47 research outputs found
A Distributed Newton Method for Network Utility Maximization
Most existing work uses dual decomposition and subgradient methods to solve
Network Utility Maximization (NUM) problems in a distributed manner, which
suffer from slow rate of convergence properties. This work develops an
alternative distributed Newton-type fast converging algorithm for solving
network utility maximization problems with self-concordant utility functions.
By using novel matrix splitting techniques, both primal and dual updates for
the Newton step can be computed using iterative schemes in a decentralized
manner with limited information exchange. Similarly, the stepsize can be
obtained via an iterative consensus-based averaging scheme. We show that even
when the Newton direction and the stepsize in our method are computed within
some error (due to finite truncation of the iterative schemes), the resulting
objective function value still converges superlinearly to an explicitly
characterized error neighborhood. Simulation results demonstrate significant
convergence rate improvement of our algorithm relative to the existing
subgradient methods based on dual decomposition.Comment: 27 pages, 4 figures, LIDS report, submitted to CDC 201
Nested Distributed Gradient Methods with Adaptive Quantized Communication
In this paper, we consider minimizing a sum of local convex objective
functions in a distributed setting, where communication can be costly. We
propose and analyze a class of nested distributed gradient methods with
adaptive quantized communication (NEAR-DGD+Q). We show the effect of performing
multiple quantized communication steps on the rate of convergence and on the
size of the neighborhood of convergence, and prove R-Linear convergence to the
exact solution with increasing number of consensus steps and adaptive
quantization. We test the performance of the method, as well as some practical
variants, on quadratic functions, and show the effects of multiple quantized
communication steps in terms of iterations/gradient evaluations, communication
and cost.Comment: 9 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1709.0299
Supply Function Equilibrium in Networked Electricity Markets
We study deregulated power markets with strategic power suppliers. In
deregulated markets, each supplier submits its supply function (i.e., the
amount of electricity it is willing to produce at various prices) to the
independent system operator (ISO), who based on the submitted supply functions,
dispatches the suppliers to clear the market with minimal total generation
cost. If all suppliers reported their true marginal cost functions as supply
functions, the market outcome would be efficient (i.e., the total generation
cost is minimized). However, when suppliers are strategic and aim to maximize
their own profits, the reported supply functions are not necessarily the true
marginal cost functions, and the resulting market outcome may be inefficient.
The efficiency loss depends crucially on the topology of the underlying
transmission network. This paper provides an analytical upper bound of the
efficiency loss due to strategic suppliers, and proves that the bound is tight
under a large class of transmission networks (i.e., weakly cyclic networks).
Our upper bound sheds light on how the efficiency loss depends on the
transmission network topology (e.g., the degrees of nodes, the admittances and
flow limits of transmission lines).Comment: 13 pages, 6 figure
Scalable Spectrum Allocation for Large Networks Based on Sparse Optimization
Joint allocation of spectrum and user association is considered for a large
cellular network. The objective is to optimize a network utility function such
as average delay given traffic statistics collected over a slow timescale. A
key challenge is scalability: given Access Points (APs), there are
ways in which the APs can share the spectrum. The number of variables is
reduced from to , where is the number of users, by
optimizing over local overlapping neighborhoods, defined by interference
conditions, and by exploiting the existence of sparse solutions in which the
spectrum is divided into segments. We reformulate the problem by
optimizing the assignment of subsets of active APs to those segments. An
constraint enforces a one-to-one mapping of subsets to spectrum, and
an iterative (reweighted ) algorithm is used to find an approximate
solution. Numerical results for a network with 100 APs serving several hundred
users show the proposed method achieves a substantial increase in total
throughput relative to benchmark schemes.Comment: Submitted to the IEEE International Symposium on Information Theory
(ISIT), 201
A General Sensitivity Analysis Approach for Demand Response Optimizations
It is well-known that demand response can improve the system efficiency as
well as lower consumers' (prosumers') electricity bills. However, it is not
clear how we can either qualitatively identify the prosumer with the most
impact potential or quantitatively estimate each prosumer's contribution to the
total social welfare improvement when additional resource capacity/flexibility
is introduced to the system with demand response, such as allowing net-selling
behavior. In this work, we build upon existing literature on the electricity
market, which consists of price-taking prosumers each with various appliances,
an electric utility company and a social welfare optimizing distribution system
operator, to design a general sensitivity analysis approach (GSAA) that can
estimate the potential of each consumer's contribution to the social welfare
when given more resource capacity. GSAA is based on existence of an efficient
competitive equilibrium, which we establish in the paper. When prosumers'
utility functions are quadratic, GSAA can give closed forms characterization on
social welfare improvement based on duality analysis. Furthermore, we extend
GSAA to a general convex settings, i.e., utility functions with strong
convexity and Lipschitz continuous gradient. Even without knowing the specific
forms the utility functions, we can derive upper and lower bounds of the social
welfare improvement potential of each prosumer, when extra resource is
introduced. For both settings, several applications and numerical examples are
provided: including extending AC comfort zone, ability of EV to discharge and
net selling. The estimation results show that GSAA can be used to decide how to
allocate potentially limited market resources in the most impactful way.Comment: 17 page
FedHybrid: A Hybrid Primal-Dual Algorithm Framework for Federated Optimization
We consider a multi-agent consensus optimization problem over a server-client
(federated) network, where all clients are connected to a central server.
Current distributed algorithms fail to capture the heterogeneity in clients'
local computation capacities. Motivated by the generalized Method of
Multipliers in centralized optimization, we derive an approximate Newton-type
primal-dual method with a practical distributed implementation by utilizing the
server-client topology. Then we propose a new primal-dual algorithm framework
FedHybrid that allows different clients to perform various types of updates.
Specifically, each client can choose to perform either gradient-type or
Newton-type updates. We propose a novel analysis framework for primal-dual
methods and obtain a linear convergence rate of FedHybrid for strongly convex
functions, regardless of clients' choices of gradient-type or Newton-type
updates. Numerical studies are provided to demonstrate the efficacy of our
method in practice. To the best of our knowledge, this is the first hybrid
algorithmic framework allowing heterogeneous local updates for distributed
consensus optimization with a provable convergence and rate guarantee