Liangxin Qian

Liangxin Qian, Wenhan Yu, Peiyuan Si et al.

Optimization problems in communication networks and information systems often contain coupled multiplicative or fractional terms, such as sum-of-products, sum-of-ratios, and logarithmic product-ratio structures. These problems are generally non-convex and difficult to solve, which motivates the development of tractable transformation and approximation techniques. In this paper, we propose an inequality-based transform framework for handling multiplicative and fractional terms involving an arbitrary number of coupled functions. The proposed framework is built upon the harmonic-mean, geometric-mean, arithmetic-mean, and quadratic-mean inequalities, and yields lower-bound and upper-bound surrogates for product-type terms. We derive the corresponding auxiliary-variable updates in closed form and show that the constructed surrogates are tight and first-order consistent at the current iterate. Based on these properties, we develop a class of successive approximation (SA) methods for sum-of-products/ratios minimization and maximization problems. When the transformed surrogate is convex for minimization or concave for maximization, the proposed method reduces to a standard successive convex approximation (SCA) method. When such convexity or concavity is not guaranteed, we further develop gradient-based SA variants and establish their sublinear convergence to an $ε$-stationary point under standard smoothness and boundedness assumptions. We also discuss extensions to logarithmic product-ratio objectives and non-convex constraints. Numerical studies and application examples, including transmit-energy minimization, age-of-information minimization, semantic utility maximization, reliability-aware routing, cooperative edge caching, and product-loss learning, demonstrate the versatility and effectiveness of the proposed transform framework.

Liangxin Qian, Chang Liu, Xuanyu Cao et al.

Federated bilevel optimization is widely used for nested learning problems across distributed clients, such as federated hyperparameter tuning and meta-learning under privacy and communication constraints. Most existing formulations assume fixed client data distributions, which can be violated by performativity, where deployed decisions reshape client behavior and data collection, inducing client-specific, decision-dependent distribution shift. We study federated bilevel performative prediction, where both upper-level (UL) and lower-level (LL) objectives are evaluated under client-dependent, decision-dependent distributions. We formalize the federated bilevel performatively stable (FBPS) point under a decoupled-risk perspective and provide sufficient conditions for its existence and uniqueness. We then develop two federated methods to compute the FBPS solution: FBi-RRM, which converges linearly under a contraction condition, and FBi-SGD, a communication-efficient stochastic method based on federated hypergradient estimation with convergence guarantees under diminishing step sizes when sensitivities are sufficiently small. Experiments on strategic regression and meta strategic classification validate the predicted stability thresholds and demonstrate improved meta-generalization over non-performative baselines, and CNN-based classification further demonstrates the practical effectiveness of the proposed methods in nonconvex neural network settings.

Peiyuan Si, Liangxin Qian, Jun Zhao et al.

Unmanned aerial vehicles (UAVs) are promising for providing communication services due to their advantages in cost and mobility, especially in the context of the emerging Metaverse and Internet of Things (IoT). This paper considers a UAV-assisted Metaverse network, in which UAVs extend the coverage of the base station (BS) to collect the Metaverse data generated at roadside units (RSUs). Specifically, to improve the data collection efficiency, resource allocation and trajectory control are integrated into the system model. The time-dependent nature of the optimization problem makes it non-trivial to be solved by traditional convex optimization methods. Based on the proposed UAV-assisted Metaverse network system model, we design a hybrid framework with reinforcement learning and convex optimization to {cooperatively} solve the time-sequential optimization problem. Simulation results show that the proposed framework is able to reduce the mission completion time with a given transmission power resource.