## 1 Introduction
### Contributions  
We investigate the joint optimization problem in the multi-user IRS-assisted ISAC system. Specifically, the design of transmit beamforming and IRS phase shift matrices for communication and radar sensing, as well as the computation offloading for local data processing, are studied in this context. Our aim is to optimize the system's data transmission and energy efficiency while meeting the radar sensing requirement and power constraints. Considering the dynamic environment and high-dimensional solution space of the optimization problem, we develop a DRL scheme for solving it. We can summarize the contributions as follows:  
* We propose the IRS-assisted ISAC framework, exploiting the IRS to assist and enhance sensing and communication functions in NLoS coverage areas. We construct a comprehensive optimization goal, covering the sensing, communication, and computation offloading. The main goal is to maximize the data sum-rate while minimizing energy consumption under the radar performance, transmit power budget, and offloading time delay constraints through the joint design of transmit beamforming and IRS phase shift.
* Considering the coupled relationship between optimization variables, the joint optimization problem is NP-hard and non-convex, making it challenging to use traditional mathematical methods. Therefore, the optimization problem is formulated as an MDP  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Ref.** & **Phases** & **Users** & **Targets** & **Radar Paths** & **Method** \\ \hline
[13] & Continuous & Single & Single & LoS, NLoS & MM \\
[8] & Continuous & Single & Multiple & NLoS & SDR \\
[15] & Continuous & Multiple & Multiple & LoS & AO \\
[18] & Continuous & Single & Single & LoS, NLoS & PDD, BCD \\
[19] & Discrete & Multiple & Multiple & LoS & AO \\
[20] & Continuous & Multiple & Single & LoS, NLoS & ADMM, AO \\
[21] & Discrete & Multiple & Multiple & NLoS & SDR \\
[22] & Continuous & Single & Multiple & LoS, NLoS & BCD \\ This paper & Continuous & Multiple & Multiple & NLoS & DRL \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison with the state of the art.  
problem, and two innovative DRL schemes are designed to solve it. Due to the continuous and large-dimension action space, we develop a deep deterministic policy gradient (DDPG) scheme, which combines prior experience replay technology to enhance training efficiency. Furthermore, a twin delayed DDPG (TD3) scheme is designed based on the DDPG framework.
* Simulation results confirm the effectiveness and convergence of our proposed scheme. In contrast with benchmarks, our proposed DRL scheme achieves a better balance between communication and sensing performance. Moreover, system's energy consumption and latency are optimized by proper computation offloading. Finally, the benefits and feasibility of the IRS-assisted ISAC framework are verified.  
Notation: Bold uppercase and lowercase letters represent matrices and vectors, respectively. \((\cdot)^{T}\) and \((\cdot)^{H}\) denote the transpose and Hermitian transpose operators. \(\text{Tr}(\cdot)\) is the rank operation. \(\text{diag}(\cdot)\) expresses the diagonal elements. \(\left\|\cdot\right\|_{F}\) and \(\left|\cdot\right|\) are the Frobenius norm and absolute operators.