Summary
In this chapter, we explored various problems that involved making optimal decisions under uncertainty using the optimal stopping theorem and randomized algorithms. We examined scenarios such as the hiring problem, the Matcher dating app, and Fang’s parking problem, each requiring a strategic balance between gathering information and making timely decisions. Through these examples, we illustrated how the optimal stopping theorem provides a structured approach to maximize the chances of selecting the best option by setting appropriate observation phases and selection criteria. This chapter demonstrated the power of probabilistic reasoning and optimal stopping rules in practical decision-making scenarios. In the next chapter, we will explore dynamic programming, a powerful technique for solving complex problems by breaking them down into simpler subproblems.
