is broadly applicable in situations where the underlying randomness can efficiently be simulated. We test the approach on three problems: the pricing of a Bermudan max-call option, the pricing of a callable multi barrier reverse convertible and the problem of optimally stopping a fractional Brownian motion. In all three cases it produces very accurate results in high-dimensional situations with short computing times.
{"title":"Deep Optimal Stopping","authors":"S. Becker, Patrick Cheridito, Arnulf Jentzen","doi":"10.3929/ETHZ-B-000344707","DOIUrl":"https://doi.org/10.3929/ETHZ-B-000344707","url":null,"abstract":"In this paper we develop a deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples. As such, it is broadly applicable in situations where the underlying randomness can efficiently be simulated. We test the approach on three problems: the pricing of a Bermudan max-call option, the pricing of a callable multi barrier reverse convertible and the problem of optimally stopping a fractional Brownian motion. In all three cases it produces very accurate results in high-dimensional situations with short computing times.","PeriodicalId":14794,"journal":{"name":"J. Mach. Learn. Res.","volume":"7 1","pages":"74:1-74:25"},"PeriodicalIF":0.0,"publicationDate":"2018-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87016819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-02-14DOI: 10.1609/aaai.v33i01.33011110
Bidisha Samanta, A. De, G. Jana, P. Chattaraj, Niloy Ganguly, Manuel Gomez Rodriguez
Deep generative models have been praised for their ability to learn smooth latent representation of images, text, and audio, which can then be used to generate new, plausible data. However, current generative models are unable to work with molecular graphs due to their unique characteristics—their underlying structure is not Euclidean or grid-like, they remain isomorphic under permutation of the nodes labels, and they come with a different number of nodes and edges. In this paper, we propose NeVAE, a novel variational autoencoder for molecular graphs, whose encoder and decoder are specially designed to account for the above properties by means of several technical innovations. In addition, by using masking, the decoder is able to guarantee a set of valid properties in the generated molecules. Experiments reveal that our model can discover plausible, diverse and novel molecules more effectively than several state of the art methods. Moreover, by utilizing Bayesian optimization over the continuous latent representation of molecules our model finds, we can also find molecules that maximize certain desirable properties more effectively than alternatives.
{"title":"NeVAE: A Deep Generative Model for Molecular Graphs","authors":"Bidisha Samanta, A. De, G. Jana, P. Chattaraj, Niloy Ganguly, Manuel Gomez Rodriguez","doi":"10.1609/aaai.v33i01.33011110","DOIUrl":"https://doi.org/10.1609/aaai.v33i01.33011110","url":null,"abstract":"Deep generative models have been praised for their ability to learn smooth latent representation of images, text, and audio, which can then be used to generate new, plausible data. However, current generative models are unable to work with molecular graphs due to their unique characteristics—their underlying structure is not Euclidean or grid-like, they remain isomorphic under permutation of the nodes labels, and they come with a different number of nodes and edges. In this paper, we propose NeVAE, a novel variational autoencoder for molecular graphs, whose encoder and decoder are specially designed to account for the above properties by means of several technical innovations. In addition, by using masking, the decoder is able to guarantee a set of valid properties in the generated molecules. Experiments reveal that our model can discover plausible, diverse and novel molecules more effectively than several state of the art methods. Moreover, by utilizing Bayesian optimization over the continuous latent representation of molecules our model finds, we can also find molecules that maximize certain desirable properties more effectively than alternatives.","PeriodicalId":14794,"journal":{"name":"J. Mach. Learn. Res.","volume":"44 1","pages":"114:1-114:33"},"PeriodicalIF":0.0,"publicationDate":"2018-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88473595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A binary classification problem is considered. The excess error probability of the k-nearestneighbor classification rule according to the error probability of the Bayes decision is revisited by a decomposition of the excess error probability into approximation and estimation errors. Under a weak margin condition and under a modified Lipschitz condition or a local Lipschitz condition, tight upper bounds are presented such that one avoids the condition that the feature vector is bounded. The concept of modified Lipschitz condition is applied for discrete distributions, too. As a consequence of both concepts, we present the rate of convergence of L2 error for the corresponding nearest neighbor regression estimate.
{"title":"Rate of Convergence of $k$-Nearest-Neighbor Classification Rule","authors":"Maik Döring, L. Györfi, Harro Walk","doi":"10.14760/OWP-2017-25","DOIUrl":"https://doi.org/10.14760/OWP-2017-25","url":null,"abstract":"A binary classification problem is considered. The excess error probability of the k-nearestneighbor classification rule according to the error probability of the Bayes decision is revisited by a decomposition of the excess error probability into approximation and estimation errors. Under a weak margin condition and under a modified Lipschitz condition or a local Lipschitz condition, tight upper bounds are presented such that one avoids the condition that the feature vector is bounded. The concept of modified Lipschitz condition is applied for discrete distributions, too. As a consequence of both concepts, we present the rate of convergence of L2 error for the corresponding nearest neighbor regression estimate.","PeriodicalId":14794,"journal":{"name":"J. Mach. Learn. Res.","volume":"27 1","pages":"227:1-227:16"},"PeriodicalIF":0.0,"publicationDate":"2017-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81261273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ryan Giordano, Tamara Broderick, Michael I. Jordan
Variational Bayes (VB) is an approximate Bayesian posterior inference technique that is increasingly popular due to its fast runtimes on large-scale datasets. However, even when VB provides accurate posterior means for certain parameters, it often mis-estimates variances and covariances. Furthermore, prior robustness measures have remained undeveloped for VB. By deriving a simple formula for the effect of infinitesimal model perturbations on VB posterior means, we provide both improved covariance estimates and local robustness measures for VB, thus greatly expanding the practical usefulness of VB posterior approximations. The estimates for VB posterior covariances rely on a result from the classical Bayesian robustness literature relating derivatives of posterior expectations to posterior covariances. Our key assumption is that the VB approximation provides good estimates of a select subset of posterior means -- an assumption that has been shown to hold in many practical settings. In our experiments, we demonstrate that our methods are simple, general, and fast, providing accurate posterior uncertainty estimates and robustness measures with runtimes that can be an order of magnitude smaller than MCMC.
{"title":"Covariances, Robustness, and Variational Bayes","authors":"Ryan Giordano, Tamara Broderick, Michael I. Jordan","doi":"10.5555/3291125.3309613","DOIUrl":"https://doi.org/10.5555/3291125.3309613","url":null,"abstract":"Variational Bayes (VB) is an approximate Bayesian posterior inference technique that is increasingly popular due to its fast runtimes on large-scale datasets. However, even when VB provides accurate posterior means for certain parameters, it often mis-estimates variances and covariances. Furthermore, prior robustness measures have remained undeveloped for VB. By deriving a simple formula for the effect of infinitesimal model perturbations on VB posterior means, we provide both improved covariance estimates and local robustness measures for VB, thus greatly expanding the practical usefulness of VB posterior approximations. The estimates for VB posterior covariances rely on a result from the classical Bayesian robustness literature relating derivatives of posterior expectations to posterior covariances. Our key assumption is that the VB approximation provides good estimates of a select subset of posterior means -- an assumption that has been shown to hold in many practical settings. In our experiments, we demonstrate that our methods are simple, general, and fast, providing accurate posterior uncertainty estimates and robustness measures with runtimes that can be an order of magnitude smaller than MCMC.","PeriodicalId":14794,"journal":{"name":"J. Mach. Learn. Res.","volume":"70 1","pages":"51:1-51:49"},"PeriodicalIF":0.0,"publicationDate":"2017-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73755059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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