The convergence of artificial intelligence, fraud detection, and multi-cloud infrastructure presents unique challenges at the intersection of software engineering, cybersecurity, and distributed systems. This review examines the current state of research on optimizing software engineering pipelines for deploying AI-based fraud detection systems across multi-cloud environments. We synthesize findings from contemporary literature, analyzing architectural patterns, security frameworks, deployment strategies, and performance optimization techniques. The review addresses three critical research questions concerning architectural patterns and pipeline optimization strategies for multi-cloud deployments, security requirements influencing pipeline design, and current limitations with future research directions. Key findings indicate that microservices-based architectures leveraging container orchestration, event-driven processing, and hierarchical feature stores enable effective multi-cloud deployment. However, significant complexities persist in model versioning, data governance, cross-cloud data transfer costs, and security orchestration. We identify critical gaps in standardized pipeline architectures and propose a research agenda focusing on AI-native infrastructure, confidential computing, automated optimization, and sustainable ML practices. Case studies from financial services and e-commerce sectors illustrate practical implementations, while identified challenges and future directions provide a roadmap for advancing this critical domain.