AI-based mission-critical software exposes a blessing and a curse: its inherent statistical nature allows for flexibility in result quality, yet the mission-critical importance demands adherence to stringent constraints such as execution deadlines. This creates a space for trade-offs between the Quality of Result (QoR)-a metric that quantifies the quality of a computational outcome-and other application attributes like execution time and energy, particularly in real-time scenarios. Fluctuating resource constraints, such as data transfer to a remote server over unstable network connections, are prevalent in mobile and edge computing environments-encompassing use cases like Vehicle-to-Everything, drone swarms, or social-VR scenarios. We introduce a novel approach that enables software engineers to easily specify alternative AI service chains-sequences of AI services encapsulated in microservices aiming to achieve a predefined goal-with varying QoR and resource requirements. Our methodology facilitates dynamic optimization at runtime, which is automatically driven by the MARQ framework. Our evaluations show that MARQ can be used effectively for the dynamic selection of AI service chains in real-time while maintaining the required application constraints of mission-critical AI software. Notably, our approach achieves a 100x acceleration in service chain selection and an average 10% improvement in QoR compared to existing methods.