生成权重平衡和双随机有向图的分布式策略

On Integer Balancing of Digraphs

A weighted digraph is balanced if the sums of the weights of the incoming and of the outgoing edges are equal at each vertex. We show that if these sums are integers, then the edge weights can be integers as well.

Distributed Random-Fixed Projected Algorithm for Constrained Optimization Over Digraphs

This paper is concerned with a constrained optimization problem over a directed graph (digraph) of nodes, in which the cost function is a sum of local objectives, and each node only knows its local objective and constraints. To collaboratively solve the optimization, most of the existing works require the interaction graph to be balanced or "doubly-stochastic", which is quite restrictive and not necessary as shown in this paper. We focus on an epigraph form of the original optimization to resolve the "unbalanced" problem, and design a novel two-step recursive algorithm with a simple structure.…

Distributed Convex Optimization with Inequality Constraints over Time-varying Unbalanced Digraphs

This paper considers a distributed convex optimization problem with inequality constraints over time-varying unbalanced digraphs, where the cost function is a sum of local objectives, and each node of the graph only knows its local objective and inequality constraints. Although there is a vast literature on distributed optimization, most of them require the graph to be balanced, which is quite restrictive and not necessary. Very recently, the unbalanced problem has been resolved only for either time-invariant graphs or unconstrained optimization. This work addresses the unbalancedness by focus…

Limited Rate Distributed Weight-Balancing and Average Consensus Over Digraphs

Distributed quantized weight-balancing and average consensus over fixed digraphs are considered. A digraph with non-negative weights associated to its edges is weight-balanced if, for each node, the sum of the weights of its out-going edges is equal to that of its incoming edges. This paper proposes and analyzes the first distributed algorithm that solves the weight-balancing problem using only finite rate and simplex communications among nodes (compliant to the directed nature of the graph edges). Asymptotic convergence of the scheme is proved and a convergence rate analysis is provided. Buil…

动态有向图上的离散化分布式优化

Discretized Distributed Optimization over Dynamic Digraphs

本文提出一种在动态有向图上进行离散化分布式优化的算法，无需双随机权重设计，在切换拓扑下利用梯度跟踪与Lyapunov理论证明收敛性，有效应对链路移除或丢包并应用于分布式学习。

Finite rate distributed weight-balancing and average consensus over digraphs

This paper proposes the first distributed algorithm that solves the weight-balancing problem using only finite rate and simplex communications among nodes, compliant with the directed nature of the graph edges. It is proved that the algorithm converges to a weight-balanced solution at sublinear rate. The analysis builds upon a new metric inspired by positional system representations, which characterizes the dynamics of information exchange over the network, and on a novel step-size rule. Building on this result, a novel distributed algorithm is proposed that solves the average consensus proble…

Distributed Averaging Problems over Directed Signed Networks

This paper aims at addressing distributed averaging problems for signed networks in the presence of general directed topologies that are represented by signed digraphs. A new class of improved Laplacian potential functions is proposed by presenting two notions of any signed digraph: induced unsigned digraph and mirror (undirected) signed graph, based on which two distributed averaging protocols are designed using the nearest neighbor rules. It is shown that with any of the designed protocols, signed-average consensus (respectively, state stability) can be achieved if and only if the associated…

在具有切换通信的子网络零和博弈中计算纳什均衡

Nash Equilibrium Computation in Subnetwork Zero-Sum Games with Switching Communications

本文研究了由两个子网络组成的时变多智能体网络的分布式纳什均衡计算问题，提出了一种基于子梯度的分布式算法，证明了在均匀联合强连通图中可收敛到纳什均衡。

Sinkhorn双重随机注意力秩衰减分析

Sinkhorn doubly stochastic attention rank decay analysis

本文研究了网络深度下注意力秩的衰减问题，发现使用Sinkhorn算法归一化的双重随机注意力矩阵比标准Softmax行随机注意力更能保持秩。通过实验验证了这一现象，并推导了纯自注意力秩衰减的理论界限。

Balanced Policy Evaluation and Learning

We present a new approach to the problems of evaluating and learning personalized decision policies from observational data of past contexts, decisions, and outcomes. Only the outcome of the enacted decision is available and the historical policy is unknown. These problems arise in personalized medicine using electronic health records and in internet advertising. Existing approaches use inverse propensity weighting (or, doubly robust versions) to make historical outcome (or, residual) data look like it were generated by a new policy being evaluated or learned. But this relies on a plug-in appr…