## 1 Introduction  
With the booming development of the Internet of Things (IoT) ecosystem, users have higher expectations for quality experiences (QoE) across various IoT applications. Following the official deployment and operation of the fifth-generation (5G) mobile system, the sixth-generation (6G) mobile system has gradually come into the limelight. High-speed communication technologies can provide a higher quality of service (QoS) for IoT applications, such as intelligent transportation, intelligent agriculture, maritime surveillance,smart cities, natural disaster relief, and so on. However, existing terrestrial communication networks cannot effectively provide QoS and QoE guarantees for intelligent and low-latency IoT applications. On the other hand, computing capacity and energy resources in edge nodes are often insufficient to meet the demands of all edge tasks [1]. Task offloading decisions are largely influenced by these factors. Some researchers have addressed these issues from the perspective of an edge-cloud collaboration [2]. Researchers have also turned their attention to the space-air-ground integrated network (SAGIN) to allocate more resources. SAGIN is an integration of the space layer, aerial layer, and ground layer. As a multidimensional network, SAGIN adopts different communication protocols in each segment or integrates different segments to achieve high throughput and reliable data delivery [3]. However, we have to face some new challenges in SAGIN, such as computationally intensive task offloading at the mobile edge and resource allocation in uncertain and heterogeneous network environments. The uncertain network parameters [4], such as uncertain latency, the uncertain amount of arrival tasks [5], and uncertain computation resources, may seriously impact the efficiency of edge task execution. The heterogeneous environment necessitates considering additional factors, such as selecting suitable frequency bands for task propagation and choosing different types of computing nodes. At the same time, the fluctuating processing capabilities make it challenging to allocate appropriate computing resources based on uncertain data when there is a surge of computational tasks. Nowadays, stochastic optimization (SO) [6] and robust optimization (RO) [7; 8; 9] methods are proposed to solve uncertainty problems. The SO method can use the probability distribution of measuring parameters to predict the potential uncertainty and obtain the mathematical expectation of the objective function. The RO method can directly solve the target value under the worst-case conditions, and it does not need to obtain the probability distributions of measuring parameters. Nonetheless, the results obtained from the SO algorithm may not accurately reflect realistic worst-case scenarios, while the RO algorithm sacrifices a significant amount of performance to obtain computation offloading decisions for worst-case situations. Distributionally robust optimization (DRO) can be viewed as a unifying framework for the SO and RO methods. The DRO method can replace the probability distribution of uncertain measuring parameters with a fuzzy set. [10]. Then it can choose the worst case in the fuzzy set to obtain better robustness. Additionally, the authors of [11] proposed the conditional value at risk (CVaR) aware DRO method, which can reflect the potential risks and improve stability. In SAGIN environments, the number of tasks requiring offloading may vary, and the availability of computational resources can fluctuate in real time. These uncertainties pose challenges in making efficient task offloading decisions. The risk-aware distributionally robust optimization task offloading (RaDROO) algorithm addresses these challenges by incorporating robust optimization techniques and considering the uncertainties in both the number of tasks and real-time computational resource availability. The two-stage offloading decision process of the RaDROO algorithm enables it to dynamically determine the most suitable task offloading targets.