###### Abstract
The aforementioned studies have made progress in delay optimization, but this metric is not able to fully satisfy the need for freshness and timeliness of information as it primarily focuses on the end-to-end transmission latency and computing latency while neglecting other critical factors that determine information utility in time-sensitive applications. Specifically, conventional delay metrics do not adequately capture the complete lifecycle of tasks, as they overlook the critical time interval between task generation and the commencement of processing, during which tasks may remain queued in the system. Age of information (AoI), an effective metric of information freshness, has been presented to describe the time interval between the reception of the latest packet by the information receiver and the generation of the packet [26]. The larger the AoI, the less fresh the information becomes. Owing to its critical role in evaluating real-time system performance, AoI has gained increasing research attention and spurred a wealth of research [27, 28, 29, 30, 31, 32, 33, 34, 35, 36]. Refs. [29, 30, 31, 32, 33, 34, 35, 36] are studies on AoI in the field of edge computing, most of them following conventional paradigms, primarily focusing on assessing the freshness of raw task data or state information while overlooking the timeliness of task computation processes in edge computing environments [29, 30, 31, 32, 33]. Some studies extend the scope of AoI to the domain of computational timeliness [34, 35, 36]. In [34], [PERSON] et al. proposed an AoI-based optimization strategy for computation offloading and transmission scheduling, aiming to optimize AoI in both the transmission and execution phases under latency and energy constraints in Internet of Things (IoT) networks. In [35], [PERSON] et al. investigated a multi-device MEC system, where status updates were achieved through task computation, and the timeliness of these updates was evaluated using AoI. And they proposed an onlinealgorithm to minimize AoI by jointly optimizing task generation, computation offloading, and resource allocation. In [36], [PERSON] et al. investigated a VEC scenario that supports only vehicle-to-infrastructure (V2I) communication, using AoI as a key metric for evaluating task timeliness. And they formulated an optimization model aimed at maximizing the utility function of AoI and computational energy efficiency (CEE). Therefore, to meet the timeliness requirements of vehicles, this paper focuses on minimizing the AoI in a VEC network that integrates both V2I and V2V offloading. To the best of our knowledge, this paper is the first work to use AoI as a metric for task timeliness in a VEC network that combines the V2I and V2V offloading. The main contributions of this paper are summarized as follows. * To fully utilize vehicular computing resources, we consider a VEC network in which vehicles can offload computational tasks to the RSU as well as vehicles with idle computational resources. To effectively optimize the characteristic of information timeliness, an optimization problem that aims to minimize the AoI by jointly optimizing task offloading ratios, service node selection strategies, and subcarrier resource allocation schemes is formulated. * Due to the time-varying channel and the coupling of continuous and discrete optimization variables, a mask-assisted hybrid proximal policy optimization (MHPPO)-based DRL method is proposed, which the mixed action space is designed to handle the challenge coupling of the continuous and discrete optimization variables. Moreover, within the MHPPO method, an action masking mechanism is employed to filter the invalid actions. * Simulation results show that the proposed MHPPO method can achieve much lower average AoI and outperforms other benchmark methods. Specifically, the proposed MHPPO method reduces AoI by approximately 28.9% compared with the HPPO method, and by about 23% and 38.2% compared with the mask-assisted deep deterministic policy gradient (MDDPG) and the conventional DDPG method.