Reinforcement learning is widely studied across various fields. "Statistical Reinforcement Learning" aims to develop a reinforcement learning process with enhanced interpretability using statistical models and methods. "Reinforcement Statistical Learning" we developed is a new research direction that seeks to develop more robust and effective statistical learning methods using the tool of limit theory in reinforcement learning processes. Both utilize their respective strengths to develop new machine learning methods. This report will detail the methods related to "Reinforcement Statistical Learning" from the perspective of pioneering strategic limit theory, based on the simplest model of reinforcement learning—the multi-armed bandit process.Recently, our team has pioneered the "Strategic Limit Theory" based on the simplest model of reinforcement learning—the multi-armed bandit model. This represents a significant breakthrough in the intersection of nonlinear probability theory and reinforcement learning, expanding the research paradigms of traditional statistical methods. This report primarily introduces subsequent research conducted based on the Strategic Limit Theory, including studies on statistical theories and methods such as two-sample test, sequential sampling, experimental design, online learning and transfer learning.
