Abstract: Dynamic diagnosis is desirable when medical tests are costly or time-consuming. In this work, we use reinforcement learning (RL) to find a dynamic policy that selects lab test panels sequentially based on previous observations, ensuring accurate testing at a low cost. Clinical diagnostic data are often highly imbalanced; therefore, we aim to maximize the F1 score instead of the error rate. However, optimizing the non-concave $F_1$ score is not a classic RL problem, thus invalidating standard RL methods. To remedy this issue, we develop a reward shaping approach, leveraging properties of the $F_1$ score and duality of policy optimization, to provably find the set of all Pareto-optimal policies for budget-constrained $F_1$ score maximization. To handle the combinatorially complex state space, we propose a Semi-Model-based Deep Diagnosis Policy Optimization (SM-DDPO) framework that is compatible with end-to-end training and online learning. SM-DDPO is tested on diverse clinical tasks: ferritin abnormality detection, sepsis mortality prediction, and acute kidney injury diagnosis. Experiments with real-world data validate that SM-DDPO trains efficiently and identify all Pareto-front solutions. Across all tasks, SM-DDPO is able to achieve state-of-the-art diagnosis accuracy (in some cases higher than conventional methods) with up to $85\%$ reduction in testing cost. Core codes are available at https://github.com/Zheng321/Deep-Reinforcement-Learning-for-Cost-Effective-Medical-Diagnosis.