Wearable devices for health monitoring are essential for tracking individuals' health status and facilitating early detection of diseases. However, processing biomedical signals online for real-time monitoring is challenging due to limited computational resources on edge devices. To address this challenge, we propose an application-agnostic methodology called ACE (Automated optimization towards classification on the Edge). ACE converts a health monitoring algorithm with feature extraction and classification into an iterative detection process, incorporating algorithms of varying complexities and minimizing re-computation of shared data. First, ACE decomposes a monolithic model, employing a single feature set and classifier, into multiple algorithms with different computational complexities. Then, our automatic analysis tool integrates buffering logic into these algorithms to prevent recomputation of shared computational-intensive data. The optimized algorithm is then converted into a low-level language in C for deployment. During runtime, the system initiates monitoring with the lowest complexity algorithm and iteratively involves algorithms with higher complexity without recomputing the existing data. The iteration process continues until a pre-defined confidence threshold is met. We demonstrate the effectiveness of ACE on two biomedical applications: seizure detection and emotional state classification. ACE achieves at least 28.9% and 18.9% runtime savings without any accuracy loss on a Cortex-A9 edge platform for the two benchmarks, respectively. We discuss and demonstrate how ACE can be used by designers of such biomedical algorithms to automatically optimize and deploy their applications on the edge.