Game among Interdependent Networks: The Impact of Rationality on System Robustness

Many real-world systems are composed of interdependent networks that rely on one another. Such networks are typically designed and operated by different entities, who aim at maximizing their own payoffs. There exists a game among these entities when designing their own networks. In this paper, we study the game investigating how the rational behaviors of entities impact the system robustness. We first introduce a mathematical model to quantify the interacting payoffs among varying entities. Then we study the Nash equilibrium of the game and compare it with the optimal social welfare. We reveal that the cooperation among different entities can be reached to maximize the social welfare in continuous game only when the average degree of each network is constant. Therefore, the huge gap between Nash equilibrium and optimal social welfare generally exists. The rationality of entities makes the system inherently deficient and even renders it extremely vulnerable in some cases. We analyze our model for two concrete systems with continuous strategy space and discrete strategy space, respectively. Furthermore, we uncover some factors (such as weakening coupled strength of interdependent networks, designing suitable topology dependency of the system) that help reduce the gap and the system vulnerability

Robust Fully-Asynchronous Methods for Distributed Training over General Architecture

Perfect synchronization in distributed machine learning problems is inefficient and even impossible due to the existence of latency, package losses and stragglers. We propose a Robust Fully-Asynchronous Stochastic Gradient Tracking method (R-FAST), where each device performs local computation and communication at its own pace without any form of synchronization. Different from existing asynchronous distributed algorithms, R-FAST can eliminate the impact of data heterogeneity across devices and allow for packet losses by employing a robust gradient tracking strategy that relies on properly designed auxiliary variables for tracking and buffering the overall gradient vector. More importantly, the proposed method utilizes two spanning-tree graphs for communication so long as both share at least one common root, enabling flexible designs in communication architectures. We show that R-FAST converges in expectation to a neighborhood of the optimum with a geometric rate for smooth and strongly convex objectives; and to a stationary point with a sublinear rate for general non-convex settings. Extensive experiments demonstrate that R-FAST runs 1.5-2 times faster than synchronous benchmark algorithms, such as Ring-AllReduce and D-PSGD, while still achieving comparable accuracy, and outperforms existing asynchronous SOTA algorithms, such as AD-PSGD and OSGP, especially in the presence of stragglers

Self-synchronization theory of a dual mass vibrating system driven by two coupled exciters. Part 2: Numeric analysis

The coupling dynamic characteristics of the vibrating system with dual mass are analyzed quantitatively. Both the load torque and the coupling torque have three items. Two of them are concerned with the translation of the system, and the third item is related to the rotation of the system. Through numerical computation, the effects of translation and rotation in the system are considered in relation to the self-synchronization. The phase difference of two eccentric blocks is caused by the difference of the rated revolution of two motors. The stability of the synchronous operation is dependent on the structural parameters of the system, such as the mass ratio of two eccentric blocks and the distance between motor and centroid of the rigid frame. Simulation is carried out to verify that the system can be synchronized and the model can ensure the stability of synchronization if the parameters of the system meet the conditions of synchronous implementation and stability. Simulations are also performed for the case of self-synchronization of two motors with different rated revolutions