The rapid growth of AI-generated content (AIGC) services has created an urgent need for effective prompt pricing strategies, yet current approaches overlook users' strategic two-step decision-making process in selecting and utilizing generative AI models. This oversight creates two key technical challenges: quantifying the relationship between user prompt capabilities and generation outcomes, and optimizing platform payoff while accounting for heterogeneous user behaviors. We address these challenges by introducing prompt ambiguity, a theoretical framework that captures users' varying abilities in prompt engineering, and developing an Optimal Prompt Pricing (OPP) algorithm. Our analysis reveals a counterintuitive insight: users with higher prompt ambiguity (i.e., lower capability) exhibit non-monotonic prompt usage patterns, first increasing then decreasing with ambiguity levels, reflecting complex changes in marginal utility. Experimental evaluation using a character-level GPT-like model demonstrates that our OPP algorithm achieves up to 31.72% improvement in platform payoff compared to existing pricing mechanisms, validating the importance of user-centric prompt pricing in AIGC services.

Federated learning (FL) algorithms usually sample a fraction of clients in each round (partial participation) when the number of participants is large and the server's communication bandwidth is limited. Recent works on the convergence analysis of FL have focused on unbiased client sampling, e.g., sampling uniformly at random, which suffers from slow wall-clock time for convergence due to high degrees of system heterogeneity and statistical heterogeneity. This paper aims to design an adaptive client sampling algorithm for FL over wireless networks that tackles both system and statistical heterogeneity to minimize the wall-clock convergence time. We obtain a new tractable convergence bound for FL algorithms with arbitrary client sampling probability. Based on the bound, we analytically establish the relationship between the total learning time and sampling probability with an adaptive bandwidth allocation scheme, which results in a non-convex optimization problem. We design an efficient algorithm for learning the unknown parameters in the convergence bound and develop a low-complexity algorithm to approximately solve the non-convex problem. Our solution reveals the impact of system and statistical heterogeneity parameters on the optimal client sampling design. Moreover, our solution shows that as the number of sampled clients increases, the total convergence time first decreases and then increases because a larger sampling number reduces the number of rounds for convergence but results in a longer expected time per-round due to limited wireless bandwidth. Experimental results from both hardware prototype and simulation demonstrate that our proposed sampling scheme significantly reduces the convergence time compared to several baseline sampling schemes.

Trilevel learning, also called trilevel optimization (TLO), has been recognized as a powerful modelling tool for hierarchical decision process and widely applied in many machine learning applications, such as robust neural architecture search, hyperparameter optimization, and domain adaptation. Tackling TLO problems has presented a great challenge due to their nested decision-making structure. In addition, existing works on TLO face the following key challenges: 1) they all focus on the non-distributed setting, which may lead to privacy breach; 2) they do not offer any non-asymptotic convergence analysis which characterizes how fast an algorithm converges. To address the aforementioned challenges, this paper proposes an asynchronous federated trilevel optimization method to solve TLO problems. The proposed method utilizes $\mu$-cuts to construct a hyper-polyhedral approximation for the TLO problem and solve it in an asynchronous manner. We demonstrate that the proposed $\mu$-cuts are applicable to not only convex functions but also a wide range of non-convex functions that meet the $\mu$-weakly convex assumption. Furthermore, we theoretically analyze the non-asymptotic convergence rate for the proposed method by showing its iteration complexity to obtain $\epsilon$-stationary point is upper bounded by $\mathcal{O}(\frac{1}{\epsilon^2})$. Extensive experiments on real-world datasets have been conducted to elucidate the superiority of the proposed method, e.g., it has a faster convergence rate with a maximum acceleration of approximately 80$\%$.

While providing machine learning model as a service to process users' inference requests, online applications can periodically upgrade the model utilizing newly collected data. Federated learning (FL) is beneficial for enabling the training of models across distributed clients while keeping the data locally. However, existing work has overlooked the coexistence of model training and inference under clients' limited resources. This paper focuses on the joint optimization of model training and inference to maximize inference performance at clients. Such an optimization faces several challenges. The first challenge is to characterize the clients' inference performance when clients may partially participate in FL. To resolve this challenge, we introduce a new notion of age of model (AoM) to quantify client-side model freshness, based on which we use FL's global model convergence error as an approximate measure of inference performance. The second challenge is the tight coupling among clients' decisions, including participation probability in FL, model download probability, and service rates. Toward the challenges, we propose an online problem approximation to reduce the problem complexity and optimize the resources to balance the needs of model training and inference. Experimental results demonstrate that the proposed algorithm improves the average inference accuracy by up to 12%.

--Knowledge distillation (KD) can enable collaborative learning among distributed clients that have different model architectures and do not share their local data and model parameters with others. Each client updates its local model using the average model output/feature of all client models as the target, known as federated KD. However, existing federated KD methods often do not perform well when clients' local models are trained with heterogeneous local datasets. In this paper, we propose Federated knowledge distillation enabled by Adversarial Learning ( FedAL) to address the data heterogeneity among clients. First, to alleviate the local model output divergence across clients caused by data heterogeneity, the server acts as a discriminator to guide clients' local model training to achieve consensus model outputs among clients through a min-max game between clients and the discriminator . Moreover, catastrophic forgetting may happen during the clients' local training and global knowledge transfer due to clients' heterogeneous local data. T owards this challenge, we design the less-forgetting regularization for both local training and global knowledge transfer to guarantee clients' ability to transfer/learn knowledge to/from others. Experimental results show that FedAL and its variants achieve higher accuracy than other federated KD baselines. To address this problem, collaborative learning among multiple clients can be useful for producing models with better accuracy. However, there are several challenges. First, clients have their own local datasets and they may not be willing to share their raw data with others due to privacy concerns [1]. Second, clients on the edge of wireless networks often have different computation and memory resources, resulting in clients with heterogeneous models that have different architectures and parameters. Clients may not want to reveal their model architectures to other clients to further prevent privacy leakage [2], [3]. We refer to a client's model with unknown architecture to other clients as a black-box model. Pengchao Han is with the School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China. Han's contribution to this work was made when she was a Postdoc research associate at The Chinese University of Hong Kong, Shenzhen, China.

Distributed ensemble learning (DEL) involves training multiple models at distributed learners, and then combining their predictions to improve performance. Existing related studies focus on DEL algorithm design and optimization but ignore the important issue of incentives, without which self-interested learners may be unwilling to participate in DEL. We aim to fill this gap by presenting a first study on the incentive mechanism design for DEL. Our proposed mechanism specifies both the amount of training data and reward for learners with heterogeneous computation and communication costs. One design challenge is to have an accurate understanding regarding how learners' diversity (in terms of training data) affects the ensemble accuracy. To this end, we decompose the ensemble accuracy into a diversity-precision tradeoff to guide the mechanism design. Another challenge is that the mechanism design involves solving a mixed-integer program with a large search space. To this end, we propose an alternating algorithm that iteratively updates each learner's training data size and reward. We prove that under mild conditions, the algorithm converges. Numerical results using MNIST dataset show an interesting result: our proposed mechanism may prefer a lower level of learner diversity to achieve a higher ensemble accuracy.

Incentive mechanism is crucial for federated learning (FL) when rational clients do not have the same interests in the global model as the server. However, due to system heterogeneity and limited budget, it is generally impractical for the server to incentivize all clients to participate in all training rounds (known as full participation). The existing FL incentive mechanisms are typically designed by stimulating a fixed subset of clients based on their data quantity or system resources. Hence, FL is performed only using this subset of clients throughout the entire training process, leading to a biased model because of data heterogeneity. This paper proposes a game theoretic incentive mechanism for FL with randomized client participation, where the server adopts a customized pricing strategy that motivates different clients to join with different participation levels (probabilities) for obtaining an unbiased and high performance model. Each client responds to the server's monetary incentive by choosing its best participation level, to maximize its profit based on not only the incurred local cost but also its intrinsic value for the global model. To effectively evaluate clients' contribution to the model performance, we derive a new convergence bound which analytically predicts how clients' arbitrary participation levels and their heterogeneous data affect the model performance. By solving a non-convex optimization problem, our analysis reveals that the intrinsic value leads to the interesting possibility of bidirectional payment between the server and clients. Experimental results using real datasets on a hardware prototype demonstrate the superiority of our mechanism in achieving higher model performance for the server as well as higher profits for the clients.

With the rapid advancement of 5G networks, billions of smart Internet of Things (IoT) devices along with an enormous amount of data are generated at the network edge. While still at an early age, it is expected that the evolving 6G network will adopt advanced artificial intelligence (AI) technologies to collect, transmit, and learn this valuable data for innovative applications and intelligent services. However, traditional machine learning (ML) approaches require centralizing the training data in the data center or cloud, raising serious user-privacy concerns. Federated learning, as an emerging distributed AI paradigm with privacy-preserving nature, is anticipated to be a key enabler for achieving ubiquitous AI in 6G networks. However, there are several system and statistical heterogeneity challenges for effective and efficient FL implementation in 6G networks. In this article, we investigate the optimization approaches that can effectively address the challenging heterogeneity issues from three aspects: incentive mechanism design, network resource management, and personalized model optimization. We also present some open problems and promising directions for future research.

Multi-arm bandit (MAB) is a classic online learning framework that studies the sequential decision-making in an uncertain environment. The MAB framework, however, overlooks the scenario where the decision-maker cannot take actions (e.g., pulling arms) directly. It is a practically important scenario in many applications such as spectrum sharing, crowdsensing, and edge computing. In these applications, the decision-maker would incentivize other selfish agents to carry out desired actions (i.e., pulling arms on the decision-maker's behalf). This paper establishes the incentivized online learning (IOL) framework for this scenario. The key challenge to design the IOL framework lies in the tight coupling of the unknown environment learning and asymmetric information revelation. To address this, we construct a special Lagrangian function based on which we propose a socially-optimal mechanism for the IOL framework. Our mechanism satisfies various desirable properties such as agent fairness, incentive compatibility, and voluntary participation. It achieves the same asymptotic performance as the state-of-art benchmark that requires extra information. Our analysis also unveils the power of crowd in the IOL framework: a larger agent crowd enables our mechanism to approach more closely the theoretical upper bound of social performance. Numerical results demonstrate the advantages of our mechanism in large-scale edge computing.

Federated learning (FL) algorithms usually sample a fraction of clients in each round (partial participation) when the number of participants is large and the server's communication bandwidth is limited. Recent works on the convergence analysis of FL have focused on unbiased client sampling, e.g., sampling uniformly at random, which suffers from slow wall-clock time for convergence due to high degrees of system heterogeneity and statistical heterogeneity. This paper aims to design an adaptive client sampling algorithm that tackles both system and statistical heterogeneity to minimize the wall-clock convergence time. We obtain a new tractable convergence bound for FL algorithms with arbitrary client sampling probabilities. Based on the bound, we analytically establish the relationship between the total learning time and sampling probabilities, which results in a non-convex optimization problem for training time minimization. We design an efficient algorithm for learning the unknown parameters in the convergence bound and develop a low-complexity algorithm to approximately solve the non-convex problem. Experimental results from both hardware prototype and simulation demonstrate that our proposed sampling scheme significantly reduces the convergence time compared to several baseline sampling schemes. Notably, our scheme in hardware prototype spends 73% less time than the uniform sampling baseline for reaching the same target loss.