Zhuqing Liu

Xin Zhang, Minghong Fang, Zhuqing Liu et al.

Federated learning (FL) has received a surge of interest in recent years thanks to its benefits in data privacy protection, efficient communication, and parallel data processing. Also, with appropriate algorithmic designs, one could achieve the desirable linear speedup for convergence effect in FL. However, most existing works on FL are limited to systems with i.i.d. data and centralized parameter servers and results on decentralized FL with heterogeneous datasets remains limited. Moreover, whether or not the linear speedup for convergence is achievable under fully decentralized FL with data heterogeneity remains an open question. In this paper, we address these challenges by proposing a new algorithm, called NET-FLEET, for fully decentralized FL systems with data heterogeneity. The key idea of our algorithm is to enhance the local update scheme in FL (originally intended for communication efficiency) by incorporating a recursive gradient correction technique to handle heterogeneous datasets. We show that, under appropriate parameter settings, the proposed NET-FLEET algorithm achieves a linear speedup for convergence. We further conduct extensive numerical experiments to evaluate the performance of the proposed NET-FLEET algorithm and verify our theoretical findings.

Zhuqing Liu, Xin Zhang, Prashant Khanduri et al.

In recent years, decentralized bilevel optimization problems have received increasing attention in the networking and machine learning communities thanks to their versatility in modeling decentralized learning problems over peer-to-peer networks (e.g., multi-agent meta-learning, multi-agent reinforcement learning, personalized training, and Byzantine-resilient learning). However, for decentralized bilevel optimization over peer-to-peer networks with limited computation and communication capabilities, how to achieve low sample and communication complexities are two fundamental challenges that remain under-explored so far. In this paper, we make the first attempt to investigate the class of decentralized bilevel optimization problems with nonconvex and strongly-convex structure corresponding to the outer and inner subproblems, respectively. Our main contributions in this paper are two-fold: i) We first propose a deterministic algorithm called INTERACT (inner-gradient-descent-outer-tracked-gradient) that requires the sample complexity of $\mathcal{O}(n ε^{-1})$ and communication complexity of $\mathcal{O}(ε^{-1})$ to solve the bilevel optimization problem, where $n$ and $ε> 0$ are the number of samples at each agent and the desired stationarity gap, respectively. ii) To relax the need for full gradient evaluations in each iteration, we propose a stochastic variance-reduced version of INTERACT (SVR-INTERACT), which improves the sample complexity to $\mathcal{O}(\sqrt{n} ε^{-1})$ while achieving the same communication complexity as the deterministic algorithm. To our knowledge, this work is the first that achieves both low sample and communication complexities for solving decentralized bilevel optimization problems over networks. Our numerical experiments also corroborate our theoretical findings.

Zhuqing Liu, Xin Zhang, Songtao Lu et al.

Recently, min-max optimization problems have received increasing attention due to their wide range of applications in machine learning (ML). However, most existing min-max solution techniques are either single-machine or distributed algorithms coordinated by a central server. In this paper, we focus on the decentralized min-max optimization for learning with domain constraints, where multiple agents collectively solve a nonconvex-strongly-concave min-max saddle point problem without coordination from any server. Decentralized min-max optimization problems with domain constraints underpins many important ML applications, including multi-agent ML fairness assurance, and policy evaluations in multi-agent reinforcement learning. We propose an algorithm called PRECISION (proximal gradient-tracking and stochastic recursive variance reduction) that enjoys a convergence rate of $O(1/T)$, where $T$ is the maximum number of iterations. To further reduce sample complexity, we propose PRECISION$^+$ with an adaptive batch size technique. We show that the fast $O(1/T)$ convergence of PRECISION and PRECISION$^+$ to an $ε$-stationary point imply $O(ε^{-2})$ communication complexity and $O(m\sqrt{n}ε^{-2})$ sample complexity, where $m$ is the number of agents and $n$ is the size of dataset at each agent. To our knowledge, this is the first work that achieves $O(ε^{-2})$ in both sample and communication complexities in decentralized min-max learning with domain constraints. Our experiments also corroborate the theoretical results.

Haibo Yang, Zhuqing Liu, Jia Liu et al.

In recent years, multi-objective optimization (MOO) emerges as a foundational problem underpinning many multi-agent multi-task learning applications. However, existing algorithms in MOO literature remain limited to centralized learning settings, which do not satisfy the distributed nature and data privacy needs of such multi-agent multi-task learning applications. This motivates us to propose a new federated multi-objective learning (FMOL) framework with multiple clients distributively and collaboratively solving an MOO problem while keeping their training data private. Notably, our FMOL framework allows a different set of objective functions across different clients to support a wide range of applications, which advances and generalizes the MOO formulation to the federated learning paradigm for the first time. For this FMOL framework, we propose two new federated multi-objective optimization (FMOO) algorithms called federated multi-gradient descent averaging (FMGDA) and federated stochastic multi-gradient descent averaging (FSMGDA). Both algorithms allow local updates to significantly reduce communication costs, while achieving the {\em same} convergence rates as those of their algorithmic counterparts in the single-objective federated learning. Our extensive experiments also corroborate the efficacy of our proposed FMOO algorithms.

Haibo Yang, Zhuqing Liu, Xin Zhang et al.

To lower the communication complexity of federated min-max learning, a natural approach is to utilize the idea of infrequent communications (through multiple local updates) same as in conventional federated learning. However, due to the more complicated inter-outer problem structure in federated min-max learning, theoretical understandings of communication complexity for federated min-max learning with infrequent communications remain very limited in the literature. This is particularly true for settings with non-i.i.d. datasets and partial client participation. To address this challenge, in this paper, we propose a new algorithmic framework called stochastic sampling averaging gradient descent ascent (SAGDA), which i) assembles stochastic gradient estimators from randomly sampled clients as control variates and ii) leverages two learning rates on both server and client sides. We show that SAGDA achieves a linear speedup in terms of both the number of clients and local update steps, which yields an $\mathcal{O}(ε^{-2})$ communication complexity that is orders of magnitude lower than the state of the art. Interestingly, by noting that the standard federated stochastic gradient descent ascent (FSGDA) is in fact a control-variate-free special version of SAGDA, we immediately arrive at an $\mathcal{O}(ε^{-2})$ communication complexity result for FSGDA. Therefore, through the lens of SAGDA, we also advance the current understanding on communication complexity of the standard FSGDA method for federated min-max learning.

Zhuqing Liu, Xin Zhang, Jia Liu

To increase the training speed of distributed learning, recent years have witnessed a significant amount of interest in developing both synchronous and asynchronous distributed stochastic variance-reduced optimization methods. However, all existing synchronous and asynchronous distributed training algorithms suffer from various limitations in either convergence speed or implementation complexity. This motivates us to propose an algorithm called STNTHESIS (semi-asynchronous path-integrated stochastic gradient search), which leverages the special structure of the variance-reduction framework to overcome the limitations of both synchronous and asynchronous distributed learning algorithms while retaining their salient features. We consider two implementations of STNTHESIS under distributed and shared memory architectures. We show that our STNTHESIS algorithms have $O(\sqrt{N}ε^{-2}(Δ+1)+N)$ and $O(\sqrt{N}ε^{-2}(Δ+1) d+N)$ computational complexities for achieving an $ε$-stationary point in non-convex learning under distributed and shared memory architectures, respectively, where N denotes the total number of training samples and $Δ$ represents the maximum delay of the workers. Moreover, we investigate the generalization performance of \algname by establishing algorithmic stability bounds for quadratic strongly convex and non-convex optimization. We further conduct extensive numerical experiments to verify our theoretical findings

Zhiyao Zhang, Zhuqing Liu, Xin Zhang et al.

As machine learning (ML) applications grow increasingly complex in recent years, modern ML frameworks often need to address multiple potentially conflicting objectives with coupled decision variables across different layers. This creates a compelling need for multi-objective bilevel learning (MOBL). So far, however, the field of MOBL remains in its infancy and many important problems remain under-explored. This motivates us to fill this gap and systematically investigate the theoretical and algorithmic foundation of MOBL. Specifically, we consider MOBL problems with multiple conflicting objectives guided by preferences at the upper-level subproblem, where part of the inputs depend on the optimal solution of the lower-level subproblem. Our goal is to develop efficient MOBL optimization algorithms to (1) identify a preference-guided Pareto-stationary solution with low oracle complexity; and (2) enable systematic Pareto front exploration. To this end, we propose a unifying algorithmic framework called weighted-Chebyshev multi-hyper-gradient-descent (WC-MHGD) for both deterministic and stochastic settings with finite-time Pareto-stationarity convergence rate guarantees, which not only implies low oracle complexity but also induces systematic Pareto front exploration. We further conduct extensive experiments to confirm our theoretical results.

Minghong Fang, Seyedsina Nabavirazavi, Zhuqing Liu et al.

Federated learning (FL) allows multiple clients to collaboratively train a global machine learning model through a server, without exchanging their private training data. However, the decentralized aspect of FL makes it susceptible to poisoning attacks, where malicious clients can manipulate the global model by sending altered local model updates. To counter these attacks, a variety of aggregation rules designed to be resilient to Byzantine failures have been introduced. Nonetheless, these methods can still be vulnerable to sophisticated attacks or depend on unrealistic assumptions about the server. In this paper, we demonstrate that there is no need to design new Byzantine-robust aggregation rules; instead, FL can be secured by enhancing the robustness of well-established aggregation rules. To this end, we present FoundationFL, a novel defense mechanism against poisoning attacks. FoundationFL involves the server generating synthetic updates after receiving local model updates from clients. It then applies existing Byzantine-robust foundational aggregation rules, such as Trimmed-mean or Median, to combine clients' model updates with the synthetic ones. We theoretically establish the convergence performance of FoundationFL under Byzantine settings. Comprehensive experiments across several real-world datasets validate the efficiency of our FoundationFL method.

Minghong Fang, Zhuqing Liu, Xuecen Zhao et al.

Federated learning (FL) has gained attention as a distributed learning paradigm for its data privacy benefits and accelerated convergence through parallel computation. Traditional FL relies on a server-client (SC) architecture, where a central server coordinates multiple clients to train a global model, but this approach faces scalability challenges due to server communication bottlenecks. To overcome this, the ring-all-reduce (RAR) architecture has been introduced, eliminating the central server and achieving bandwidth optimality. However, the tightly coupled nature of RAR's ring topology exposes it to unique Byzantine attack risks not present in SC-based FL. Despite its potential, designing Byzantine-robust RAR-based FL algorithms remains an open problem. To address this gap, we propose BRACE (Byzantine-robust ring-all-reduce), the first RAR-based FL algorithm to achieve both Byzantine robustness and communication efficiency. We provide theoretical guarantees for the convergence of BRACE under Byzantine attacks, demonstrate its bandwidth efficiency, and validate its practical effectiveness through experiments. Our work offers a foundational understanding of Byzantine-robust RAR-based FL design.