Federated learning (FL) necessitates that edge devices conduct local training and communicate with a parameter server, resulting in significant energy consumption. A key challenge in practical FL systems is the rapid depletion of battery-limited edge devices, which limits their operational lifespan and impacts learning performance. To tackle this issue, we implement energy harvesting techniques in FL systems to capture ambient energy, thereby providing continuous power to edge devices. We first establish the convergence bound for the wireless FL system with energy harvesting devices, illustrating that the convergence is affected by partial device participation and packet drops, both of which depend on the energy supply. To accelerate the convergence, we formulate a joint device scheduling and power control problem and model it as a Markov decision process (MDP). By solving this MDP, we derive the optimal transmission policy and demonstrate that it possesses a monotone structure with respect to the battery and channel states. To overcome the curse of dimensionality caused by the exponential complexity of computing the optimal policy, we propose a low-complexity algorithm, which is asymptotically optimal as the number of devices increases. Furthermore, for unknown channels and harvested energy statistics, we develop a structure-enhanced deep reinforcement learning algorithm that leverages the monotone structure of the optimal policy to improve the training performance. Finally, extensive numerical experiments on real-world datasets are presented to validate the theoretical results and corroborate the effectiveness of the proposed algorithms.

Decentralized federated learning (DFL) enables edge devices to collaboratively train models through local training and fully decentralized device-to-device (D2D) model exchanges. However, these energy-intensive operations often rapidly deplete limited device batteries, reducing their operational lifetime and degrading the learning performance. To address this limitation, we apply energy harvesting technique to DFL systems, allowing edge devices to extract ambient energy and operate sustainably. We first derive the convergence bound for wireless DFL with energy harvesting, showing that the convergence is influenced by partial device participation and transmission packet drops, both of which further depend on the available energy supply. To accelerate convergence, we formulate a joint device scheduling and power control problem and model it as a multi-agent Markov decision process (MDP). Traditional MDP algorithms (e.g., value or policy iteration) require a centralized coordinator with access to all device states and exhibit exponential complexity in the number of devices, making them impractical for large-scale decentralized networks. To overcome these challenges, we propose a fully decentralized policy iteration algorithm that leverages only local state information from two-hop neighboring devices, thereby substantially reducing both communication overhead and computational complexity. We further provide a theoretical analysis showing that the proposed decentralized algorithm achieves asymptotic optimality. Finally, comprehensive numerical experiments on real-world datasets are conducted to validate the theoretical results and corroborate the effectiveness of the proposed algorithm.

Federated learning (FL) has garnered significant attention from academia and industry in recent years due to its advantages in data privacy, scalability, and communication efficiency. However, current FL algorithms face a critical limitation: their performance heavily depends on meticulously tuned hyperparameters, particularly the learning rate or stepsize. This manual tuning process is challenging in federated settings due to data heterogeneity and limited accessibility of local datasets. Consequently, the reliance on problem-specific parameters hinders the widespread adoption of FL and potentially compromises its performance in dynamic or diverse environments. To address this issue, we introduce PAdaMFed, a novel algorithm for nonconvex FL that carefully combines adaptive stepsize and momentum techniques. PAdaMFed offers two key advantages: 1) it operates autonomously without relying on problem-specific parameters; and 2) it manages data heterogeneity and partial participation without requiring heterogeneity bounds. Despite these benefits, PAdaMFed provides several strong theoretical guarantees: 1) It achieves state-of-the-art convergence rates with a sample complexity of $\mathcal{O}(\epsilon^{-4})$ and communication complexity of $\mathcal{O}(\epsilon^{-3})$ to obtain an accuracy of $||\nabla f\left(\boldsymbol{\theta}\right)|| \leq \epsilon$, even using constant learning rates; 2) these complexities can be improved to the best-known $\mathcal{O}(\epsilon^{-3})$ for sampling and $\mathcal{O}(\epsilon^{-2})$ for communication when incorporating variance reduction; 3) it exhibits linear speedup with respect to the number of local update steps and participating clients at each global round. These attributes make PAdaMFed highly scalable and adaptable for various real-world FL applications. Extensive empirical evidence on both image classification and sentiment analysis tasks validates the efficacy of our approaches.

We introduce the framework of performative control, where the policy chosen by the controller affects the underlying dynamics of the control system. This results in a sequence of policy-dependent system state data with policy-dependent temporal correlations. Following the recent literature on performative prediction \cite{perdomo2020performative}, we introduce the concept of a performatively stable control (PSC) solution. We first propose a sufficient condition for the performative control problem to admit a unique PSC solution with a problem-specific structure of distributional sensitivity propagation and aggregation. We further analyze the impacts of system stability on the existence of the PSC solution. Specifically, for {almost surely strongly stable} policy-dependent dynamics, the PSC solution exists if the sum of the distributional sensitivities is small enough. However, for almost surely unstable policy-dependent dynamics, the existence of the PSC solution will necessitate a temporally backward decaying of the distributional sensitivities. We finally provide a repeated stochastic gradient descent scheme that converges to the PSC solution and analyze its non-asymptotic convergence rate. Numerical results validate our theoretical analysis.

Distribution variations in machine learning, driven by the dynamic nature of deployment environments, significantly impact the performance of learning models. This paper explores endogenous distribution shifts in learning systems, where deployed models influence environments and subsequently alter data distributions. This phenomenon is formulated by a decision-dependent distribution mapping within the recently proposed framework of performative prediction (PP) Perdomo et al. (2020). We investigate the performative effect in a decentralized noncooperative game, where players aim to minimize private cost functions while simultaneously managing coupled inequality constraints. Under performativity, we examine two equilibrium concepts for the studied game: performative stable equilibrium (PSE) and Nash equilibrium (NE), and establish sufficient conditions for their existence and uniqueness. Notably, we provide the first upper bound on the distance between the PSE and NE in the literature, which is challenging to evaluate due to the absence of strong convexity on the joint cost function. Furthermore, we develop a decentralized stochastic primal-dual algorithm for efficiently computing the PSE point. By carefully bounding the performative effect in theoretical analysis, we prove that the proposed algorithm achieves sublinear convergence rates for both performative regrets and constraint violation and maintains the same order of convergence rate as the case without performativity. Numerical experiments validate the effectiveness of our algorithm and theoretical results.

Performative prediction is a recently proposed framework where predictions guide decision-making and hence influence future data distributions. Such performative phenomena are ubiquitous in various areas, such as transportation, finance, public policy, and recommendation systems. To date, work on performative prediction has only focused on unconstrained problems, neglecting the fact that many real-world learning problems are subject to constraints. This paper bridges this gap by studying performative prediction under inequality constraints. Unlike most existing work that provides only performative stable points, we aim to find the optimal solutions. Anticipating performative gradient is a challenging task, due to the agnostic performative effect on data distributions. To address this issue, we first develop a robust primal-dual framework that requires only approximate gradients up to a certain accuracy, yet delivers the same order of performance as the stationary stochastic primal-dual algorithm without performativity. Based on this framework, we then propose an adaptive primal-dual algorithm for location families. Our analysis demonstrates that the proposed adaptive primal-dual algorithm attains $\mathcal{O}(\sqrt{T})$ regret and constraint violations, using only $\sqrt{T} + 2T$ samples, where $T$ is the time horizon. To our best knowledge, this is the first study and analysis on the optimality of the performative prediction problem under inequality constraints. Finally, we validate the effectiveness of our algorithm and theoretical results through numerical simulations.

Distributed machine learning is envisioned as the bedrock of future intelligent networks, where agents exchange information with each other to train models collaboratively without uploading data to a central processor. Despite its broad applicability, a downside of distributed learning is the need for iterative information exchange between agents, which may lead to high communication overhead unaffordable in many practical systems with limited communication resources. To resolve this communication bottleneck, we need to devise communication-efficient distributed learning algorithms and protocols that can reduce the communication cost and simultaneously achieve satisfactory learning/optimization performance. Accomplishing this goal necessitates synergistic techniques from a diverse set of fields, including optimization, machine learning, wireless communications, game theory, and network/graph theory. This Special Issue is dedicated to communication-efficient distributed learning from multiple perspectives, including fundamental theories, algorithm design and analysis, and practical considerations.

Distributed learning is envisioned as the bedrock of next-generation intelligent networks, where intelligent agents, such as mobile devices, robots, and sensors, exchange information with each other or a parameter server to train machine learning models collaboratively without uploading raw data to a central entity for centralized processing. By utilizing the computation/communication capability of individual agents, the distributed learning paradigm can mitigate the burden at central processors and help preserve data privacy of users. Despite its promising applications, a downside of distributed learning is its need for iterative information exchange over wireless channels, which may lead to high communication overhead unaffordable in many practical systems with limited radio resources such as energy and bandwidth. To overcome this communication bottleneck, there is an urgent need for the development of communication-efficient distributed learning algorithms capable of reducing the communication cost and achieving satisfactory learning/optimization performance simultaneously. In this paper, we present a comprehensive survey of prevailing methodologies for communication-efficient distributed learning, including reduction of the number of communications, compression and quantization of the exchanged information, radio resource management for efficient learning, and game-theoretic mechanisms incentivizing user participation. We also point out potential directions for future research to further enhance the communication efficiency of distributed learning in various scenarios.

Reconfigurable intelligent surface (RIS) based reflection modulation (RM) has been considered as a promising information delivery mechanism, and has the potential to realize passive information transfer of a RIS without consuming any additional radio frequency chain and time/frequency/energy resource. The existing on-off RM (ORM) schemes are based on manipulating the “on/off” states of RIS reflection elements, which may lead to the degradation of RIS reflection efficiency. This paper proposes a frequency RM (FRM) method for RIS-aided OFDM systems. The FRM-OFDM scheme modulates the frequency of the incident electromagnetic waves, and the RIS information is embedded in the frequency-hopping states of RIS elements. Unlike the ORM-OFDM scheme, the FRM-OFDM scheme can achieve higher reflection efficiency, since the latter does not turn off any reflection element in RM. We show that, for the RIS phase shift optimization, the multiplicative multiple access channel in the FRM-OFDM system can be converted to an equivalent RIS-aided multiple-input multiple-output channel. Then, we propose an alternating optimization AO) algorithm for sum rate maximization of the FRM-OFDM system. A low-complexity recursive AO algorithm is further developed to avoid direct channel matrix inversion in the AO algorithm with negligible performance degradation. In addition, we design a bilinear message passing (BMP) algorithm for the bilinear recovery of both the user symbols and the RIS data. Numerical simulations verify the efficiency of the designed optimization algorithms for system optimization and the BMP algorithm for signal detection, as well as the superiority of the proposed FRM-OFDM scheme over the existing ORM-OFDM scheme and the RIS-aided OFDM system.

In this paper, online convex optimization (OCO) problem with time-varying constraints is studied from the perspective of an agent taking sequential actions. Both the objective function and the constraint functions are dynamic and unknown a priori to the agent. We first consider the scenario of function feedback, in which complete information about the objective function and constraint functions is revealed to the agent after an action is submitted. We propose a computationally efficient online algorithm, which only involves direct closed-form computations at each time instant. It is shown that the algorithm possesses sublinear regret with respect to the dynamic benchmark sequence and sublinear constraint violations, as long as the drift of the benchmark sequence is sublinear, or in other words, the underlying dynamic optimization problems do not vary too drastically. Furthermore, we investigate the scenario of bandit feedback, in which, after an action is chosen, only the values of the objective function and the constraint functions at several random points close to the action are announced to the agent. A bandit version of online algorithm is proposed and we also establish its sublinear expected regret and sublinear expected constraint violations. Finally, two numerical examples, namely online quadratic programming and online logistic regression, are presented to corroborate the effectiveness of the proposed algorithms and to confirm the theoretical guarantees.

In this work, we study a generic network cost minimization problem, in which every node has a local decision vector to determine. Each node incurs a cost depending on its decision vector and each link also incurs a cost depending on the decision vectors of its two end nodes. All nodes cooperate to minimize the overall network cost. To obtain a decentralized algorithm for this problem, we resort to the distributed alternating direction method of multipliers (DADMM). However, each iteration of the DADMM involves solving a local optimization problem at each node, leading to intractable computational burden in many circumstances. As such, we propose a distributed linearized ADMM (DLADMM) algorithm, in which each iteration only involves closed-form computations and avoids local optimization problems. This greatly reduces the computational complexity and makes the proposed DLADMM amenable to devices with low computational capability, such as vastly deployed sensors, to which the computationally intensive traditional DADMM is not applicable. We prove that the DLADMM converges to an optimal point when the local cost functions are convex and have Lipschitz continuous gradients. Linear convergence rate of the DLADMM is also established if the local cost functions are further strongly convex. Numerical experiments are conducted to corroborate the effectiveness of the DLADMM and we observe that the DLADMM has similar convergence performance as DADMM does while the former enjoys much lower computational overhead.

In this paper, online convex optimization (OCO) problems with time-varying objective and constraint functions are studied from the perspective of an agent who takes actions in real-time. Information about the current objective and constraint functions is revealed only after the corresponding action is already chosen. Inspired by a fast converging algorithm for time-invariant optimization in the very recent work [1], we develop a novel online algorithm based on virtual queues for constrained OCO. Optimal points of the dynamic optimization problems with full knowledge of the current objective and constraint functions are used as a dynamic benchmark sequence. Upper bounds on the regrets with respect to the dynamic benchmark and the constraint violations are derived for the presented algorithm in terms of the temporal variations of the underlying dynamic optimization problems. It is observed that the proposed algorithm possesses sublinear regret and sublinear constraint violations, as long as the temporal variations of the optimization problems are sublinear, i.e., the objective and constraint functions do not vary too drastically across time. The performance bounds of the proposed algorithm are superior to those of the state-of-the-art OCO method in most scenarios.

In this paper, joint energy procurement and demand response is studied from the perspective of the operator of a power system. The operator procures energy from both renewable energy sources (RESs) and the spot market. We observe the fact that the RESs may incur considerable infrastructure cost. This cost is taken into account and the optimal planning of renewables is examined by controlling the investment in RES infrastructures. Due to the uncertainty of renewables, the operator can also purchase energy directly from the spot market to compensate for the possible deficit incurred by the realization of the random renewable energy. By setting appropriate prices, the operator sells the collected energy to heterogeneous end users with different demand response characteristics. We model the decision making process of the operator as a two-stage optimization problem. The optimal decisions on the renewable deployment, energy purchase from the spot market and pricing schemes are derived. Several solution structures are observed and a computationally efficient algorithm, requiring only closed-form calculation and simple bisection search, is proposed to compute the optimal decisions. Finally, numerical experiments are conducted to verify the optimality of the proposed algorithm and the solution structures observed theoretically.

With the explosive growth of wireless data, mobile edge caching has emerged as a promising paradigm to support mobile traffic recently, in which the service providers (SPs) prefetch some popular contents in advance and cache them locally at the network edge. When requested, those locally cached contents can be directly delivered to users with low latency, thus alleviating the traffic load over backhaul channels during peak hours and enhancing the quality-of-experience (QoE) of users simultaneously. Due to the limited available cache space, it makes sense for the SP to cache the most profitable contents. Nevertheless, users' true valuations of contents are their private knowledge, which is unknown to the SP in general. This information asymmetry poses a significant challenge for effective caching at the SP side. Further, the cached contents can be delivered with different quality, which needs to be chosen judiciously to balance delivery costs and user satisfaction. To tackle these difficulties, in this paper, we propose an optimal auction mechanism from the perspective of the SP. In the auction, the SP determines the cache space allocation over contents and user payments based on the users' (possibly untruthful) reports of their valuations so that the SP's expected revenue is maximized. The advocated mechanism is designed to elicit true valuations from the users (incentive compatibility) and to incentivize user participation (individual rationality). In addition, we devise a computationally efficient method for calculating the optimal cache space allocation and user payments. We further examine the optimal choice of the content delivery quality for the case with a large number of users and derive a closed-form solution to compute the optimal delivery quality. Finally, extensive simulations are implemented to evaluate the performance of the proposed optimal auction mechanism, and the impact of various model parameters is highlighted to obtain engineering insights into the content caching problem.

The rapid growth of cloud computing and data centers with skyrocketing energy consumption, together with the accelerating penetration of renewable energy sources, is creating both severe challenges and tremendous opportunities. Data centers offering large flexible loads in the grid, opens up a unique opportunity to smooth out the significant fluctuation and uncertainty of renewable generation and hence enable seamless integration. To take the market power of data centers into consideration, this paper proposes a bargaining solution to the market program for data center demand response when the load serving entity (LSE) has power supply deficiency. Specifically, due to the uncertainty of load flexibility of data centers incurred by the intermittent on-site renewable generation and dynamic service requests, there exists information asymmetry between the LSE and the data center, which complicates the design of the bargaining solution. Making use of the log-concavity of the (expected) utility functions, a computationally efficient method to implement the best response updates in the bargaining procedure is presented. Furthermore, it is shown analytically that the bid sequences of the LSE and the data center are guaranteed to converge and the final price clinched by the bargaining algorithm is indeed the Nash bargaining solution, which is proportionally fair. In addition, the proposed bargaining solution is compared with two other schemes, namely the Stackelberg game and the social welfare maximization schemes. Finally, extensive numerical experiments are conducted to validate the theoretical guarantees of the bargaining and to examine the impact of various model parameters. Empirical comparison indicates the fairness advantage of the bargaining approach over the other two schemes, especially when the load of the data center is not very flexible, highlighting the importance of information feedback embodied by the bargaining procedure.

In the big data era, it is vital to allocate the vast amount of data to various users efficiently. However, the data agents (data owners, collectors and users) are selfish and seek to maximize their own utilities instead of the overall system efficiency. In this paper, the data trading problem of a data market with multiple data owners, collectors and users is formulated and an iterative auction mechanism is proposed to coordinate the data trading. The proposed mechanism guilds the selfish data agents to trade data efficiently and avoids direct access of the agents' private information. We theoretically prove that the proposed mechanism can achieve the socially optimal operation point. Moreover, we demonstrate that the mechanism satisfies appealing economic properties such as individual rationality and weakly balanced budget. Simulations as well as real data experiments validate the theoretical properties of the mechanism.

In this work, we study the social learning problem, in which agents of a networked system collaborate to detect the state of the nature based on their private signals. A novel distributed graphical evolutionary game-theoretic learning method is proposed. In the proposed game-theoretic method, agents only need to communicate their binary decisions rather than the real-valued beliefs with their neighbors, which endows the method with low communication complexity. Under mean field approximations, we theoretically analyze the steady-state equilibria of the game and show that the evolutionarily stable states coincide with the decisions of the benchmark centralized detector. Numerical experiments are implemented to confirm the effectiveness of the proposed game-theoretic learning method.

Real-world networks are often cluttered and hard to organize. Recent studies show that most networks have the community structure, i.e., nodes with similar attributes form a certain community, which enables people to better understand the constitution of the networks. Hitherto, various community detection methods have been proposed in the literature yet none of them takes the strategic interactions among nodes into consideration. Additionally, many real-world observations of networks are noisy and incomplete, i.e., with some missing links or fake links, due to either technology constraints or privacy regulations. In this work, a game-theoretic framework of community detection is established, where nodes interact and produce links with each other in a rational way based on mutual benefits. Given the proposed game-theoretic generative models for communities, we use expectation maximization (EM) algorithm to detect communities. Simulations on synthetic networks and experiments on real-world networks demonstrate that the proposed detection method outperforms the state-of-the-art.

In this paper, we investigate the impact of information-theoretic secrecy constraint on the capacity and delay of mobile ad hoc networks (MANETs) with mobile legitimate nodes and static eavesdroppers whose location and channel state information (CSI) are both unknown. We assume n legitimate nodes move according to the fast i.i.d. mobility pattern and each desires to communicate with one randomly selected destination node. There are also nνstatic eavesdroppers located uniformly in the network and we assume the number of eavesdroppers is much larger than that of legitimate nodes, i.e., ν > 1. We propose a novel simple secure communication model, i.e., the secure protocol model, and prove its equivalence to the widely accepted secure physical model under a few technical assumptions. Based on the proposed model, a framework of analyzing the secrecy capacity and delay in MANETs is established. Given a delay constraint D, we find that the optimal secrecy throughput capacity is ~Θ(W((D/n))(2/3)), where W is the data rate of each link. We observe that: 1) the capacity-delay tradeoff is independent of the number of eavesdroppers, which indicates that adding more eavesdroppers will not degenerate the performance of the legitimate network as long as ν > 1; 2) the capacity-delay tradeoff of our paper outperforms the previous result Θ((1/nψe)) in , where ψe=nν-1=ω(1) is the density of the eavesdroppers. Throughout this paper, for functions f(n) and g(n), we denote f(n)=o(g(n)) if limn→∞(f(n)/g(n))=0; f(n)=ω(g(n)) if g(n)=o(f(n)); f(n)=O(g(n)) if there is a positive constant c such that f(n) ≤ cg(n) for sufficiently large n; f(n)=Ω(g(n)) if g(n)=O(f(n)); f(n)=Θ(g(n)) if both f(n)=O(g(n)) and f(n)=Ω(g(n)) hold. Besides, the order notation ~Θ omits the polylogarithmic factors for better readability.

In this paper, we investigate the optimal spectrum procurement and pricing from the perspective of a cognitive mobile virtual network operator (C-MVNO), which is a second market between the spectrum owner and the secondary users (SUs). The spectrum procurement consists of spectrum leasing and spectrum sensing, where the latter has an uncertain outcome. The SUs are assumed to be heterogeneous in their valuations and demands of the spectrum, which is generally the case in reality. Hence, we use differentiated pricing among the heterogeneous SUs to improve the profit of the C-MVNO and allow the C-MVNO to perform necessary admission control. Modeling the spectrum procurement and trading procedure as a five-stage Stackelberg game, we analyze the optimal decisions for the C-MVNO by using backward induction. The optimal decisions of spectrum sensing, spectrum leasing, admission control, and differentiated pricing are derived, and an algorithm is proposed to compute those optimal decisions efficiently. Our theoretical results are also corroborated by numerical experiments, and a threshold structure of the solution is observed.

The problem of function computation in large scale heterogeneous wireless sensor networks (WSNs) is studied. Suppose n sensors are placed in a disk network area with radius nα, where α is a positive constant. The sensors are located heterogeneously around the sink node, i.e, the density of sensors decreases as the distance from the sink node increases. At one instant, each sensor is assigned an input bit. The target of the sink is to compute a function f of the input bits, where f is either a symmetric or the identity function. Energy-efficient algorithms based on inhomogeneous tessellation of the network are designed and the corresponding optimal energy consumption scaling laws are derived. We show that the proposed algorithms are indeed optimal (except for some polylogarithmic terms) by deriving matching lower bounds on the energy consumption required to compute f. At last, based on the results obtained in this paper as well as those obtained by previous works, some discussions and comparisons are presented. We observe that 1) the heterogeneity extent has a great impact on the computation of both symmetric function and identity function, and 2) the energy usage of computing symmetric function can be significantly smaller than that of computing identity function under certain parameter condition, i.e, performing in-network computation helps save energy.

The problem of jointly estimating clock skew and offset for wireless sensor networks (WSNs) in a pairwise broadcast synchronization (PBS) protocol is considered. The random part of the delay is supposed to be an exponential random variable. We consider two estimators, i.e., joint maximum-likelihood estimator (JMLE) and generalized ML-like estimator (GMLLE) proposed by Leng and Wu . For both estimators, the corresponding algorithms are explicitly derived and presented. For the GMLLE, the corresponding performance bound based on the reduced set of observations is derived and the optimal value of a user-defined parameter is identified accordingly. At last, analytical results are corroborated by numerical experiments. We observe that: (i) JMLE usually outperforms GMLLE at the cost of larger computational complexity; (ii) JMLE, while achieving the same estimation accuracy as that of the LP method presented in , enjoys significantly lower computational complexity than that of the latter.