240 research outputs found
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
- …