Zhan Gao

Lorenzo Mario Amorosa, Zhan Gao, Roberto Verdone et al.

In large-scale Internet of things networks, efficient medium access control (MAC) is critical due to the growing number of devices competing for limited communication resources. In this work, we consider a new challenge in which a set of nodes must transmit a set of shared messages to a central controller, without inter-node communication or retransmissions. To our knowledge, this is the first work to formalize and analyze the multi-shared-message decentralized random access problem. Messages are distributed among random subsets of nodes, which must implicitly coordinate their transmissions over shared communication opportunities. The objective is to guarantee the delivery of all shared messages, regardless of which nodes transmit them. We first prove the existence of an optimal deterministic strategy, and characterize the success rate degradation of a deterministic strategy under dynamic message-transmission patterns. To solve this problem, we propose a decentralized learning-based framework that enables nodes to autonomously synthesize deterministic transmission strategies aiming to maximize message delivery success, together with an online adaptation mechanism that maintains stable performance in dynamic scenarios. Extensive simulations validate the framework's effectiveness, scalability, and adaptability, demonstrating its robustness to varying network sizes and fast adaptation to dynamic changes in transmission patterns, outperforming state-of-the-art approaches.

Zhan Gao, Aryan Mokhtari, Alec Koppel

Non-asymptotic convergence analysis of quasi-Newton methods has gained attention with a landmark result establishing an explicit local superlinear rate of O$((1/\sqrt{t})^t)$. The methods that obtain this rate, however, exhibit a well-known drawback: they require the storage of the previous Hessian approximation matrix or all past curvature information to form the current Hessian inverse approximation. Limited-memory variants of quasi-Newton methods such as the celebrated L-BFGS alleviate this issue by leveraging a limited window of past curvature information to construct the Hessian inverse approximation. As a result, their per iteration complexity and storage requirement is O$(τd)$ where $τ\le d$ is the size of the window and $d$ is the problem dimension reducing the O$(d^2)$ computational cost and memory requirement of standard quasi-Newton methods. However, to the best of our knowledge, there is no result showing a non-asymptotic superlinear convergence rate for any limited-memory quasi-Newton method. In this work, we close this gap by presenting a Limited-memory Greedy BFGS (LG-BFGS) method that can achieve an explicit non-asymptotic superlinear rate. We incorporate displacement aggregation, i.e., decorrelating projection, in post-processing gradient variations, together with a basis vector selection scheme on variable variations, which greedily maximizes a progress measure of the Hessian estimate to the true Hessian. Their combination allows past curvature information to remain in a sparse subspace while yielding a valid representation of the full history. Interestingly, our established non-asymptotic superlinear convergence rate demonstrates an explicit trade-off between the convergence speed and memory requirement, which to our knowledge, is the first of its kind. Numerical results corroborate our theoretical findings and demonstrate the effectiveness of our method.

Zhan Gao, Fernando Gama, Alejandro Ribeiro

Graph neural networks (GNNs) are naturally distributed architectures for learning representations from network data. This renders them suitable candidates for decentralized tasks. In these scenarios, the underlying graph often changes with time due to link failures or topology variations, creating a mismatch between the graphs on which GNNs were trained and the ones on which they are tested. Online learning can be leveraged to retrain GNNs at testing time to overcome this issue. However, most online algorithms are centralized and usually offer guarantees only on convex problems, which GNNs rarely lead to. This paper develops the Wide and Deep GNN (WD-GNN), a novel architecture that can be updated with distributed online learning mechanisms. The WD-GNN consists of two components: the wide part is a linear graph filter and the deep part is a nonlinear GNN. At training time, the joint wide and deep architecture learns nonlinear representations from data. At testing time, the wide, linear part is retrained, while the deep, nonlinear one remains fixed. This often leads to a convex formulation. We further propose a distributed online learning algorithm that can be implemented in a decentralized setting. We also show the stability of the WD-GNN to changes of the underlying graph and analyze the convergence of the proposed online learning procedure. Experiments on movie recommendation, source localization and robot swarm control corroborate theoretical findings and show the potential of the WD-GNN for distributed online learning.

Zhan Gao, Elvin Isufi, Alejandro Ribeiro

Graph convolutional neural networks (GCNNs) are nonlinear processing tools to learn representations from network data. A key property of GCNNs is their stability to graph perturbations. Current analysis considers deterministic perturbations but fails to provide relevant insights when topological changes are random. This paper investigates the stability of GCNNs to stochastic graph perturbations induced by link losses. In particular, it proves the expected output difference between the GCNN over random perturbed graphs and the GCNN over the nominal graph is upper bounded by a factor that is linear in the link loss probability. We perform the stability analysis in the graph spectral domain such that the result holds uniformly for any graph. This result also shows the role of the nonlinearity and the architecture width and depth, and allows identifying handle to improve the GCNN robustness. Numerical simulations on source localization and robot swarm control corroborate our theoretical findings.

Zhan Gao, Subhrajit Bhattacharya, Leiming Zhang et al.

Graph neural networks (GNNs) are processing architectures that exploit graph structural information to model representations from network data. Despite their success, GNNs suffer from sub-optimal generalization performance given limited training data, referred to as over-fitting. This paper proposes Topology Adaptive Edge Dropping (TADropEdge) method as an adaptive data augmentation technique to improve generalization performance and learn robust GNN models. We start by explicitly analyzing how random edge dropping increases the data diversity during training, while indicating i.i.d. edge dropping does not account for graph structural information and could result in noisy augmented data degrading performance. To overcome this issue, we consider graph connectivity as the key property that captures graph topology. TADropEdge incorporates this factor into random edge dropping such that the edge-dropped subgraphs maintain similar topology as the underlying graph, yielding more satisfactory data augmentation. In particular, TADropEdge first leverages the graph spectrum to assign proper weights to graph edges, which represent their criticality for establishing the graph connectivity. It then normalizes the edge weights and drops graph edges adaptively based on their normalized weights. Besides improving generalization performance, TADropEdge reduces variance for efficient training and can be applied as a generic method modular to different GNN models. Intensive experiments on real-life and synthetic datasets corroborate theory and verify the effectiveness of the proposed method.

Zhan Gao, Fernando Gama, Alejandro Ribeiro

Spherical convolutional neural networks (Spherical CNNs) learn nonlinear representations from 3D data by exploiting the data structure and have shown promising performance in shape analysis, object classification, and planning among others. This paper investigates the properties that Spherical CNNs exhibit as they pertain to the rotational structure inherent in spherical signals. We build upon the rotation equivariance of spherical convolutions to show that Spherical CNNs are stable to general structure perturbations. In particular, we model arbitrary structure perturbations as diffeomorphism perturbations, and define the rotation distance that measures how far from rotations these perturbations are. We prove that the output change of a Spherical CNN induced by the diffeomorphism perturbation is bounded proportionally by the perturbation size under the rotation distance. This stability property coupled with the rotation equivariance provide theoretical guarantees that underpin the practical observations that Spherical CNNs exploit the rotational structure, maintain performance under structure perturbations that are close to rotations, and offer good generalization and faster learning.

Zhan Gao, Mark Eisen, Alejandro Ribeiro

This paper investigates the general problem of resource allocation for mitigating channel fading effects in Free Space Optical (FSO) communications. The resource allocation problem is modeled as the constrained stochastic optimization framework, which covers a variety of FSO scenarios involving power adaptation, relay selection and their joint allocation. Under this framework, we propose two algorithms that solve FSO resource allocation problems. We first present the Stochastic Dual Gradient (SDG) algorithm that is shown to solve the problem exactly by exploiting the strong duality but whose implementation necessarily requires explicit and accurate system models. As an alternative we present the Primal-Dual Deep Learning (PDDL) algorithm based on the SDG algorithm, which parametrizes the resource allocation policy with Deep Neural Networks (DNNs) and optimizes the latter via a primal-dual method. The parametrized resource allocation problem incurs only a small loss of optimality due to the strong representational power of DNNs, and can be moreover implemented without knowledge of system models. A wide set of numerical experiments are performed to corroborate the proposed algorithms in FSO resource allocation problems. We demonstrate their superior performance and computational efficiency compared to the baseline methods in both continuous power allocation and binary relay selection settings.

Zhan Gao, Mark Eisen, Alejandro Ribeiro

This paper investigates the optimal resource allocation in free space optical (FSO) fronthaul networks. The optimal allocation maximizes an average weighted sum-capacity subject to power limitation and data congestion constraints. Both adaptive power assignment and node selection are considered based on the instantaneous channel state information (CSI) of the links. By parameterizing the resource allocation policy, we formulate the problem as an unsupervised statistical learning problem. We consider the graph neural network (GNN) for the policy parameterization to exploit the FSO network structure with small-scale training parameters. The GNN is shown to retain the permutation equivariance that matches with the permutation equivariance of resource allocation policy in networks. The primal-dual learning algorithm is developed to train the GNN in a model-free manner, where the knowledge of system models is not required. Numerical simulations present the strong performance of the GNN relative to a baseline policy with equal power assignment and random node selection.

Zhan Gao, Fernando Gama, Alejandro Ribeiro

Graph neural networks (GNNs) learn representations from network data with naturally distributed architectures, rendering them well-suited candidates for decentralized learning. Oftentimes, this decentralized graph support changes with time due to link failures or topology variations. These changes create a mismatch between the graphs on which GNNs were trained and the ones on which they are tested. Online learning can be used to retrain GNNs at testing time, overcoming this issue. However, most online algorithms are centralized and work on convex problems (which GNNs rarely lead to). This paper proposes the Wide and Deep GNN (WD-GNN), a novel architecture that can be easily updated with distributed online learning mechanisms. The WD-GNN comprises two components: the wide part is a bank of linear graph filters and the deep part is a GNN. At training time, the joint architecture learns a nonlinear representation from data. At testing time, the deep part (nonlinear) is left unchanged, while the wide part is retrained online, leading to a convex problem. We derive convergence guarantees for this online retraining procedure and further propose a decentralized alternative. Experiments on the robot swarm control for flocking corroborate theory and show potential of the proposed architecture for distributed online learning.

Zhan Gao, Elvin Isufi, Alejandro Ribeiro

Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link fluctuations that occur due to environment, human factors, or external attacks. In these situations, the GNN fails to address its distributed task if the topological randomness is not considered accordingly. To overcome this issue, we put forth the stochastic graph neural network (SGNN) model: a GNN where the distributed graph convolution module accounts for the random network changes. Since stochasticity brings in a new learning paradigm, we conduct a statistical analysis on the SGNN output variance to identify conditions the learned filters should satisfy for achieving robust transference to perturbed scenarios, ultimately revealing the explicit impact of random link losses. We further develop a stochastic gradient descent (SGD) based learning process for the SGNN and derive conditions on the learning rate under which this learning process converges to a stationary point. Numerical results corroborate our theoretical findings and compare the benefits of SGNN robust transference with a conventional GNN that ignores graph perturbations during learning.

Zhan Gao, Mark Eisen, Alejandro Ribeiro

Radio on Free Space Optics (RoFSO), as a universal platform for heterogeneous wireless services, is able to transmit multiple radio frequency signals at high rates in free space optical networks. This paper investigates the optimal design of power allocation for Wavelength Division Multiplexing (WDM) transmission in RoFSO systems. The proposed problem is a weighted total capacity maximization problem with two constraints of total power limitation and eye safety concern. The model-based Stochastic Dual Gradient algorithm is presented first, which solves the problem exactly by exploiting the null duality gap. The model-free Primal-Dual Deep Learning algorithm is then developed to learn and optimize the power allocation policy with Deep Neural Network (DNN) parametrization, which can be utilized without any knowledge of system models. Numerical simulations are performed to exhibit significant performance of our algorithms compared to the average equal power allocation.