arXiv subjects

Minh N. Dao

Publications and source records attributed to Minh N. Dao.

At least 37 records · Page 2Linked to original sources

arXiv2024

Joint User Association and Power Control for Cell-Free Massive MIMO

This work proposes novel approaches that jointly design user equipment (UE) association and power control (PC) in a downlink user-centric cell-free massive multiple-input multiple-output (CFmMIMO) network, where each UE is only served by a set of access points (APs) for reducing the fronthaul signalling and computational complexity. In order to maximize the sum spectral efficiency (SE) of the UEs, we formulate a mixed-integer nonconvex optimization problem under constraints on the per-AP transmit power, quality-of-service rate requirements, maximum fronthaul signalling load, and maximum number of UEs served by each AP. In order to solve the formulated problem efficiently, we propose two different schemes according to the different sizes of the CFmMIMO systems. For small-scale CFmMIMO systems, we present a successive convex approximation (SCA) method to obtain a stationary solution and also develop a learning-based method (JointCFNet) to reduce the computational complexity. For large-scale CFmMIMO systems, we propose a low-complexity suboptimal algorithm using accelerated projected gradient (APG) techniques. Numerical results show that our JointCFNet can yield similar performance and significantly decrease the run time compared with the SCA algorithm in small-scale systems. The presented APG approach is confirmed to run much faster than the SCA algorithm in the large-scale system while obtaining an SE performance close to that of the SCA approach. Moreover, the median sum SE of the APG method is up to about 2.8 fold higher than that of the heuristic baseline scheme.

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arXiv2023

Douglas--Rachford is the best projection method

We prove that the Douglas--Rachford method applied to two closed convex cones in the Euclidean plane converges in finitely many steps if and only if the set of fixed points of the Douglas--Rachford operator is nontrivial. We analyze this special case using circle dynamics. We also construct explicit examples for a broad family of projection methods for which the set of fixed points of the relevant projection method operator is nontrivial, but the convergence is not finite. This three-parametric family is well known in the projection method literature and includes both the Douglas--Rachford method and the classic method of alternating projections. Even though our setting is fairly elementary, this work contributes in a new way to the body of theoretical research justifying the superior performance of the Douglas--Rachford method compared to other techniques. Moreover, our result leads to a neat sufficient condition for finite convergence of the Douglas--Rachford method in the locally polyhedral case on the plane, unifying and expanding several special cases available in the literature.

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arXiv2023

Locating Theorems of Differential Inclusions Governed by Maximally Monotone Operators

In this paper, we are interested in studying the asymptotic behavior of the solutions of differential inclusions governed by maximally monotone operators. In the case where the LaSalle's invariance principle is inconclusive, we provide a refined version of the invariance principle theorem. This result derives from the problem of locating the $ω$-limit set of a bounded solution of the dynamic. In addition, we propose an extension of LaSalle's invariance principle, which allows us to give a sharper location of the $ω$-limit set. The provided results are given in terms of nonsmooth Lyapunov pair-type functions.

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arXiv2023

Inertial Proximal Block Coordinate Method for a Class of Nonsmooth Sum-of-Ratios Optimization Problems

In this paper, we consider a class of nonsmooth sum-of-ratios fractional optimization problems with block structure. This model class is ubiquitous and encompasses several important nonsmooth optimization problems in the literature. We first propose an inertial proximal block coordinate method for solving this class of problems by exploiting the underlying structure. The global convergence of our method is guaranteed under the Kurdyka--Lojasiewicz (KL) property and some mild assumptions. We then identify the explicit exponents of the KL property for three important structured fractional optimization problems. In particular, for the sparse generalized eigenvalue problem with either cardinality regularization or sparsity constraint, we show that the KL exponents are 1/2, and so, the proposed method exhibits linear convergence rate. Finally, we illustrate our theoretical results with both analytic and simulated numerical examples.

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arXiv2023

A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems

In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is Lipschitz continuous, subtracted by a weakly convex function. This type of structured problems has many practical applications in machine learning and statistics such as compressed sensing, signal recovery, sparse dictionary learning, clustering, matrix factorization, and others. We develop a flexible extrapolated proximal subgradient algorithm for solving these problems with guaranteed subsequential convergence to a stationary point. The global convergence of the whole sequence generated by our algorithm is also established under the Kurdyka-Lojasiewicz property. To illustrate the promising numerical performance of the proposed algorithm, we conduct numerical experiments on two important nonconvex models. This includes a least squares problem with a nonconvex regularization and an optimal power flow problem with distributed energy resources.

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arXiv2022

Energy-Efficient Massive MIMO for Federated Learning: Transmission Designs and Resource Allocations

This work proposes novel synchronous, asynchronous, and session-based designs for energy-efficient massive multiple-input multiple-output networks to support federated learning (FL). The synchronous design relies on strict synchronization among users when executing each FL communication round, while the asynchronous design allows more flexibility for users to save energy by using lower computing frequencies. The session-based design splits the downlink and uplink phases in each FL communication round into separate sessions. In this design, we assign users such that one of the participating users in each session finishes its transmission and does not join the next session. As such, more power and degrees of freedom will be allocated to unfinished users, leading to higher rates, lower transmission times, and hence, a higher energy efficiency. In all three designs, we use zero-forcing processing for both uplink and downlink, and develop algorithms that optimize user assignment, time allocation, power, and computing frequencies to minimize the energy consumption at the base station and users, while guaranteeing a predefined maximum execution time of one FL communication round.

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arXiv2022

A New Look and Convergence Rate of Federated Multi-Task Learning with Laplacian Regularization

Non-Independent and Identically Distributed (non- IID) data distribution among clients is considered as the key factor that degrades the performance of federated learning (FL). Several approaches to handle non-IID data such as personalized FL and federated multi-task learning (FMTL) are of great interest to research communities. In this work, first, we formulate the FMTL problem using Laplacian regularization to explicitly leverage the relationships among the models of clients for multi-task learning. Then, we introduce a new view of the FMTL problem, which in the first time shows that the formulated FMTL problem can be used for conventional FL and personalized FL. We also propose two algorithms FedU and dFedU to solve the formulated FMTL problem in communication-centralized and decentralized schemes, respectively. Theoretically, we prove that the convergence rates of both algorithms achieve linear speedup for strongly convex and sublinear speedup of order 1/2 for nonconvex objectives. Experimentally, we show that our algorithms outperform the algorithm FedAvg, FedProx, SCAFFOLD, and AFL in FL settings, MOCHA in FMTL settings, as well as pFedMe and Per-FedAvg in personalized FL settings.

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arXiv2022

Joint Resource Allocation to Minimize Execution Time of Federated Learning in Cell-Free Massive MIMO

Due to its communication efficiency and privacy-preserving capability, federated learning (FL) has emerged as a promising framework for machine learning in 5G-and-beyond wireless networks. Of great interest is the design and optimization of new wireless network structures that support the stable and fast operation of FL. Cell-free massive multiple-input multiple-output (CFmMIMO) turns out to be a suitable candidate, which allows each communication round in the iterative FL process to be stably executed within a large-scale coherence time. Aiming to reduce the total execution time of the FL process in CFmMIMO, this paper proposes choosing only a subset of available users to participate in FL. An optimal selection of users with favorable link conditions would minimize the execution time of each communication round, while limiting the total number of communication rounds required. Toward this end, we formulate a joint optimization problem of user selection, transmit power, and processing frequency, subject to a predefined minimum number of participating users to guarantee the quality of learning. We then develop a new algorithm that is proven to converge to the neighbourhood of the stationary points of the formulated problem. Numerical results confirm that our proposed approach significantly reduces the FL total execution time over baseline schemes. The time reduction is more pronounced when the density of access point deployments is moderately low.

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arXiv2022

Data Size-Aware Downlink Massive MIMO: A Session-Based Approach

This letter considers the development of transmission strategies for the downlink of massive multiple-input multiple-output networks, with the objective of minimizing the completion time of the transmission. Specifically, we introduce a session-based scheme that splits time into sessions and allocates different rates in different sessions for the different users. In each session, one user is selected to complete its transmission and will not join subsequent sessions, which results in successively lower levels of interference when moving from one session to the next. An algorithm is developed to assign users and allocate transmit power that minimizes the completion time. Numerical results show that our proposed session-based scheme significantly outperforms conventional non-session-based schemes.

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arXiv2022

Graph Augmentation Learning

Graph Augmentation Learning (GAL) provides outstanding solutions for graph learning in handling incomplete data, noise data, etc. Numerous GAL methods have been proposed for graph-based applications such as social network analysis and traffic flow forecasting. However, the underlying reasons for the effectiveness of these GAL methods are still unclear. As a consequence, how to choose optimal graph augmentation strategy for a certain application scenario is still in black box. There is a lack of systematic, comprehensive, and experimentally validated guideline of GAL for scholars. Therefore, in this survey, we in-depth review GAL techniques from macro (graph), meso (subgraph), and micro (node/edge) levels. We further detailedly illustrate how GAL enhance the data quality and the model performance. The aggregation mechanism of augmentation strategies and graph learning models are also discussed by different application scenarios, i.e., data-specific, model-specific, and hybrid scenarios. To better show the outperformance of GAL, we experimentally validate the effectiveness and adaptability of different GAL strategies in different downstream tasks. Finally, we share our insights on several open issues of GAL, including heterogeneity, spatio-temporal dynamics, scalability, and generalization.

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arXiv2021

Generalized Bregman envelopes and proximity operators

Every maximally monotone operator can be associated with a family of convex functions, called the Fitzpatrick family or family of representative functions. Surprisingly, in 2017, Burachik and Martínez-Legaz showed that the well-known Bregman distance is a particular case of a general family of distances, each one induced by a specific maximally monotone operator and a specific choice of one of its representative functions. For the family of generalized Bregman distances, sufficient conditions for convexity, coercivity, and supercoercivity have recently been furnished. Motivated by these advances, we introduce in the present paper the generalized left and right envelopes and proximity operators, and we provide asymptotic results for parameters. Certain results extend readily from the more specific Bregman context, while others only extend for certain generalized cases. To illustrate, we construct examples from the Bregman generalizing case, together with the natural "extreme" cases that highlight the importance of which generalized Bregman distance is chosen.

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arXiv2021

An adaptive splitting algorithm for the sum of three operators

Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm for finding a zero of the sum of three operators. We assume that two of the operators are generalized monotone and their resolvents are computable, while the other operator is cocoercive but its resolvent is missing or costly to compute. Our splitting algorithm adapts new parameters to the generalized monotonicity of the operators and, at the same time, combines appropriate forward and backward steps to guarantee convergence to a solution of the problem.

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arXiv2020

Conical averagedness and convergence analysis of fixed point algorithms

We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the stability under relaxations, convex combinations and compositions. We derive conical averagedness properties of resolvents of generalized monotone operators. These properties are then utilized in order to analyze the convergence of the proximal point algorithm, the forward-backward algorithm, and the adaptive Douglas-Rachford algorithm. Our study unifies, improves and casts new light on recent studies of these topics.

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arXiv2020

Extrapolated Proximal Subgradient Algorithms for Nonconvex and Nonsmooth Fractional Programs

In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, where the numerator can be written as the sum of a continuously differentiable convex function whose gradient is Lipschitz continuous and a proper lower semicontinuous (possibly nonconvex) function, and the denominator is weakly convex over the constraint set. This model problem includes the composite optimization problems studied extensively lately, and encompasses many important modern fractional optimization problems arising from diverse areas such as the recently proposed scale invariant sparse signal reconstruction problem in signal processing. We propose a proximal subgradient algorithm with extrapolations for solving this optimization model and show that the iterated sequence generated by the algorithm is bounded and any of its limit points is a stationary point of the model problem. The choice of our extrapolation parameter is flexible and includes the popular extrapolation parameter adopted in the restarted Fast Iterative Shrinking-Threshold Algorithm (FISTA). By providing a unified analysis framework of descent methods, we establish the convergence of the full sequence under the assumption that a suitable merit function satisfies the Kurdyka--Łojasiewicz (KL) property. In particular, our algorithm exhibits linear convergence for the scale invariant sparse signal reconstruction problem and the Rayleigh quotient problem over spherical constraint. In the case where the denominator is the maximum of finitely many continuously differentiable weakly convex functions, we also propose an enhanced extrapolated proximal subgradient algorithm with guaranteed convergence to a stronger notion of stationary points of the model problem. Finally, we illustrate the proposed methods by both analytical and simulated numerical examples.

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arXiv2020

The Generalized Bregman Distance

Recently, a new distance has been introduced for the graphs of two point-to-set operators, one of which is maximally monotone. When both operators are the subdifferential of a proper lower semicontinuous convex function, this distance specializes under modest assumptions to the classical Bregman distance. We name this new distance the generalized Bregman distance, and we shed light on it with examples that utilize the other two most natural representative functions: the Fitzpatrick function and its conjugate. We provide sufficient conditions for convexity, coercivity, and supercoercivity: properties that are essential for implementation in proximal point type algorithms. We establish these results for both the left and right variants of this new distance. We construct examples closely related to the Kullback--Leibler divergence, which was previously considered in the context of Bregman distances, and whose importance in information theory is well known. In so doing, we demonstrate how to compute a difficult Fitzpatrick conjugate function, and we discover natural occurrences of the Lambert $\W$ function, whose importance in optimization is of growing interest.

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arXiv2020

Cell-Free Massive MIMO for Wireless Federated Learning

This paper proposes a novel scheme for cell-free massive multiple-input multiple-output (CFmMIMO) networks to support any federated learning (FL) framework. This scheme allows each instead of all the iterations of the FL framework to happen in a large-scale coherence time to guarantee a stable operation of an FL process. To show how to optimize the FL performance using this proposed scheme, we consider an existing FL framework as an example and target FL training time minimization for this framework. An optimization problem is then formulated to jointly optimize the local accuracy, transmit power, data rate, and users' processing frequency. This mixed-timescale stochastic nonconvex problem captures the complex interactions among the training time, and transmission and computation of training updates of one FL process. By employing the online successive convex approximation approach, we develop a new algorithm to solve the formulated problem with proven convergence to the neighbourhood of its stationary points. Our numerical results confirm that the presented joint design reduces the training time by up to $55\%$ over baseline approaches. They also show that CFmMIMO here requires the lowest training time for FL processes compared with cell-free time-division multiple access massive MIMO and collocated massive MIMO.

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arXiv2019

Adaptive Douglas-Rachford splitting algorithm for the sum of two operators

The Douglas-Rachford algorithm is a classical and powerful splitting method for minimizing the sum of two convex functions and, more generally, finding a zero of the sum of two maximally monotone operators. Although this algorithm is well understood when the involved operators are monotone or strongly monotone, the convergence theory for weakly monotone settings is far from being complete. In this paper, we propose an adaptive Douglas-Rachford splitting algorithm for the sum of two operators, one of which is strongly monotone while the other one is weakly monotone. With appropriately chosen parameters, the algorithm converges globally to a fixed point from which we derive a solution of the problem. When one operator is Lipschitz continuous, we prove global linear convergence, which sharpens recent known results.

math.OC↗

arXiv2018

Regularizing with Bregman-Moreau envelopes

Moreau's seminal paper, introducing what is now called the Moreau envelope and the proximity operator (also known as the proximal mapping), appeared in 1965. The Moreau envelope of a given convex function provides a regularized version which has additional desirable properties such as differentiability and full domain. Fifty years ago, Attouch proposed using the Moreau envelope for regularization. Since then, this branch of convex analysis has developed in many fruitful directions. In 1967, Bregman introduced what is nowadays known as the Bregman distance as a measure of discrepancy between two points generalizing the square of the Euclidean distance. Proximity operators based on the Bregman distance have become a topic of significant research as they are useful in the algorithmic solution of optimization problems. More recently, in 2012, Kan and Song studied regularization aspects of the left Bregman-Moreau envelope even for nonconvex functions. In this paper, we complement previous works by analyzing the left and right Bregman-Moreau envelopes and by providing additional asymptotic results. Several examples are provided.

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