## 1 Introduction
### Related Works  
Adopting the IRS to improve communication quality has provided certain benefits; inspired by this, researchers have conducted extensive studies to explore the potential of employing IRS in ISAC systems [8; 13; 15; 16; 17; 18; 19; 20; 21]. In [8], the virtual LoS channel was created with the IRS's assistance to enhance the communication and sensing performance in an ISAC system, and the semi-definite relaxation (SDR) was adopted for the beam-pattern gain maximization problem. The authors in [13] exploited the IRS to strengthen the radar detection function in the dual-function radar and communication system, in which a joint optimization of precoding and IRS phase shift matrices was proposed, and a majorization--minimization (MM) method was used to solve it. A hybrid IRS model was investigated in [15], which comprised active and passive elements for enhancing ISAC systems and realizing worst-case target illumination power maximization through an alternating optimization (AO) algorithm. In [16], the authors proposed an IRS-aided radar system architecture and studied the benefits of IRSs and the deployment location issues. Through a joint beamforming design, the authors in [17] optimized the total transmit power while meeting signal-to-interference-plus-noise (SINR) requirements for communication and radar signal cross-correlation pattern constraint for sensing in IRS-assisted ISAC systems. The authors in [18] proposed penalty dual decomposition (PDD) and block coordinated descent (BCD) methods for the joint optimization problem in the IRS-aided communication radar coexistence system. In [19], the authors studied the joint waveform and discrete phase design in the IRS-aided ISAC system to mitigate the multi-user interference. In [20], an alternative direction method of multipliers (ADMMs) and MM approaches were proposed to optimize the sensing performance while satisfying the communication requirements. The authors in [22] developed an ISAC-assisted MEC and employed IRS to reduce the mutual interference between MEC offloading transmission and radar sensing, and a BCD algorithm was employed. Inspired by the above-mentioned work, we investigate the joint computation offloading and resource allocation problems in the IRS-aided ISAC system.  
Recently, the excellent performance of artificial intelligence (AI) algorithms in dealing with nonlinear and high computational complexity problems has triggered a revolution in the industry and academia [23; 24; 25; 26]. Considering that there are numerous elements in the IRS-assisted ISAC system, the high-dimensional optimization problems in this system are difficult to solve using traditional mathematical methods. However, it is very suitable for AI technology. Meanwhile, deep reinforcement learning (DRL) takes advantage of deep learning in neural network training and the extraordinary ability of reinforcement learning on large-scale non-convex problems [25]. Therefore, DRL finds a broad array of applications within the domain of wireless communications, including computing offloading [27], power allocation [28], task scheduling [29], etc. The authors in [30] designed a DRL approach to address a joint transmit precoding and phase shift matrix design with the maximizing data rate optimization goal. An adaptive DRL framework twin delayed deep deterministic policy gradient was developed in [31] to deal with the joint beamformer design problem in IRS-aided wireless systems. The authors in [6] designed a distributed reinforcement learning scheme for the joint optimization problem in the terahertz band IRS-aided ISAC system. Therefore, given the time-varying channel conditions and dynamic resources, we reformulated the proposed optimization problem in our work as a Markov decision process (MDP). Then, an innovative DRL-based framework is developed for solving the joint resource optimization and computation offloading problem. Table 1 lists the main closely-related existing efforts and compares them with our work.