12 research outputs found
A Faithful Distributed Implementation of Dual Decomposition and Average Consensus Algorithms
We consider large scale cost allocation problems and consensus seeking
problems for multiple agents, in which agents are suggested to collaborate in a
distributed algorithm to find a solution. If agents are strategic to minimize
their own individual cost rather than the global social cost, they are endowed
with an incentive not to follow the intended algorithm, unless the tax/subsidy
mechanism is carefully designed. Inspired by the classical
Vickrey-Clarke-Groves mechanism and more recent algorithmic mechanism design
theory, we propose a tax mechanism that incentivises agents to faithfully
implement the intended algorithm. In particular, a new notion of asymptotic
incentive compatibility is introduced to characterize a desirable property of
such class of mechanisms. The proposed class of tax mechanisms provides a
sequence of mechanisms that gives agents a diminishing incentive to deviate
from suggested algorithm.Comment: 8 page
Distributed Weight Selection in Consensus Protocols by Schatten Norm Minimization
In average consensus protocols, nodes in a network perform an iterative
weighted average of their estimates and those of their neighbors. The protocol
converges to the average of initial estimates of all nodes found in the
network. The speed of convergence of average consensus protocols depends on the
weights selected on links (to neighbors). We address in this paper how to
select the weights in a given network in order to have a fast speed of
convergence for these protocols. We approximate the problem of optimal weight
selection by the minimization of the Schatten p-norm of a matrix with some
constraints related to the connectivity of the underlying network. We then
provide a totally distributed gradient method to solve the Schatten norm
optimization problem. By tuning the parameter p in our proposed minimization,
we can simply trade-off the quality of the solution (i.e. the speed of
convergence) for communication/computation requirements (in terms of number of
messages exchanged and volume of data processed). Simulation results show that
our approach provides very good performance already for values of p that only
needs limited information exchange. The weight optimization iterative procedure
can also run in parallel with the consensus protocol and form a joint
consensus-optimization procedure.Comment: N° RR-8078 (2012
Fast-Convergent Dynamics for Distributed Resource Allocation Over Sparse Time-Varying Networks
In this paper, distributed dynamics are deployed to solve resource allocation
over time-varying multi-agent networks. The state of each agent represents the
amount of resources used/produced at that agent while the total amount of
resources is fixed. The idea is to optimally allocate the resources among the
group of agents by reducing the total cost functions subject to fixed amount of
total resources. The information of each agent is restricted to its own state
and cost function and those of its immediate neighbors. This is motivated by
distributed applications such as in mobile edge-computing, economic dispatch
over smart grids, and multi-agent coverage control. The non-Lipschitz dynamics
proposed in this work shows fast convergence as compared to the linear and some
nonlinear solutions in the literature. Further, the multi-agent network
connectivity is more relaxed in this paper. To be more specific, the proposed
dynamics even reaches optimal solution over time-varying disconnected
undirected networks as far as the union of these networks over some bounded
non-overlapping time-intervals includes a spanning-tree. The proposed
convergence analysis can be applied for similar 1st-order resource allocation
nonlinear dynamics. We provide simulations to verify our results
Newton-Raphson Consensus for Distributed Convex Optimization
We address the problem of distributed uncon- strained convex optimization
under separability assumptions, i.e., the framework where each agent of a
network is endowed with a local private multidimensional convex cost, is
subject to communication constraints, and wants to collaborate to compute the
minimizer of the sum of the local costs. We propose a design methodology that
combines average consensus algorithms and separation of time-scales ideas. This
strategy is proved, under suitable hypotheses, to be globally convergent to the
true minimizer. Intuitively, the procedure lets the agents distributedly
compute and sequentially update an approximated Newton- Raphson direction by
means of suitable average consensus ratios. We show with numerical simulations
that the speed of convergence of this strategy is comparable with alternative
optimization strategies such as the Alternating Direction Method of
Multipliers. Finally, we propose some alternative strategies which trade-off
communication and computational requirements with convergence speed.Comment: 18 pages, preprint with proof
A novel decentralized economic operation in islanded AC microgrids
Droop schemes are usually applied to the control of distributed generators (DGs) in microgrids (MGs) to realize proportional power sharing. The objective might, however, not suit MGs well for economic reasons. Addressing that issue, this paper proposes an alternative droop scheme for reducing the total active generation costs (TAGC). Optimal economic operation, DGs’ capacity limitations and system stability are fully considered basing on DGs’ generation costs. The proposed scheme utilizes the frequency as a carrier to realize the decentralized economic operation of MGs without communication links. Moreover, a fitting method is applied to balance DGs’ synchronous operation and economy. The effectiveness and performance of the proposed scheme are verified through simulations and experiments
Understanding A Class of Decentralized and Federated Optimization Algorithms: A Multi-Rate Feedback Control Perspective
Distributed algorithms have been playing an increasingly important role in
many applications such as machine learning, signal processing, and control.
Significant research efforts have been devoted to developing and analyzing new
algorithms for various applications. In this work, we provide a fresh
perspective to understand, analyze, and design distributed optimization
algorithms. Through the lens of multi-rate feedback control, we show that a
wide class of distributed algorithms, including popular decentralized/federated
schemes, can be viewed as discretizing a certain continuous-time feedback
control system, possibly with multiple sampling rates, such as decentralized
gradient descent, gradient tracking, and federated averaging. This key
observation not only allows us to develop a generic framework to analyze the
convergence of the entire algorithm class. More importantly, it also leads to
an interesting way of designing new distributed algorithms. We develop the
theory behind our framework and provide examples to highlight how the framework
can be used in practice