## 1 Introduction
### Literature Review
[12], for a given management strategy, defined the corresponding benefit as the probability of risk reduction achieved through structural retrofitting. [PERSON] et al. [13] assigned scores to various factors related to elements and conditions, health indexes, safety, and risk, as well as calculated the corresponding repair costs. They assigned different weights to each factor and calculated the benefit value using a benefit calculation formula. [PERSON] et al. [14] defined maintenance benefit as an actual improvement in reliability before and after maintenance actions. [PERSON] et al. [15] modified the specific parameters, the time-dependent cross-sectional area of internal reinforcement, and the plastic section modulus associated with steel beams, included in the performance function defined in maintenance effect studies, to assess the benefits of maintenance actions. [PERSON] et al. [16] defined bridge maintenance benefits as an improvement in the NBI deck condition rating after the application of deck maintenance measures. In practical applications, some states in the United States have also provided relevant definitions of bridge maintenance benefits [17]. For example, Connecticut defines bridge maintenance benefits based on the improvement in bridge condition compared to no maintenance work, while New Mexico defines bridge maintenance benefits by measuring the ability to improve the NBI rating. With the rapid development of artificial intelligence in recent years, there is a growing trend of integrating knowledge from the field of artificial intelligence with bridge maintenance management. This integration aligns with the development of intelligent bridge maintenance practices. In the field of artificial intelligence, planning and learning are central to many problems. In a discrete or continuous time domain, an intelligent agent interacts with the environment to choose appropriate sequences of actions to achieve predefined goals. This decision-making process is known as sequential decision making. In sequential decision making, the intelligent agent must balance between short-term greedy objectives and long-term planning, which aligns with the requirements of bridge maintenance decision making. In order to find the optimal maintenance strategies in bridge maintenance processes, attempts have been made to apply the sequential decision-making process of intelligent agents to the decision-making process of intelligent bridge maintenance management. This involves simulating the interaction between a bridge and its natural environment. The purpose of this interaction is to maximize the improvement in bridge structural performance. [PERSON] et al. [17] proposed a semi-Markov decision model that enables wind farm operators to automate the mid-term and short-term maintenance planning process for a batch or for all turbines rather than making decisions for individual turbines to determine their maintenance strategies. [PERSON] et al. [18] combined sequential decision making with deep learning to explore maintenance strategies for simply supported beam bridge deck elements and long-span cable-stayed bridge elements. Maintenance strategies were classified into minor repair, major repair, and replacement. However, these strategies were not specifically tailored to the level of individual defects, and no detailed maintenance plans were formulated. [PERSON] et al. [19] considered time-varying reliability in the degradation process of bridges and proposed a semi-Markov process model based on Weibull distribution for predicting the degradation of urban bridges.