Lower Complexity Bounds of Finite-Sum Optimization Problems: The Results and Construction

The contribution of this paper includes two aspects. First, we study the lower bound complexity for the minimax optimization problem whose objective function is the average of $n$ individual smooth component functions. We consider Proximal Incremental First-order (PIFO) algorithms which have access to gradient and proximal oracle for each individual component. We develop a novel approach for constructing adversarial problems, which partitions the tridiagonal matrix of classical examples into $n$ groups. This construction is friendly to the analysis of incremental gradient and proximal oracle. With this approach, we demonstrate the lower bounds of first-order algorithms for finding an $\varepsilon$-suboptimal point and an $\varepsilon$-stationary point in different settings. Second, we also derive the lower bounds of minimization optimization with PIFO algorithms from our approach, which can cover the results in \citep{woodworth2016tight} and improve the results in \citep{zhou2019lower}

Finite Element Analysis of Elastic Behavior of Suction Caisson

As the demand on energy increases rapidly, exploration and production in deep water and facilities in shallow water are in imperative need. Suction caissons are most commonly used as anchoring system for offshore floating structures and are used as foundations for coastal wind turbines in relatively shallow water. For a long time, suction caisson loaded in soft clay such as in Gulf of Mexico are considered rigid due to the stiffness being stronger than soft clay. The objective of this study is to investigate the elastic behavior of suction caissons in soft clay. A new 3-D finite element analysis method using coupled caisson-springs model is introduced. The properties of springs are developed based on a 2-D continuum finite element analysis and scaled to 3-D scenario. Computer program ABAQUS is used for the numerical analysis for the coupled caisson-springs model. Results show that elastic behavior of caissons is quite different with a rigid caisson particularly under small displacement. Taking the advantage of the newly developed model, the structural response of the caisson is also assessed

Stochastic Distributed Optimization under Average Second-order Similarity: Algorithms and Analysis

We study finite-sum distributed optimization problems involving a master node and $n-1$ local nodes under the popular $\delta$-similarity and $\mu$-strong convexity conditions. We propose two new algorithms, SVRS and AccSVRS, motivated by previous works. The non-accelerated SVRS method combines the techniques of gradient sliding and variance reduction and achieves a better communication complexity of $\tilde{\mathcal{O}}(n {+} \sqrt{n}\delta/\mu)$ compared to existing non-accelerated algorithms. Applying the framework proposed in Katyusha X, we also develop a directly accelerated version named AccSVRS with the $\tilde{\mathcal{O}}(n {+} n^{3/4}\sqrt{\delta/\mu})$ communication complexity. In contrast to existing results, our complexity bounds are entirely smoothness-free and exhibit superiority in ill-conditioned cases. Furthermore, we establish a nearly matched lower bound to verify the tightness of our AccSVRS method.Comment: Camera-ready version for NeurIPS 202

China is on the track tackling Enteromorpha spp forming green tide

Green tide management is supposed to be a long term fight rather than an episode during the 29th Olympic Games for China, since it has been gaining in scale and frequency during the past 3 decades in both marine and estuary environment all over the world. A number of rapid-responding studies including oceanographic comprehensive surveys along the coastline have been conducted during the bloom and post-bloom periods in 2008 by Chinese marine scientists. The preliminary results are as below: (1) phylogenetic analysis indicates that the bloom forming alga forms a clade with representatives of the green seaweed Enteromorpha linza, though, the alga has been identified as E. proliera by means of morphological; (2) the present data suggest that the bloom was originated from south of Yellow Sea, but not the severely affected area near Qingdao City; (3) pathways of reproduction for E. prolifera have approved to be multifarious, including sexual, asexual and vegetative propagation; (4) somatic cells may act as a propagule bank, which is supposed to be a very dangerous transmitting way for its marked movability, adaptability and viability; (5) pyrolysis of the alga showed that three stages appeared during the process, which are dehydration (18–20^o^C), main devolatilization (200–450^o^C) and residual decomposition (450–750^o^C), and activation energy of the alga was determined at 237.23 KJ•mol^-1^. Although the scarce knowlegde on E. prolifera not yet allow a fully understanding of the green tide, some of the results suggests possible directions in further green tide research and management

Reliable Federated Learning for Mobile Networks

Federated learning, as a promising machine learning approach, has emerged to leverage a distributed personalized dataset from a number of nodes, e.g., mobile devices, to improve performance while simultaneously providing privacy preservation for mobile users. In the federated learning, training data is widely distributed and maintained on the mobile devices as workers. A central aggregator updates a global model by collecting local updates from mobile devices using their local training data to train the global model in each iteration. However, unreliable data may be uploaded by the mobile devices (i.e., workers), leading to frauds in tasks of federated learning. The workers may perform unreliable updates intentionally, e.g., the data poisoning attack, or unintentionally, e.g., low-quality data caused by energy constraints or high-speed mobility. Therefore, finding out trusted and reliable workers in federated learning tasks becomes critical. In this article, the concept of reputation is introduced as a metric. Based on this metric, a reliable worker selection scheme is proposed for federated learning tasks. Consortium blockchain is leveraged as a decentralized approach for achieving efficient reputation management of the workers without repudiation and tampering. By numerical analysis, the proposed approach is demonstrated to improve the reliability of federated learning tasks in mobile networks

A Review of Wind Turbine Icing Prediction Technology

The global wind energy business has grown considerably in recent years. Wind energy has a bright future as a major component of the renewable energy sector. However, one of the major barriers to the growth of wind energy is the freezing of wind turbine blades. The major solution to overcome the aforementioned problem will be to foresee wind turbine ice using existing anti-icing technologies. As a result, improving wind turbine ice prediction technology can assist wind farms in achieving more precise operation scheduling, avoiding needless shutdowns, and increasing power generation efficiency. Traditional wind turbine icing prediction methods have problems such as misjudgment and omission, while machine learning algorithms have higher accuracy and precision. Because of the rapid advancement of deep learning technology, machine learning algorithms have become an important tool for predicting wind turbine icing. However, in real applications, machine learning algorithms still face obstacles and limits such as inadequate data and poor model interpretability, which require additional study and refinement. This chapter discusses the application of machine learning algorithms in wind turbine icing prediction, provides a comprehensive description of the applicability and accuracy of various machine learning algorithms in wind turbine icing prediction, and summarizes the applications and advantages