A Stochastic View of Optimal Regret through Minimax Duality

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary

Closing the Gap Between Bandit and Full-Information Online Optimization: High-Probability Regret Bound

We demonstrate a modification of the algorithm of Dani et al for the online linear optimization problem in the bandit setting, which allows us to achieve an O( √{T ln T} ) regret bound in high probability against an adaptive adversary, as opposed to the in expectation result against an oblivious adversary of Dani et al. We obtain the same dependence on the dimension (n3/2)as that exhibited by Dani et al. The results of this paper rest firmly on those of Dani et al and the remarkable technique of Auer et al for obtaining high-probability bounds via optimistic estimates. This paper answers an open question: it eliminates the gap between the high-probability bounds obtained in the full-information vs bandit settings

Optimal Strategies and Minimax Lower Bounds for Online Convex Games

A number of learning problems can be cast as an Online Convex Game: on each round, a learner makes a prediction x from a convex set, the environment plays a loss function f, and the learner’s long-term goal is to minimize regret. Algorithms have been proposed by Zinkevich, when f is assumed to be convex, and Hazan et al., when f is assumed to be strongly convex, that have provably low regret. We consider these two settings and analyze such games from a minimax perspective, proving minimax strategies and lower bounds in each case. These results prove that the existing algorithms are essentially optimal

Spectral Sparsification and Regret Minimization Beyond Matrix Multiplicative Updates

In this paper, we provide a novel construction of the linear-sized spectral sparsifiers of Batson, Spielman and Srivastava [BSS14]. While previous constructions required $\Omega(n^4)$ running time [BSS14, Zou12], our sparsification routine can be implemented in almost-quadratic running time $O(n^{2+\varepsilon})$. The fundamental conceptual novelty of our work is the leveraging of a strong connection between sparsification and a regret minimization problem over density matrices. This connection was known to provide an interpretation of the randomized sparsifiers of Spielman and Srivastava [SS11] via the application of matrix multiplicative weight updates (MWU) [CHS11, Vis14]. In this paper, we explain how matrix MWU naturally arises as an instance of the Follow-the-Regularized-Leader framework and generalize this approach to yield a larger class of updates. This new class allows us to accelerate the construction of linear-sized spectral sparsifiers, and give novel insights on the motivation behind Batson, Spielman and Srivastava [BSS14]

Antibodies against insulin measured by electrochemiluminescence predicts insulitis severity and disease onset in non-obese diabetic mice and can distinguish human type 1 diabetes status

Abstract Background The detection of insulin autoantibodies (IAA) aids in the prediction of autoimmune diabetes development. However, the long-standing, gold standard 125I-insulin radiobinding assay (RBA) has low reproducibility between laboratories, long sample processing times and requires the use of newly synthesized radiolabeled insulin for each set of assays. Therefore, a rapid, non-radioactive, and reproducible assay is highly desirable. Methods We have developed electrochemiluminescence (ECL)-based assays that fulfill these criteria in the measurement of IAA and anti-insulin antibodies (IA) in non-obese diabetic (NOD) mice and in type 1 diabetic individuals, respectively. Using the murine IAA ECL assay, we examined the correlation between IAA, histopathological insulitis, and blood glucose in a cohort of female NOD mice from 4 up to 36 weeks of age. We developed a human IA ECL assay that we compared to conventional RBA and validated using samples from 34 diabetic and 59 non-diabetic individuals in three independent laboratories. Results Our ECL assays were rapid and sensitive with a broad dynamic range and low background. In the NOD mouse model, IAA levels measured by ECL were positively correlated with insulitis severity, and the values measured at 8-10 weeks of age were predictive of diabetes onset. Using human serum and plasma samples, our IA ECL assay yielded reproducible and accurate results with an average sensitivity of 84% at 95% specificity with no statistically significant difference between laboratories. Conclusions These novel, non-radioactive ECL-based assays should facilitate reliable and fast detection of antibodies to insulin and its precursors sera and plasma in a standardized manner between laboratories in both research and clinical settings. Our next step is to evaluate the human IA assay in the detection of IAA in prediabetic subjects or those at risk of type 1 diabetes and to develop similar assays for other autoantibodies that together are predictive for the diagnosis of this common disorder, in order to improve prediction and facilitate future therapeutic trials.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

СИНТЕЗ И ХАРАКТЕРИЗАЦИЯ ТРИМЕТИЛ(ФЕНИЛ)СИЛАНА — ПРЕДШЕСТВЕННИКА ДЛЯ ГАЗОФАЗНЫХ ПРОЦЕССОВ ОСАЖДЕНИЯ ПЛЕНОК SiCx : H

The technique of synthesis and purification of trimethyl(phenyl)silane PhSiMe3, allowing to obtain the product with high yield. Individuality of the product was confirmed by elemental analysis for C, H, Si. IR, UV and 1H NMR–spectroscopic studies, defined its spectral characteristics. Complex thermal analysis and thermogravimetric defined thermoanalytical behavior effects of PhSiMe3 in an inert atmosphere. Tensimetric studies have shown that the compound has sufficient volatility and thermal stability for use as a precursor in the process of chemical vapor deposition (CVD). The composition and temperature limits of the possible crystalline phase complexes in equilibrium with the gas phase of different composition has been determed by method of thermodynamic modeling. Calculated CVD diagrams allow us to select the optimum conditions of film deposition. The possibility of using trimethyl(phenyl)silane in CVD processes for producing dielectric films of hydrogenated silicon carbide has been demonstrated. Разработана методика синтеза и очистки триметил(фенил)силана PhSiMe3, позволяющая получать целевой продукт с высоким выходом. Индивидуальность соединения подтверждена элементным анализом на C, H, Si. ИК−, УФ− и ЯМР−спектроскопическими исследованиями (1Н, 13C, 29Si) определены его спектральные характеристики. С помощью комплексного термического анализа определены термоаналитические и термогравиметрические эффекты поведения PhSiMe3 в инертной атмосфере. На основе данных тензометрических исследований показано, что это соединение обладает достаточной летучестью и термической устойчивостью для использования в качестве прекурсора в процессах химического осаждения из газовой фазы (CVD). Методом термодинамического моделирования определен состав и температурные границы возможных кристаллических фазовых комплексов в равновесии с газовой фазой различного состава. Рассчитанные CVD− диаграммы позволяют выбрать оптимальные условия процессов осаждения из газовой фазы пленок. Показана возможность использования PhSiMe3 в процессах CVD для получения диэлектрических пленок гидрогенизированного карбида кремния.

Closing the gap between bandit and full-information online optimization : high-probability regret bound

We demonstrate a modification of the algorithm of Dani et al for the online linear optimization problem in the bandit setting, which allows us to achieve an O( \sqrt{T ln T} ) regret bound in high probability against an adaptive adversary, as opposed to the in expectation result against an oblivious adversary of Dani et al. We obtain the same dependence on the dimension as that exhibited by Dani et al. The results of this paper rest firmly on those of Dani et al and the remarkable technique of Auer et al for obtaining high-probability bounds via optimistic estimates. This paper answers an open question: it eliminates the gap between the high-probability bounds obtained in the full-information vs bandit settings

Deep learning: a statistical viewpoint

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting, that is, accurate predictions despite overfitting training data. In this article, we survey recent progress in statistical learning theory that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behaviour of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favourable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.</jats:p