Bayesian learning, a fundamental concept in statistical inference and decision-making, has gained significant traction across various fields due to its ability to integrate prior knowledge with new information. As a robust methodology, Bayesian learning has been widely acknowledged for its adaptability and precision in handling uncertainty and updating beliefs (Gelman et al., 1995). This manuscript expands upon the Bayesian learning framework (Baley and Veldkamp, 2023) through uniquely addressing the action and state-dependent signal variance in the agents' information set. At the core of this framework is the concept that the precision of the signal received by an agent is contingent upon both the agent's action and the actual state, for example, based on their congruence or tracking error (Daly, 2018; du Sart and van Vuuren, 2021; Orlik and Veldkamp, 2014; Rompotis, 2011; Stone et al., 2013; Yang and Huang, 2022).

Bus bunching is a natural-occurring phenomenon that undermines the efficiency and stability of the public transportation system. The mainstream solutions control the bus to intentionally stay longer at certain stations. Existing control methods include conventional methods that provide a formula to calculate the control time and reinforcement learning (RL) methods that determine the control policy through repeated interactions with the system. In this paper, we propose an integrated proximal policy optimization model with dual-headway (IPPO-DH). IPPO-DH integrates the conventional headway control with reinforcement learning, so that it acquires the advantages of both algorithms -- it is more efficient in normal environments and more stable in harsh ones. To demonstrate such an advantage, we design a bus simulation environment and compare IPPO-DH with RL and several conventional methods. The results show that the proposed model maintains the application value of the conventional method by avoiding the instability of the RL method in certain environments, and improves the efficiency compared with the conventional control, shedding new light on real-world bus transit system optimization.

It is a classic win-win situation: In the town of Manno, located not far from Lugano in the canton of Ticino, researchers from the Dalle Molle Institute for Artificial Intelligence ( IDSIA) and experts from UBS have been working together since the end of 2018. The IDSIA benefits from concrete applications for its research, while the global banking giant aims to use data analysis to optimize its processes and expand its services. "What will genuinely change our lives in the coming years are machine learning and artificial intelligence," says Sabine Keller-Busse, UBS Group Chief Operating Officer. The collaboration was announced at the beginning of 2018 and was already launched by the end of the year, thanks in large part to the location. "The launch at our existing base in Manno was extremely favorable. We found precisely the right experts there for our needs," says Sabine Magri, UBS GCOO Chief Operating Manager.