Counterfactual explanations (CE) are the de facto method for providing insights into black-box decision-making models by identifying alternative inputs that lead to different outcomes. However, existing CE approaches, including group and global methods, focus predominantly on specific input modifications, lacking the ability to capture nuanced distributional characteristics that influence model outcomes across the entire input-output spectrum. This paper proposes distributional counterfactual explanation (DCE), shifting focus to the distributional properties of observed and counterfactual data, thus providing broader insights. DCE is particularly beneficial for stakeholders making strategic decisions based on statistical data analysis, as it makes the statistical distribution of the counterfactual resembles the one of the factual when aligning model outputs with a target distribution—something that the existing CE methods cannot fully achieve. We leverage optimal transport (OT) to formulate a chance-constrained optimization problem, deriving a counterfactual distribution aligned with its factual counterpart, supported by statistical confidence. The efficacy of this approach is demonstrated through experiments, highlighting its potential to provide deeper insights into decision-making models.

Federated Learning (FL) on low earth orbit (LEO) satellites represents a promising frontier for on-orbit edge intelligence. However, the inherent network dynamics and heterogeneity of datasets and resource across satellites pose challenges to efficient on-orbit FL. In this work, we model client selection and inter-satellite routing as a joint optimization problem. We derive and minimize an upper bound of the global empirical loss as the objective function, to enable fast convergence. We model the constraints of inter-satellite routing via time-varying graphs and network flow theory. We propose both exact and approximate solutions for the joint optimization problem. In addition, we formalize and prove the convergence property of our approach. Last, by simulation we demonstrate the efficiency and superiority of the proposed scheme for realistic satellite networking scenarios.

Time Series Representation Learning (TSRL) focuses on generating informative representations for various Time Series (TS) modeling tasks. Traditional Self-Supervised Learning (SSL) methods in TSRL fall into four main categories: reconstructive, adversarial, contrastive, and predictive, each with a common challenge of sensitivity to noise and intricate data nuances. Recently, diffusion-based methods have shown advanced generative capabilities. However, they primarily target specific application scenarios like imputation and forecasting, leaving a gap in leveraging diffusion models for generic TSRL. Our work, Time Series Diffusion Embedding (TSDE), bridges this gap as the first diffusion-based SSL TSRL approach. TSDE segments TS data into observed and masked parts using an Imputation-Interpolation-Forecasting (IIF) mask. It applies a trainable embedding function, featuring dual-orthogonal Transformer encoders with a crossover mechanism, to the observed part. We train a reverse diffusion process conditioned on the embeddings, designed to predict noise added to the masked part. Extensive experiments demonstrate TSDE's superiority in imputation, interpolation, forecasting, anomaly detection, classification, and clustering. We also conduct an ablation study, present embedding visualizations, and compare inference speed, further substantiating TSDE's efficiency and validity in learning representations of TS data.

Passively cooled base stations (PCBSs) are highly relevant for achieving better efficiency in cost and energy. However, dealing with the thermal issue via load management, particularly for outdoor deployment of PCBS, becomes crucial. This is a challenge because the heat dissipation efficiency is subject to (uncertain) fluctuation over time. Moreover, load management is an online decision-making problem by its nature. In this paper, we demonstrate that a reinforcement learning (RL) approach, specifically Soft Actor-Critic (SAC), enables to make a PCBS stay cool. The proposed approach has the capability of adapting the PCBS load to the time-varying heat dissipation. In addition, we propose a denial and reward mechanism to mitigate the risk of overheating from the exploration such that the proposed RL approach can be implemented directly in a practical environment, i.e., online RL. Numerical results demonstrate that the learning approach can achieve as much as 88.6% of the global optimum. This is impressive, as our approach is used in an online fashion to perform decision-making without the knowledge of future heat dissipation efficiency, whereas the global optimum is computed assuming the presence of oracle that fully eliminates uncertainty. This paper pioneers the approach to the online PCBSs load management problem.

Wireless-based federated learning (FL), as an emerging distributed learning approach, has been widely studied for 6G systems. When the paradigm shifts from terrestrial to non-terrestrial networks (NTN), FL may need to address several open challenges, e.g., the limited service time of low earth orbit (LEO) satellites, the straggler issue in synchronous FL, and time-efficient uploading and aggregation for massive devices. In this work, we exploit the synergy of LEO and FL for future integrated 6G-satellite systems by taking advantage of ubiquitous wireless access provided by LEO and appealing characteristics of collaborative training and data privacy preservation in FL. The studied LEO-FL framework may need to improve multi-metric performance in practice. Different from most FL works, we simultaneously improve the communication-training efficiency and local training accuracy from a multi-objective optimization (MOO) perspective. To solve the problem, we propose a decomposition and meta-deep reinforcement learning based MOO algorithm for FL (DMMA-FL), aiming at adapting to the dynamic satellite-terrestrial environments, achieving efficient uploading and aggregation, and approaching Pareto optimal sets. Compared to single-objective optimization, heuristics-based, and learning-based MOO algorithms, the effectiveness and advantages of the proposed LEO-FL framework and DMMA-FL algorithm are assessed on MNIST and CIFAR-10 datasets.

The paper investigates the weighted sum-rate maximization (WSRM) problem with latent interfering sources outside the known network, whose power allocation policy is hidden from and uncontrollable to optimization. The paper extends the famous alternate optimization algorithm weighted minimum mean square error (WMMSE) [1] under a causal inference framework to tackle with WSRM. Specifically, with the possibility of power policy shifting in the hidden network, computing an iterating direction based only on the observed interference inherently implies that counterfactual is ignored in decision making. A method called synthetic control (SC) is used to estimate the counterfactual. For any link in the known network, SC constructs a convex combination of the interference on other links and uses it as an estimate for the counterfactual. Power iteration in the proposed SC-WMMSE is performed taking into account both the observed interference and its counterfactual. SC-WMMSE requires no more information than the original WMMSE in the optimization stage. To our best knowledge, this is the first paper explores the potential of SC in assisting mathematical optimization in addressing classic wireless optimization problems. Numerical results suggest the superiority of the SC-WMMSE over the original in both convergence and objective.

In this technical note, we present a new theoretical result for multi-cell non-orthogonal multiple access (NOMA). For multi-cell scenarios, a so-called load-coupling model has been proposed earlier to characterize the presence of mutual interference for NOMA, and the optimization process relies on the use of fixed-point iterations across cells. One difficulty here is that the order of decoding for successive interference cancellation (SIC) in NOMA is generally not known a priori. This is because the decoding order in one cell depends on interference, which, in turn, is governed by resource usage in other cells, and vice versa. To achieve convergence, previous works have used workarounds that pose restrictions to NOMA, such that the SIC decoding order remains throughout the fixed-point iterations. As a comment to the previous works, we derive and prove the following result: The convergence is guaranteed, even if the order changes over the iterations. The result not only waives the need of previous workarounds, but also implies that a wide class of optimization problems for multi-cell NOMA is tractable, as long as that for single cell is.

In a cloud radio access network (C-RAN), distributed remote radio heads (RRHs) are coordinated by baseband units (BBUs) in the cloud. The centralization of signal processing provides flexibility for coordinated multipoint transmission (CoMP) of RRHs to cooperatively serve user equipments (UEs). We target enhancing UEs' capacity performance, by jointly optimizing the selection of RRHs for serving UEs, i.e., CoMP selection, and resource allocation. We analyze the computational complexity of the problem. Next, we prove that under fixed CoMP selection, the optimal resource allocation amounts to solving a so-called iterated function. Towards user-centric network optimization, we propose an algorithm for the joint optimization problem, aiming at scaling up the capacity maximally for any target UE group of interest. The proposed algorithm enables network-level performance evaluation for quality of experience.

Towards energy savings in large-scale nonorthogonal multiple access (NOMA) networks, we investigate power and load optimization for multi-cell and multi-carrier NOMA systems in this paper. To capture the coupling relation of mutual interference among cells, firstly, we extend a load-coupling model from orthogonal multiple access (OMA) to NOMA networks. Next, with this analytical tool, we formulate the considered optimization problem in NOMA-based load-coupled systems, where optimizing load, power, and determining decoding order are the key aspects in the optimization. Theoretically, we prove that the minimum network energy consumption can be achieved by using all the time-frequency resources in each cell to deliver users' demand. To achieve the optimal load and enable efficient power optimization, we develop a power-adjustment algorithm. Numerical results demonstrate promising energy-saving gains of NOMA over OMA in large-scale cellular networks, in particular for the high-demand and resource-limited scenarios.

We address an energy-efficient scheduling problem for practical multiple-input single-output (MISO) systems with stringent execution-time requirements. Optimal user-group scheduling is adopted to enable timely and energy-efficient data transmission, such that all the users' demand can be delivered within a limited time. The high computational complexity in optimal iterative algorithms limits their applications in real-time network operations. In this paper, we rethink the conventional optimization algorithms, and embed machine-learning based predictions in the optimization process, aiming at improving the computational efficiency and meeting the stringent execution-time limits in practice, while retaining competitive energy-saving performance for the MISO system. Numerical results demonstrate that the proposed method, i.e., optimization with machine- learning predictions (OMLP), is able to provide a time-efficient and high-quality solution for the considered scheduling problem. Towards online scheduling in real-time communications, OMLP is of high computational efficiency compared to conventional optimal iterative algorithms. OMLP guarantees the optimality as long as the machine- learning based predictions are accurate.

Optimizing non-orthogonal multiple access (NOMA) in multi-cell scenarios is much more challenging than the single-cell case because inter-cell interference must be considered. Most papers addressing NOMA consider a single cell. We take a significant step in analyzing NOMA in multi-cell scenarios. We explore the potential of NOMA networks in achieving optimal resource utilization with arbitrary topologies. Towards this goal, we investigate a broad class of problems consisting of optimizing power allocation and user pairing for any cost function that is monotonically increasing in time-frequency resource consumption. We propose an algorithm that achieves global optimality for this problem class. The basic idea is to prove that solving the joint optimization problem of power allocation, user pair selection, and time-frequency resource allocation amounts to solving a so-called iterated function without a closed form. We prove that the algorithm approaches optimality with fast convergence. Numerically, we evaluate and demonstrate the performance of NOMA for multi-cell scenarios in terms of resource efficiency and load balancing.

Non-orthogonal multiple access (NOMA) allows multiple users to simultaneously access the same time-frequency resource by using superposition coding and successive interfer- ence cancellation (SIC). Thus far, most papers on NOMA have focused on performance gain for one or sometimes two base stations. In this paper, we study multi-cell NOMA and provide a general framework for user clustering and power allocation, taking into account inter-cell interference, for optimizing resource allocation of NOMA in multi-cell networks of arbitrary topology. We provide a series of theoretical analysis, to algorithmically en- able optimization approaches. The resulting algorithmic notion is very general. Namely, we prove that for any performance metric that monotonically increases in the cells' resource consumption, we have convergence guarantee for global optimum. We apply the framework with its algorithmic concept to a multi-cell scenario to demonstrate the gain of NOMA in achieving significantly higher efficiency.

Cloud-based Radio Access Network (C-RAN) is a promising architecture for future cellular networks, in which Baseband Units (BBUs) are placed at a centralized location, with capacity-constrained fronthaul connected to multiple distributed Remote Radio Heads (RRHs) that are far away from the BBUs. The centralization of signal processing enables the flexibility for coordinated multi-point transmission (CoMP) to meet high traffic demand of users. We investigate how to jointly optimize CoMP-cell selection and base station resource allocation so as to enhance the quality of service (QoS), subject to the fronthaul capacity constraint in orthogonal frequency-division multiple access (OFDMA) based C-RAN. The problem is proved to be NP-hard in this paper. To deal with the computational complexity, we derive a partial optimality condition as the foundation for designing a cell-selection algorithm. Besides, we provide a solution method of the optimum of the time-frequency resource allocation problem without loss of fairness on the QoS enhancement of all users. The simulations show good performance of the proposed algorithms for jointly optimizing the cell selection and resource allocation in a C-RAN, with respect to QoS.

We extend the problem of optimizing user association for load balancing in cellular networks along 2-dimensions. First, we consider joint transmission, which is one of the coordinated multipoint techniques with which a user may be simultaneously served by multiple base stations. Second, we account for, mathematically, the coupling relation between the base stations' load levels that are dependent on each other due to inter-cell interference. We formulate two optimization problems, sum load minimization (MinSumL) and maximum load minimization (MinMaxL). We prove that both MinSumL and MinMaxL are NP-hard. We propose a mixed integer linear programming based scheme by means of linearization. This approach also leads to a bounding scheme for performance benchmarking. Then, we derive a set of partial optimality conditions. Fulfillment of the conditions will guarantee performance improvement for both MinSumL and MinMaxL. A solution algorithm is then derived based on the conditions. Simulation results are provided to demonstrate the effectiveness of the approaches.

We consider an energy minimization problem for cooperative LTE networks. To reduce energy consumption, we investigate how to jointly optimize the transmit power and the association between cells and user equipments (UEs), by taking into consideration joint transmission (JT), one of the coordinated multipoint (CoMP) techniques. We formulate the optimization problem mathematically. For solving the problem, a dynamic power allocation algorithm that adjusts the transmit power of all cells, and an algorithm for optimizing the cell-UE association, are proposed. The two algorithms are iteratively used in an algorithmic framework to enhance the energy performance. Numerically, the proposed algorithms can lead to lower energy consumption than the optimal energy setting in the non-JT case. In comparison to fixed power allocation in JT, the proposed dynamic power allocation algorithm is able to significantly reduce the energy consumption.

As one of the Coordinated Multipoint (CoMP) techniques, Joint Transmission (JT) can improve the overall system performance. In this paper, from the load balancing perspective, we study how the maximum load can be reduced by optimizing JT pattern that characterizes the association between cells and User Equipments (UEs). To give a model of the interference caused by cells with different time-frequency resource usage, we extend a load coupling model, by taking into account JT. In this model, the mutual interference depends on the load of cells coupled in a non-linear system with each other. Under this model, we study a two-cell case and proved that the optimality is achieved in linear time in the number of UEs. After showing the complexity of load balancing in the general network scenario, an iterative algorithm for minimizing the maximum load, named JT-MinMax, is proposed. We evaluate JT-MinMax in a Heterogeneous Network (HetNet), though it is not limited to this type of scenarios. Numerical results demonstrate the significant performance improvement of JT-MinMax on min-max cell load, compared to the conventional non-JT solution where each UE is served by the cell with best received transmit signal.