Federated learning (FL) is a privacy-preserving distributed machine learning framework where multiple devices collaborate with the assistance of an aggregator. However, the limitations of aggregator communication result in only a portion of clients with high data quality being selected to participate in FL, but the quality of clients' data cannot be evaluated without access to the original data. Most existing methods for selecting clients employ a data quality metric with empirically defined scores, which may select clients with high non-ID degrees, thereby reducing the accuracy and freshness of the model. Furthermore, due to the unknown quality of clients' data, current incentive mechanisms lack FL convergence guarantees, which prevent the client behavior from improving the global model accuracy. To address these issues, in this paper, we propose using the gradient difference as a metric for the quality of clients' data, which can quantify the non-IID degree and contribution potential of each client. We formulate a client selection problem using the Combinatorial Multi-Armed Bandit (CMAB) model and design an effective selection strategy, improving the worst-case regret proof to provide a theoretical guarantee for it. Based on these results, we develop an incentive mechanism by the FL convergence analysis, quantifying the utility functions of the aggregator and clients, and modeling their interaction as a two-stage Stackelberg game. For the non-convex utility function, our method establishes the existence and uniqueness of the Stackelberg equilibrium, thereby enabling the determination of the optimal strategy for maximizing the utility of all participants. Finally, extensive simulation experiments on real-world datasets demonstrate the effectiveness of our proposed method compared to state-of-the-art approaches.

We consider decentralized online convex optimization with time-varying constraints and conduct performance analysis using two stringent metrics: network dynamic regret with respect to the online global solution benchmark, and hard constraint violation that does not allow any compensated violation over time and learners. We propose an efficient algorithm called Constrained Online Learning with Doubly-bounded Queue (COLDQ), which introduces a novel virtual queue that is both lower and upper bounded, allowing tight control of the constraint violation without needing the Slater’s condition. We prove via a new Lyapunov drift analysis that COLDQ providesO(T1+Vx/2) network dynamic regret andO(min{T3+Vx/4;TVg}) hard constraint violation, whereVxandVgcapture the dynamics of the loss and constraint functions. For the first time, the two bounds smoothly approach to the best-knownO(T1/2) regret andO(1) violation, as the dynamics of the losses and constraints diminish, under both centralized and decentralized settings. For strongly convex loss functions, COLDQ providesO(logT) static regret andO(min{T1/2(logT)1/2,TVg}) hard constraint violation. Simulation results based on synthetic and canonical datasets demonstrate that COLDQ substantially outperforms the state-of-the-art approaches for both convex and non-convex loss functions.

We consider online convex optimization with time-varying constraints and conduct performance analysis using two stringent metrics: dynamic regret with respect to the online solution benchmark, and hard constraint violation that does not allow any compensated violation over time. We propose an efficient algorithm called Constrained Online Learning with Doubly-bounded Queue (COLDQ), which introduces a novel virtual queue that is both lower and upper bounded, allowing tight control of the constraint violation without the need for the Slater condition. We prove via a new Lyapunov drift analysis that COLDQ achieves O(T^(1+Vx)/2) dynamic regret and O(T^Vg) hard constraint violation, where Vx and Vg capture the dynamics of the loss and constraint functions. For the first time, the two bounds smoothly approach to the best-known O(T^1/2) regret and O(1) violation, as the dynamics of the losses and constraints diminish. For strongly convex loss functions, COLDQ matches the best-known O(logT) static regret while maintaining the O(T^Vg) hard constraint violation. We further introduce an expert-tracking variation of COLDQ, which achieves the same performance bounds without any prior knowledge of the system dynamics. Simulation results demonstrate that COLDQ outperforms the state-of-the-art approaches.

The excessive proliferation of Low Earth Orbit (LEO) satellites inescapably bring the explosive growth of space data in LEO Satellite Networks (LSNs). Meanwhile, the stochastic arrivals of space data together with the time-varying satellite-ground links in LSNs pose significant challenges for offloading a large volume of space data from LSNs to ground stations. To circumvent these challenges, we systematically study the energy-constrained online data offloading problem to jointly optimize power allocation and task scheduling for LSNs. First, we leverage Lyapunov optimization to decouple our formulated long-term stochastic joint optimization problem into a set of per-time-slot subproblems. Then, each subproblem is decoupled into a task scheduling problem and a power allocation problem. Next, we derive the optimal solution to the power allocation problem and propose a multi-armed bandit based quasi-optimal solution to the task scheduling problem. Finally, extensive simulation results show that our proposed algorithm has superior performance over the state-of-the-art solutions.

This paper addresses the joint beamforming and data stream allocation (DSA) optimization problem for non-coherent joint transmission (NCJT). A critical yet neglected issue in NCJT beamforming is the tightly related DSA, which involves determining the number of streams transmitted from access points (APs) to their serving user equipments (UEs) according to the channel quality, so that the weighted sum-rate (WSR) can be maximized. However, since the integer number of streams directly determines the dimensions of beamformers, the joint optimization problem is mixed-integer and nonconvex with tightly coupled decision variables, making it NP-hard. To solve this problem, we first fix the DSA variables and propose a distributed and reduced weighted minimum mean square error (WMMSE) beamforming algorithm, called distributed RWMMSE, by leveraging the low-dimensional subspace property of the beamformer obtained by the traditional WMMSE. The distributed RWMMSE achieves the same WSR as the traditional WMMSE but with significantly lower computational complexity (scaling linearly with the number of AP antennas) and reduced interaction cost. Building on this, a joint beamforming and DSA optimization algorithm, named RWMMSE-LSA, is proposed by decoupling the decision variables through introduced stream indicator matrices. The RWMMSE-LSA optimizes beamformers and DSA via the distributed RWMMSE and linear programming, respectively, both of which have closed-form solutions. Simulations validate substantial performance gain of our proposed algorithms over existing alternatives in computational and interaction costs.

In Non-Geostationary Orbit Satellite Networks (NGOSNs) with a large number of battery-carrying satellites, proper power allocation and task scheduling are crucial to improving data offloading efficiency. In this work, we jointly optimize power allocation and task scheduling to achieve energy-efficient data offloading in NGOSNs. Our goal is to properly balance the minimization of the total energy consumption and the maximization of the sum weights of tasks. Due to the tight coupling between power allocation and task scheduling, we first derive the optimal power allocation solution to the joint optimization problem with any given task scheduling policy. We then leverage the conflict graph model to transform the joint optimization problem into an Integer Linear Programming (ILP) problem with any given power allocation strategy. We explore the unique structure of the ILP problem to derive an efficient semidefinite relaxation-based solution. Finally, we utilize the genetic framework to combine the above special solutions as a two-layer solution for the original joint optimization problem. Simulation results demonstrate that our proposed solution can properly balance the reduction of total energy consumption and the improvement of the sum weights of tasks, thus achieving superior system performance over the current literature.

We consider online distributed optimization in a networked system, where multiple devices assisted by a server collaboratively minimize the accumulation of a sequence of global loss functions that can vary over time. To reduce the amount of communication, the devices send quantized and compressed local decisions to the server, resulting in noisy global decisions. Therefore, there exists a tradeoff between the optimization performance and the communication overhead. Existing works separately optimize computation and communication. In contrast, we jointly consider computation and communication over time, by proactively encouraging temporal similarity in the decision sequence to control the communication overhead. We propose an efficient algorithm, termed Online Distributed Optimization with Temporal Similarity (ODOTS), where the local decisions are both computation- and communication-aware. Furthermore, ODOTS uses a novel tunable virtual queue, which removes the commonly assumed Slater’s condition through a modified Lyapunov drift analysis. ODOTS delivers provable performance bounds on both the optimization objective and constraint violation. Furthermore, we consider a variant of ODOTS with multi-step local gradient descent updates, termed ODOTS-MLU, and show that it provides improved performance bounds. As an example application, we apply both ODOTS and ODOTS-MLU to enable communication-efficient federated learning. Our experimental results based on canonical image classification demonstrate that ODOTS and ODOTS-MLU obtain higher classification accuracy and lower communication overhead compared with the current best alternatives for both convex and non-convex loss functions.

We consider online distributed optimization where a server and multiple devices collaborate to minimize a sequence of time-varying global loss functions. To accommodate slow devices that may require multiple time slots to compute their local decisions, the server uses semi-asynchronous aggregation of the local decisions, which complicates device scheduling and performance optimization. In this work, we first analyze the convergence of semi-asynchronous aggregation in the presence of time-varying local update delays and loss-function weights. Our analysis leads to an online scheduling problem to minimize the accumulated age of information on the local decision updates, subject to individual long-term constraints on the total weights of the scheduled devices. We then design an efficient scheduling policy, termed Age-of-Information Minimization with Weight Limits (AIMWeL), through a modified Lyapunov optimization approach that uses the weighted sum of linear age-of-information values and quadratic virtual queues as a new Lyapunov function. We show that AIMWeL has bounded optimality ratio, via a novel double relaxation approach to handle the unique scheduling-dependent communication indicator with time-varying probabilities of completing local decision update caused by semi-asynchronous aggregation. When AIMWeL is applied to semi-asynchronous federated learning, our simulation results based on standard image classification datasets demonstrate that AIMWeL uses significantly less time to reach the same classification accuracy achieved by the current best alternatives for both convex logistic regression and non-convex convolutional neural networks.

The rapid growth in demand for large language models (LLMs) has strained cloud-edge infrastructure. While edges offer low latency and clouds provide vast resources, scheduling LLM requests efficiently remains a major challenge due to their unpredictable processing times, which leads to Headof-Line (HOL) blocking that degrades system throughput and responsiveness. To address this, we introduce the Online CloudEdge Collaborative Request Scheduling (OCE-CRS) framework. OCE-CRS models the proactive scheduling of LLM requests as a contextual combinatorial bandit problem. At its core is our novel Combinatorial Neural Delayed Upper Confidence Bound (CN DUCB) algorithm, which learns to predict request processing times from the semantic content of the request prompt alone. This enables an inspired policy based on Shortest Job First (SJF) that prioritizes shorter jobs for edge execution, simultaneously maximizing throughput and mitigating HOL blocking. To prevent time-consuming neural network training from blocking scheduling decisions, we employ an asynchronous mechanism. This decouples model updates from the real-time scheduling loop, effectively handling the resultant delayed feedback where observations from past rounds are used in later training steps. We provide a theoretical sublinear regret bound for our algorithm. Extensive experiments validate that OCE-CRS significantly improves throughput, Job Completion Time (JCT), and queueing delay, demonstrating superior performance and robustness in both static and continuous batching environments.

Learning to optimize (L20) is an emerging technique to solve mathematical optimization problems with learning-based methods. Although with great success in many real-world scenarios such as wireless communications, computer networks, and electronic design, existing L2O works lack theoretical demonstration of their performance and robustness in out-of-distribution (OOD) scenarios. We address this gap by providing comprehensive proofs. First, we prove a sufficient condition for a robust L2O model with ho-mogeneous convergence rates over all In-Distribution (InD) instances. We assume an L2O model achieves robustness for an InD scenario. Based on our proposed methodology of aligning OOD problems to InD problems, we also demonstrate that the L2O model's convergence rate in OOD scenarios will deteriorate by an equation of the L2O model's input features. Moreover, we propose an L2O model with a concise gradient-only feature construction and a novel gradient-based history modeling method. Numerical simulation demonstrates that our proposed model outperforms the state-of-the-art baseline in both InD and OOD scenar-ios and achieves up to 10 × convergence speedup. The code of our method can be found from https://github.com/NetX-lab/GoMathL2O-Official.

We consider ergodic weighted sum rate (WSR) maximization in a massive multi-user multiple-input multiple-output system. Existing solutions iteratively minimize the average WSR based on all the historical information, and use bisection search to satisfy the power constraint at each iteration, resulting in both high storage burden and high computational complexity. In contrast, we propose an efficient stochastic proximal weighted minimum mean-square error (SPWMMSE) algorithm, which updates the precoder only based on the current single channel realization, without checking the power constraint at each iteration. Furthermore, we propose a novel proximal term to incorporate all the previous channel and surrogate function information in precoder updates. Our analysis shows that SPWMMSE converges to the stationary point of the original ergodic WSR maximization problem almost surely. Simulation results demonstrate the effectiveness of SPWMMSE over the current best alternatives.

Federated Learning (FL) algorithms commonly sample a random subset of clients to address the straggler issue and improve communication efficiency. While recent works have proposed various client sampling methods, they have limitations in joint system and data heterogeneity design, which may not align with practical heterogeneous wireless networks. In this work, we advocate a new independent client sampling strategy to minimize the wall-clock training time of FL, while considering data heterogeneity and system heterogeneity in both communication and computation. We first derive a new convergence bound for non-convex loss functions with independent client sampling and then propose an adaptive bandwidth allocation scheme. Furthermore, we propose an efficient independent client sampling algorithm based on the upper bounds on the convergence rounds and the expected per-round training time, to minimize the wall-clock time of FL, while considering both the data and system heterogeneity. Experimental results under practical wireless network settings with real-world prototype demonstrate that the proposed independent sampling scheme substantially outperforms the current best sampling schemes under various training models and datasets.

In modern applications, the underlying computation and communication networks are often hierarchical, which is typified by the three-layer client-edge-cloud system that has become prominent in recent times. We study minimax fairness in distributed optimization over such systems, to provide robust performance guarantee for the worst-case mixture of loss functions. We propose HierMinimax, a communication efficient distributed algorithm to solve the minimax optimization problem. We provide convergence analysis for both convex and non-convex loss functions, leading to performance bounds that enable tuning the tradeoff between the communication complexity and the optimization convergence rate. Our experiments on classification problems with canonical datasets show that HierMinimax substantially improves the fairness in learning accuracy and reduces the communication overhead compared with the current best alternatives.

Solving the sum rate maximization problem for interference reduction in multi-cell multi-user multiple-input multiple-output (MIMO) wireless communication systems has been investigated for a decade. Several machine learning-assisted methods have been proposed under conventional sum rate maximization frameworks, such as the Weighted Minimum Mean Square Error (WMMSE) framework. However, existing learning-assisted methods suffer from a deficiency in parallelization, and their performance is intrinsically bounded by WMMSE. In contrast, we propose a structural learning-only framework from the abstraction of WMMSE. Our proposed framework increases the solvability of the original MIMO sum rate maximization problem by dimension expansion via a unitary learnable parameter matrix to create an equivalent problem in a higher dimension. We then propose a structural solution updating method to solve the higher dimensional problem, utilizing neural networks to generate the learnable matrix-multiplication parameters. We show that the proposed structural learning framework achieves lower complexity than WMMSE thanks to its parallel implementation. Simulation results under practical communication network settings demonstrate that our proposed learning-only framework achieves up to 98% optimality over state-of-the-art algorithms while providing up to 47× acceleration in various scenarios.

In Earth Observation Satellite Networks (EOSNs) with a large number of battery-carrying satellites, proper power allocation and task scheduling are crucial to improving the data offloading efficiency. As such, we jointly optimize power allocation and task scheduling to achieve energy-efficient data offloading in EOSNs, aiming to balance the objectives of reducing the total energy consumption and increasing the sum weights of tasks. First, we derive the optimal power allocation solution to the joint optimization problem when the task scheduling policy is given. Second, leveraging the conflict graph model, we transform the original joint optimization problem into a maximum weight independent set problem when the power allocation strategy is given. Finally, we utilize the genetic framework to combine the above special solutions as a two-layer solution for the joint optimization problem. Simulation results demonstrate that our proposed solution can properly balance the sum weights of tasks and the total energy consumption, thus achieving superior system performance over the current best alternatives.

We consider federated learning in a wireless edge network, where multiple power-limited mobile devices collaboratively train a global model, using their local data with the assistance of an edge server. Exploiting over-the-air computation, the edge server updates the global model via analog aggregation of the local models over noisy wireless fading channels. Unlike existing works that separately optimize computation and communication at each step of the learning algorithm, in this work, we jointly optimize the training of the global model and the analog aggregation of the local models over time. Our objective is to minimize the accumulated training loss at the edge server, subject to individual long-term transmit power constraints at the mobile devices. We propose an efficient algorithm, termed Online Model Updating with Analog Aggregation (OMUAA), to adaptively update the local and global models based on the time-varying communication environment. The trained model of OMUAA is channel-and power-aware, and it is in closed form incurring low computational complexity. We study the mutual impact between model training and analog aggregation over time, to derive performance bounds on the computation and communication performance metrics. Furthermore, we consider a variant of OMUAA with double regularization on both the local and global models, termed OMUAA-DR, and show that it can significantly reduce the convergence time to reach long-term transmit power constraints. In addition, we extend both OMUAA and OMUAA-DR to enable analog gradient aggregation, while preserving their performance bounds. Simulation results based on real-world image classification datasets and typical wireless network settings demonstrate substantial performance gain of OMUAA and OMUAA-DR over the known best alternatives.

We consider cooperative multiple-input multiple-output (MIMO) precoding design with multiple access points (APs) assisted by a central controller (CC) in a fading environment. Even though each AP may have its own local channel state information (CSI), due to the communication delay in the backhaul, neither the APs nor the CC has timely global CSI. Under this hierarchical semi-online setting, our goal is to minimize the accumulated precoding deviation, between the actual local precoders executed by the APs and an ideal cooperative precoder based on timely and perfect global CSI, subject to per-AP transmit power limits. We propose an efficient algorithm, termed Semi-Online Precoding with Information Parsing (SOPIP), which accounts for the network heterogeneity in information timeliness and computational capacity. SOPIP does not require the CC to send the full global CSI to each AP. Instead, it takes advantage of the precoder structure to substantially lower the communication overhead, while allowing each AP to effectively combine its own timely local CSI with the delayed global CSI to enable adaptive precoder updates. We analyze the performance of SOPIP in the presence of multi-slot communication delay, CSI inaccuracy, and gradient estimation error, showing that it has a bounded performance gap from an offline optimal solution. Simulation results under typical cellular system settings further demonstrate the substantial performance gain of SOPIP over other centralized and distributed schemes.

We consider downlink beamforming design to maximize the weighted sum rate (WSR) in a user-centric cell-free network, where distributed access points (APs) are organized in a cluster to jointly serve each user equipment (UE). This architecture ensures uniform service quality even at the cell edge, but synchronization between APs can be problematic, necessitating the utilization of non-coherent joint transmission (NCJT) that eliminates the need for strict synchronization. Most existing works on beamforming design for NCJT assume that the classic weighted minimum mean square error (WMMSE) approach is not applicable, and design their beamforming algorithms based on the successive convex approximation (SCA) method with high computational complexity. In this work, we for the first time demonstrate the applicability of the WMMSE approach for NCJT in cell-free networks. Based on the unique observations on the structures of the WSR maximization problem for NCJT, we propose an efficient WMMSE based beamforming algorithm. Our proposed algorithm is guaranteed to converge to a stationary point of the WSR maximization problem. Furthermore, our beamforming updates are in closed form with low computational complexity. Simulation results demonstrate substantial performance gain of our proposed algorithm over the current best SCA based alternatives in both computational complexity and convergence time.

We consider online distributed optimization in a networked system, where multiple devices assisted by a server collaboratively minimize the accumulation of a sequence of global loss functions that can vary over time. To reduce the amount of communication, the devices send quantized and compressed local decisions to the server, resulting in noisy global decisions. Therefore, there exists a tradeoff between the optimization performance and the communication overhead. Existing works separately optimize computation and communication. In contrast, we jointly consider computation and communication over time, by encouraging temporal similarity in the decision sequence to control the communication overhead. We propose an efficient algorithm, termed Online Distributed Optimization with Temporal Similarity (ODOTS), where the local decisions are both computation- and communication-aware. Furthermore, ODOTS uses a novel tunable virtual queue, which completely removes the commonly assumed Slater’s condition through a modified Lyapunov drift analysis. ODOTS delivers provable performance bounds on both the optimization objective and constraint violation. As an example application, we apply ODOTS to enable communication-efficient federated learning. Our experimental results based on real-world image classification demonstrate that ODOTS obtains higher classification accuracy and lower communication overhead compared with the current best alternatives for both convex and non-convex loss functions.

In many dynamic systems, decisions on system operation are updated over time, and the decision maker requires an online learning approach to optimize its strategy in response to the changing environment. When the loss and constraint functions are convex, this belongs to the general family of online convex optimization (OCO). In existing OCO works, the environment is assumed to vary in a time-slotted fashion, while the decisions are updated at each time slot. However, many wireless communication systems permit only periodic decision updates,i.e.each decision is fixed over multiple time slots, while the environment changes between the decision epochs. The standard OCO model is inadequate for these systems. Therefore, in this work, we consider periodic decision updates for OCO. We aim to minimize the accumulation of time-varying convex loss functions, subject to both short-term and long-term constraints. Feedback information about the loss functions within the current update period may be delayed and incomplete. We propose an efficient algorithm, termed Periodic Queueing and Gradient Aggregation (PQGA), which employs novel periodic queues together with possibly multi-step aggregated gradient descent to update the decisions over time. We derive upper bounds on the dynamic regret, static regret, and constraint violation of PQGA. As an example application, we study the performance of PQGA for network virtualization in a large-scale multi-antenna system shared by multiple wireless service providers. Simulation results show that PQGA converges fast and substantially outperforms the current best alternative.

We consider online convex optimization (OCO) with multi-slot feedback delay. An agent selects a sequence of online decisions to minimize the accumulation of time-varying convex loss functions, subject to short-term and long-term constraints that may be time-varying. Both the convex loss function and the long-term constraint function may experience multiple time slots of feedback delay to be received by the agent. Existing works on OCO under this general setting has focused on the static regret, which measures the gap of losses between an online decision sequence and a time-invariant static offline benchmark. In this work, besides the static regret, we also consider a more practically meaningful metric, the dynamic regret, where the benchmark is a time-varying online optimal decision sequence. We propose an efficient algorithm, termed Delay-Tolerant Constrained-OCO (DTC-OCO), which uses a novel double regularization together with a new penalty mechanism on the long-term constraint violation, to tackle the asynchrony between information feedback and decision updates. We obtain upper bounds for its static regret, dynamic regret, and constraint violation, proving that they are sublinear under mild conditions. Furthermore, we consider a variation of DTC-OCO with multi-step gradient descent, and show it provides improved dynamic regret and constraint violation bounds for strongly convex loss functions. For numerical demonstration, we apply DTC-OCO to a general network resource allocation problem. Our simulation results suggest substantial performance gain by DTC-OCO over the current best alternative.

We consider federated learning in a wireless edge network, where multiple power-limited mobile devices collaboratively train a global model, using their local data with the assistance of an edge server. Exploiting over-the-air computation, the edge server updates the global model via analog aggregation of the local models over noisy wireless fading channels. Unlike existing works that separately optimize computation and communication at each step of the learning algorithm, in this work, we jointly optimize the training of the global model and the analog aggregation of local models over time. Our objective is to minimize the accumulated training loss at the edge server, subject to individual long-term transmit power constraints at the mobile devices. We propose an efficient algorithm, termed Online Model Updating with Analog Aggregation (OMUAA), to adaptively update the local and global models based on the time-varying communication environment. The trained model of OMUAA is channel- and power-aware, and it is in closed form with low computational complexity. We study the mutual impact between model training and analog aggregation over time, to derive performance bounds on the computation and communication performance metrics. Simulation results based on real-world image classification datasets and typical Long-Term Evolution network settings demonstrate substantial performance gain of OMUAA over the known best alternatives.

We consider cooperative multiple-input multiple-output (MIMO) precoding design with multiple access points (APs) assisted by a central controller (CC) in a fading environment. Even though each AP may have its own local channel state information (CSI), due to the communication delay in the backhaul, neither the APs nor the CC has timely global CSI. Under this semi-online setting, our goal is to minimize the accumulated precoding deviation between the actual local precoders executed by the APs and an ideal cooperative precoder based on the global CSI, subject to per-AP transmit power limits. We propose an efficient algorithm, termed Semi-Online Precoding with Information Parsing (SOPIP), which accounts for the network heterogeneity in information timeliness and computational capacity. SOPIP does not require the CC to send the full global CSI to each AP. Instead, it takes advantage of the precoder structure to substantially lower the communication overhead, while allowing each AP to effectively combine its own timely local CSI with the delayed global CSI to enable adaptive precoder updates. We analyze the performance of SOPIP in the presence of both multi-slot communication delay and gradient estimation error, showing that it has a bounded performance gap from an offline optimal solution. Simulation results under typical Long-Term Evolution network settings further demonstrate the substantial performance gain of SOPIP over other centralized and distributed schemes.

This paper presents a new virtualization method for the downlink of a multi-cell multiple-input multiple-output (MIMO) network, to achieve service isolation among multiple Service Providers (SPs) that share the base station resources of an Infrastructure Provider (InP). Each SP designs a virtual precoder for its users in each cell, as its service demand to the InP, without the need to be aware of the existence of the other SPs or to know the channel state information (CSI) outside the cell. The InP performs network virtualization to meet the SPs’ service demands while managing both the inter-SP and inter-cell interference. We consider coordinated multi-cell precoding at the InP and formulate an optimization problem to minimize a weighted sum of signal leakage and precoding deviation, with per-cell transmit power constraints. We propose a fully distributed semi-closed-form solution at each cell, without any CSI exchange across cells. We further propose a low-complexity scheme to allocate the virtual transmit power, for the InP to regulate between interference elimination and virtual demand maximization. Simulation results demonstrate that our precoding solution for network virtualization substantially outperforms the traditional spectrum isolation alternative. It can approach the performance of fully cooperative precoding when the number of antennas is large.

We consider online coordinated precoding design for downlink wireless network virtualization (WNV) in a multi-cell multiple-input multiple-output (MIMO) network with imperfect channel state information (CSI). In our WNV framework, an infrastructure provider (InP) owns each base station that is shared by several service providers (SPs) oblivious of each other. The SPs design their precoders as virtualization demands for user services, while the InP designs the actual precoding solution to meet the service demands from the SPs. Our aim is to minimize the long-term time-averaged expected precoding deviation over MIMO fading channels, subject to both per-cell long-term and short-term transmit power limits. We propose an online coordinated precoding algorithm for virtualization, which provides a fully distributed semi-closed-form precoding solution at each cell, based only on the current imperfect CSI without any CSI exchange across cells. Taking into account the two-fold impact of imperfect CSI on both the InP and the SPs, we show that our proposed algorithm is within an$O(\delta)$gap from the optimum over any time horizon, where$\delta $is a CSI inaccuracy indicator. Simulation results validate the performance of our proposed algorithm under two commonly used precoding techniques in a typical urban micro-cell network environment.

We consider online convex optimization (OCO) with multi-slot feedback delay, where an agent makes a sequence of online decisions to minimize the accumulation of time-varying convex loss functions, subject to short-term and long-term constraints that are possibly time-varying. The current convex loss function and the long-term constraint function are revealed to the agent only after the decision is made, and they may be delayed for multiple time slots. Existing work on OCO under this general setting has focused on the static regret, which measures the gap of losses between the online decision sequence and an offline benchmark that is fixed over time. In this work, we consider both the static regret and the more practically meaningful dynamic regret, where the benchmark is a time-varying sequence of per-slot optimizers. We propose an efficient algorithm, termed Delay-Tolerant Constrained-OCO (DTC-OCO), which uses a novel constraint penalty with double regularization to tackle the asynchrony between information feedback and decision updates. We derive upper bounds on its dynamic regret, static regret, and constraint violation, proving them to be sublinear under mild conditions. We further apply DTC-OCO to a general network resource allocation problem, which arises in many systems such as data networks and cloud computing. Simulation results demonstrate substantial performance gain of DTC-OCO over the known best alternative.

We consider online downlink precoding design for multiple-input multiple-output (MIMO) wireless network virtualization (WNV) in a fading environment with imperfect channel state information (CSI). In our WNV framework, a base station owned by an infrastructure provider (InP) is shared by several service providers (SPs) that are oblivious to each other. The SPs design their virtual MIMO transmission demands to serve their own users, while the InP designs the actual downlink precoding to meet the service demands from the SPs. Therefore, the impact of imperfect CSI is two-fold, on both the InP and the SPs. We aim to minimize the long-term time-averaged expected precoding deviation, considering both long-term and short-term transmit power limits. We propose a new online MIMO WNV algorithm to provide a semi-closed-form precoding solution based only on the current imperfect CSI. We derive a performance bound for our proposed algorithm and show that it is within an O(δ) gap from the optimum over any given time horizon, where δ is a normalized measure of CSI inaccuracy. Simulation results with two popular precoding techniques validate the performance of our proposed algorithm under typical urban micro-cell Long-Term Evolution network settings.

We consider downlink multiple-input multiple-output (MIMO) wireless network virtualization (WNV) in a fading environment, via a base station (BS) precoding design. The BS is owned by an infrastructure provider (InP) and is shared by several service providers (SPs) who are oblivious to each other. The SPs realize their virtual-cell transmissions via MIMO precoding provided by the InP. We aim to minimize the time-averaged expected deviation of the precoding provided by the InP from the SPs' virtualization demands, considering both long-term and short-term transmit power limits at the BS. We propose an online MIMO WNV algorithm to provide a precoding solution through Lyapunov optimization. Our online precoding solution only requires the current channel state information, and it has a semi-closed form with low computational complexity. We provide an upper bound on the performance of the proposed algorithm, showing that it can be arbitrarily close to the optimum over any given time horizon. Simulation results validate the performance of our proposed algorithm under typical urban micro-cell settings.