462 research outputs found
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
DISH: A Distributed Hybrid Optimization Method Leveraging System Heterogeneity
We study distributed optimization problems over multi-agent networks,
including consensus and network flow problems. Existing distributed methods
neglect the heterogeneity among agents' computational capabilities, limiting
their effectiveness. To address this, we propose DISH, a distributed hybrid
method that leverages system heterogeneity. DISH allows agents with higher
computational capabilities or lower computational costs to perform local
Newton-type updates while others adopt simpler gradient-type updates. Notably,
DISH covers existing methods like EXTRA, DIGing, and ESOM-0 as special cases.
To analyze DISH's performance with general update directions, we formulate
distributed problems as minimax problems and introduce GRAND (gradient-related
ascent and descent) and its alternating version, Alt-GRAND, for solving these
problems. GRAND generalizes DISH to centralized minimax settings, accommodating
various descent ascent update directions, including gradient-type, Newton-type,
scaled gradient, and other general directions, within acute angles to the
partial gradients. Theoretical analysis establishes global sublinear and linear
convergence rates for GRAND and Alt-GRAND in strongly-convex-nonconcave and
strongly-convex-PL settings, providing linear rates for DISH. In addition, we
derive the local superlinear convergence of Newton-based variations of GRAND in
centralized settings. Numerical experiments validate the effectiveness of our
methods
DISH: A Distributed Hybrid Primal-Dual Optimization Framework to Utilize System Heterogeneity
We consider solving distributed consensus optimization problems over
multi-agent networks. Current distributed methods fail to capture the
heterogeneity among agents' local computation capacities. We propose DISH as a
distributed hybrid primal-dual algorithmic framework to handle and utilize
system heterogeneity. Specifically, DISH allows those agents with higher
computational capabilities or cheaper computational costs to implement
Newton-type updates locally, while other agents can adopt the much simpler
gradient-type updates. We show that DISH is a general framework and includes
EXTRA, DIGing, and ESOM-0 as special cases. Moreover, when all agents take both
primal and dual Newton-type updates, DISH approximates Newton's method by
estimating both primal and dual Hessians. Theoretically, we show that DISH
achieves a linear (Q-linear) convergence rate to the exact optimal solution for
strongly convex functions, regardless of agents' choices of gradient-type and
Newton-type updates. Finally, we perform numerical studies to demonstrate the
efficacy of DISH in practice. To the best of our knowledge, DISH is the first
hybrid method allowing heterogeneous local updates for distributed consensus
optimization under general network topology with provable convergence and rate
guarantees
New isoforms and assembly of glutamine synthetase in the leaf of wheat (Triticum aestivum L.).
Glutamine synthetase (GS; EC 6.3.1.2) plays a crucial role in the assimilation and re-assimilation of ammonia derived from a wide variety of metabolic processes during plant growth and development. Here, three developmentally regulated isoforms of GS holoenzyme in the leaf of wheat (Triticum aestivum L.) seedlings are described using native-PAGE with a transferase activity assay. The isoforms showed different mobilities in gels, with GSII>GSIII>GSI. The cytosolic GSI was composed of three subunits, GS1, GSr1, and GSr2, with the same molecular weight (39.2kDa), but different pI values. GSI appeared at leaf emergence and was active throughout the leaf lifespan. GSII and GSIII, both located in the chloroplast, were each composed of a single 42.1kDa subunit with different pI values. GSII was active mainly in green leaves, while GSIII showed brief but higher activity in green leaves grown under field conditions. LC-MS/MS experiments revealed that GSII and GSIII have the same amino acid sequence, but GSII has more modification sites. With a modified blue native electrophoresis (BNE) technique and in-gel catalytic activity analysis, only two GS isoforms were observed: one cytosolic and one chloroplastic. Mass calibrations on BNE gels showed that the cytosolic GS1 holoenzyme was ~490kDa and likely a dodecamer, and the chloroplastic GS2 holoenzyme was ~240kDa and likely a hexamer. Our experimental data suggest that the activity of GS isoforms in wheat is regulated by subcellular localization, assembly, and modification to achieve their roles during plant development
Electromagnetic Scattering by Open-Ended Cavities: An Analysis Using Precorrected-FFT Approach
In this paper, the precorrected-FFT method is used to solve the electromagnetic scattering from two-dimensional cavities of arbitrary shape. The integral equation is discretized by the method of moments and the resultant matrix equation is solved iteratively by the generalized conjugate residual method. Instead of directly computing the matrix-vector multiplication, which requires N² operations, this approach reduces the computation complexity to O(N log N) as well as avoids the storage of large matrices. At the same time, a technique known as the complexifying k is applied to accelerate the convergence of the iterative method in solving this resonance problem. Some examples are considered and excellent agreements of radar cross sections between these computed using the present method and those from the direct solution are observed, demonstrating the feasibility and efficiency of the present method.Singapore-MIT Alliance (SMA
Exact Community Recovery in the Geometric SBM
We study the problem of exact community recovery in the Geometric Stochastic
Block Model (GSBM), where each vertex has an unknown community label as well as
a known position, generated according to a Poisson point process in
. Edges are formed independently conditioned on the community
labels and positions, where vertices may only be connected by an edge if they
are within a prescribed distance of each other. The GSBM thus favors the
formation of dense local subgraphs, which commonly occur in real-world
networks, a property that makes the GSBM qualitatively very different from the
standard Stochastic Block Model (SBM). We propose a linear-time algorithm for
exact community recovery, which succeeds down to the information-theoretic
threshold, confirming a conjecture of Abbe, Baccelli, and Sankararaman. The
algorithm involves two phases. The first phase exploits the density of local
subgraphs to propagate estimated community labels among sufficiently occupied
subregions, and produces an almost-exact vertex labeling. The second phase then
refines the initial labels using a Poisson testing procedure. Thus, the GSBM
enjoys local to global amplification just as the SBM, with the advantage of
admitting an information-theoretically optimal, linear-time algorithm
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