Near-Optimal Algorithms for Making the Gradient Small in Stochastic Minimax Optimization

We study the problem of finding a near-stationary point for smooth minimax optimization. The recent proposed extra anchored gradient (EAG) methods achieve the optimal convergence rate for the convex-concave minimax problem in deterministic setting. However, the direct extension of EAG to stochastic optimization is not efficient.In this paper, we design a novel stochastic algorithm called Recursive Anchored IteratioN (RAIN). We show that the RAIN achieves near-optimal stochastic first-order oracle (SFO) complexity for stochastic minimax optimization in both convex-concave and strongly-convex-strongly-concave cases. In addition, we extend the idea of RAIN to solve structured nonconvex-nonconcave minimax problem and it also achieves near-optimal SFO complexity

Bilevel Optimization without Lower-Level Strong Convexity from the Hyper-Objective Perspective

Bilevel optimization reveals the inner structure of otherwise oblique optimization problems, such as hyperparameter tuning and meta-learning. A common goal in bilevel optimization is to find stationary points of the hyper-objective function. Although this hyper-objective approach is widely used, its theoretical properties have not been thoroughly investigated in cases where the lower-level functions lack strong convexity. In this work, we take a step forward and study the hyper-objective approach without the typical lower-level strong convexity assumption. Our hardness results show that the hyper-objective of general convex lower-level functions can be intractable either to evaluate or to optimize. To tackle this challenge, we introduce the gradient dominant condition, which strictly relaxes the strong convexity assumption by allowing the lower-level solution set to be non-singleton. Under the gradient dominant condition, we propose the Inexact Gradient-Free Method (IGFM), which uses the Switching Gradient Method (SGM) as the zeroth order oracle, to find an approximate stationary point of the hyper-objective. We also extend our results to nonsmooth lower-level functions under the weak sharp minimum condition

Communication Efficient Distributed Newton Method with Fast Convergence Rates

We propose a communication and computation efficient second-order method for distributed optimization. For each iteration, our method only requires $\mathcal{O}(d)$ communication complexity, where $d$ is the problem dimension. We also provide theoretical analysis to show the proposed method has the similar convergence rate as the classical second-order optimization algorithms. Concretely, our method can find~$\big(\epsilon, \sqrt{dL\epsilon}\,\big)$-second-order stationary points for nonconvex problem by $\mathcal{O}\big(\sqrt{dL}\,\epsilon^{-3/2}\big)$ iterations, where $L$ is the Lipschitz constant of Hessian. Moreover, it enjoys a local superlinear convergence under the strongly-convex assumption. Experiments on both convex and nonconvex problems show that our proposed method performs significantly better than baselines.Comment: Accepted in SIGKDD 202

Evidence for perinatal and child health care guidelines in crisis settings: can Cochrane help?

<p>Abstract</p> <p>Background</p> <p>It is important that healthcare provided in crisis settings is based on the best available research evidence. We reviewed guidelines for child and perinatal health care in crisis situations to determine whether they were based on research evidence, whether Cochrane systematic reviews were available in the clinical areas addressed by these guidelines and whether summaries of these reviews were provided in Evidence Aid.</p> <p>Methods</p> <p>Broad internet searches were undertaken to identify relevant guidelines. Guidelines were appraised using AGREE and the clinical areas that were relevant to perinatal or child health were extracted. We searched The Cochrane Database of Systematic Reviews to identify potentially relevant reviews. For each review we determined how many trials were included, and how many were conducted in resource-limited settings.</p> <p>Results</p> <p>Six guidelines met selection criteria. None of the included guidelines were clearly based on research evidence. 198 Cochrane reviews were potentially relevant to the guidelines. These reviews predominantly addressed nutrient supplementation, breastfeeding, malaria, maternal hypertension, premature labour and prevention of HIV transmission. Most reviews included studies from developing settings. However for large portions of the guidelines, particularly health services delivery, there were no relevant reviews. Only 18 (9.1%) reviews have summaries in Evidence Aid.</p> <p>Conclusions</p> <p>We did not identify any evidence-based guidelines for perinatal and child health care in disaster settings. We found many Cochrane reviews that could contribute to the evidence-base supporting future guidelines. However there are important issues to be addressed in terms of the relevance of the available reviews and increasing the number of reviews addressing health care delivery.</p

Global prevalence and genotype distribution of hepatitis C virus infection in 2015 : A modelling study

Publisher Copyright: © 2017 Elsevier LtdBackground The 69th World Health Assembly approved the Global Health Sector Strategy to eliminate hepatitis C virus (HCV) infection by 2030, which can become a reality with the recent launch of direct acting antiviral therapies. Reliable disease burden estimates are required for national strategies. This analysis estimates the global prevalence of viraemic HCV at the end of 2015, an update of—and expansion on—the 2014 analysis, which reported 80 million (95% CI 64–103) viraemic infections in 2013. Methods We developed country-level disease burden models following a systematic review of HCV prevalence (number of studies, n=6754) and genotype (n=11 342) studies published after 2013. A Delphi process was used to gain country expert consensus and validate inputs. Published estimates alone were used for countries where expert panel meetings could not be scheduled. Global prevalence was estimated using regional averages for countries without data. Findings Models were built for 100 countries, 59 of which were approved by country experts, with the remaining 41 estimated using published data alone. The remaining countries had insufficient data to create a model. The global prevalence of viraemic HCV is estimated to be 1·0% (95% uncertainty interval 0·8–1·1) in 2015, corresponding to 71·1 million (62·5–79·4) viraemic infections. Genotypes 1 and 3 were the most common cause of infections (44% and 25%, respectively). Interpretation The global estimate of viraemic infections is lower than previous estimates, largely due to more recent (lower) prevalence estimates in Africa. Additionally, increased mortality due to liver-related causes and an ageing population may have contributed to a reduction in infections. Funding John C Martin Foundation.publishersversionPeer reviewe

A Simple and Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization

This paper studies the stochastic optimization for decentralized nonconvex-strongly-concave minimax problem. We propose a simple and efficient algorithm, called Decentralized Recursive-gradient descEnt Ascent Method (\texttt{DREAM}), which achieves the best-known theoretical guarantee for finding the $\epsilon$-stationary point of the primal function. For the online setting, the proposed method requires $\mathcal{O}(\kappa^3\epsilon^{-3})$ stochastic first-order oracle (SFO) calls and $\mathcal{O}\big(\kappa^2\epsilon^{-2}/\sqrt{1-\lambda_2(W)}\,\big)$ communication rounds to find an $\epsilon$-stationary point, where $\kappa$ is the condition number and $\lambda_2(W)$ is the second-largest eigenvalue of the gossip matrix~$W$. For the offline setting with totally $N$ component functions, the proposed method requires $\mathcal{O}\big(\kappa^2 \sqrt{N} \epsilon^{-2}\big)$ SFO calls and the same communication complexity as the online setting

Cloud thermodynamic phase detection using a directional polarimetric camera (DPC)

International audienceCloud phase detection via satellites is essential in the accurate estimation of cloud radiative forcing at global and regional scales. The difference in polarized reflectance features between liquid and ice clouds can be used for detecting the cloud phase. The directional polarimetric camera (DPC) onboard the Chinese GaoFen-5 satellite was launched in May 2018. The multidirectional, multispectral, and multipolarization capabilities of the DPC provide essential measurements to better understand the distribution of clouds and their physical properties. Numerous studies have demonstrated that the angular polarization signatures of ice crystals and liquid cloud droplets are effective in the detection of liquid and ice clouds. This study uses cloud phase profiles from Cloud Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) to select reliable liquid and ice cloud pixels via the DPC and analyzes the angular polarization signatures of ice and cloud clouds. These extracted angular polarization signatures are compared with the simulated results. Then, based on the earlier POLDER cloud phase algorithm, we propose a cloud phase detection method (P-CP) for DPC using multiple tests developed based on the extracted angular polarization signatures. Finally, P-CP algorithm is applied to the measurements of DPC and POLDER on 1 June 2008, and the analysis indicates that our cloud phase detection results agree well with the MODIS and POLDER cloud phase products