China's "Thirteenth Five-Year Plan" for ecological environmental protection clearly states that "focus on improving environmental quality, implement the target management of atmospheric environmental quality and planning of reaching quality standard within a definite time", and emphasizes environmental quality compliance planning by laws. This paper aims at the precise management of regional air quality, focusing on the research of optimal decision methods for air quality compliance management, and systematically studies the system, models and methods of air quality compliance management. A two-layer hierarchical optimization model based on stackelberg game theory is constructed. The research shows that the results of the optimization decision-making can not only come to the exact reduction amount of each area, each sector (industry), each pollutant under the regional optimal control scheme and the minimum emission reduction cost, but also clearly and precisely present the combination of pollution control technological measures of emission reduction for each area, each sector (industry) and each pollutant. This method can better guide the formulation and implementation of regional air quality standards management policies. The conclusions in this paper can provide technical support for the development of China's air quality improvement strategies, and provide practical guidance for municipal and regional air quality compliance management. This would help to achieve the comprehensive realization of scientific decision-making of air pollution control based on synergism of five elements including "economic development, environment quality, energy substitution, pollution control, cost saving". Finally, this study presents policy implications of development of detailed management initiatives align with regional air quality management requirements, such as strengthening regional top-level design, promoting data sharing, integrating industrial reality, combining short-term and long-term compliance planning. These implications will provide practical methods and paths for the precise management of regional air quality in China.