## 5 Conclusions and Future Directions  
In this paper, we presented a novel blockchain-based zero-trust supply chain security framework integrated with deep reinforcement learning, SAC-rainbow, to address the complex challenges faced by modern supply chain systems. The proposed framework leverages the strengths of blockchain technology, smart contracts, and the SAC algorithm with prioritized experience replay to enhance security, transparency, and efficiency in supply chain management.  
The decentralized blockchain architecture ensures secure participant registration, authentication, and access control, fostering trust among stakeholders. Smart contracts automate supply chain transactions, reducing manual errors and improving operational efficiency. The SAC-based inventory optimization model learns adaptive policies to handle demand uncertainty and dynamic supply chain conditions, thus minimizing costs and maintaining optimal inventory levels.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Average Reward** & **Training Time (mins)** \\ \hline PPO & 0.76 & 13.6 \\ \hline DDPG & 0.71 & 12.9 \\ \hline SAC & 0.87 & 13.2 \\ \hline TD3 & 0.74 & 12.4 \\ \hline SAC-rainbow (our proposed algorithm) & 0.92 & 10.7 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The results of comparison methods.  
The integration of the zero-trust security model into the SAC-rainbow framework enables continuous verification and validation of all supply chain entities and transactions, thus mitigating the risk of security breaches and unauthorized access. By operating in a zero-trust environment, the proposed framework proactively detects and responds to potential threats, enhancing the overall resilience and robustness of the supply chain system.  
The experiment conducted using real-world supply chain data demonstrates the superior performance of the SAC-rainbow framework in terms of reward maximization, inventory stability, and security metrics. The results highlight the effectiveness of the proposed approach in addressing the complex challenges of modern supply chains, such as lack of transparency, inefficient inventory management, and vulnerability to disruptions and security threats.  
While the SAC-rainbow framework offers a promising solution for secure and efficient supply chain management, several challenges and future research directions remain. Scaling the blockchain architecture to handle large-scale supply chain networks and ensuring interoperability among different blockchain platforms are critical for widespread adoption. Developing more advanced and adaptive reinforcement learning algorithms to handle the increasing complexity and variability of supply chain environments is another important research avenue.  
Methodology, X.C.; software, Y.C.W.; validation, Z.M.; formal analysis, M.Z.; investigation, Y.C.W.; writing--original draft preparation, Z.M.; writing--review and editing, X.W., T.S. and M.Z.; supervision, X.W.; All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the unanimous decision of all authors.  
Author [PERSON] was employed by the company Sage IT Consulting Group. Author [PERSON] was employed by the company Ping An Property & Casualty Insurance Company of China, Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.