# What is Optimal Stopping

##### Optimal Stopping: Making Better Decisions in Life and in AI

In order to make better decisions, we need to understand Optimal Stopping. Optimal Stopping is a mathematical concept that can be applied in various fields, including computer science, economics, and psychology. This concept involves making decisions based on the probability of achieving the best outcome.

Optimal Stopping is also known as the Secretary Problem, the Marriage Problem, or the Sultan’s Dowry Problem. In this article, we will discuss the basics of Optimal Stopping, its applications in real life, and its impact on the field of Artificial Intelligence.

##### What is Optimal Stopping?

Optimal stopping is the process of determining the best time to take a decision by calculating the maximum probability of achieving the desired outcome. This concept is applied when we have a limited number of opportunities to explore and evaluate different options. We need to decide which option to choose from, based on the information we have gathered so far.

The simplest example of Optimal Stopping is the Secretary Problem. Imagine you are a boss hiring a secretary. You have a number of candidates to interview, but you can only interview them once. After the interview, you need to decide whether to hire a candidate or let them go. If you hire someone, you cannot change your mind later. If you reject a candidate, you cannot go back and interview them again.

The question is, what is the optimal number of candidates you should interview before making a decision?

##### The Solution to the Secretary Problem

The solution to the Secretary Problem is that you should interview the first 37% of candidates, then reject them all, and then hire the next candidate that is better than the first 37%.

The reasoning behind this solution is that if you interview only the first 37% of candidates, you can only evaluate them, but you cannot compare them to other candidates. This means that you have to reject the first 37% of candidates, but you keep a record of their performance so far. The first 37% of candidates act as a benchmark for the remaining candidates, and you can use this benchmark to compare them.

One of the main advantages of Optimal Stopping is that it saves time and resources. For example, in the Secretary Problem, if you interview too many candidates, you may end up hiring someone who is not the best fit for the job. On the other hand, if you interview too few candidates, you may miss out on the best candidate.

##### Applications of Optimal Stopping in Real Life

Optimal Stopping has many applications in real life, including the following:

• Job Interviews: Employers can use Optimal Stopping to determine the best candidate to hire, without spending too much time and resources on interviews. This is especially useful for companies that receive a large number of job applications.
• Apartment Hunting: People who are looking for an apartment can use Optimal Stopping to find the best apartment without spending too much time and money on viewing apartments that are not suitable.
• Choosing a Partner: Optimal Stopping can also be applied in the dating world. For example, one can use Optimal Stopping to determine the best person to marry or enter into a long-term relationship with.

Optimal Stopping can also be applied in decision-making in general. For example, in business, Optimal Stopping can be used to determine whether to launch a new product, invest in a new project, or sell a company. In each of these cases, Optimal Stopping can help decision-makers to make the best decision based on the available data.

##### Optimal Stopping in Artificial Intelligence

Optimal Stopping has also revolutionized the field of Artificial Intelligence (AI). In AI, Optimal Stopping is applied in Reinforcement Learning, a type of machine learning that involves learning by trial and error.

Reinforcement Learning involves an agent that interacts with an environment to learn a policy that maximizes a reward. Optimal Stopping is used in Reinforcement Learning to determine the optimal time to take an action.

Optimal Stopping is also used in Deep Learning, a subfield of AI that involves training a neural network to learn patterns from data. In Deep Learning, Optimal Stopping is applied to determine the optimal number of iterations to train a neural network. If we train a neural network for too many iterations, it may overfit the data. If we train it for too few iterations, it may underfit the data.

Finally, Optimal Stopping is also used in Natural Language Processing (NLP), a subfield of AI that involves analyzing, understanding, and generating human language. In NLP, Optimal Stopping is applied to determine the optimal length of a text. For example, in text summarization, Optimal Stopping is used to determine the optimal length of a summary based on the length of the original text and the desired level of detail.

##### Conclusion

Optimal Stopping is a powerful concept that can be applied in various fields, including computer science, economics, and psychology. Optimal Stopping involves making decisions based on the probability of achieving the best outcome. The Secretary Problem is the simplest example of Optimal Stopping, which can be applied to various real-life problems, including job interviews, apartment hunting, and choosing a partner.

Optimal Stopping has also revolutionized the field of Artificial Intelligence, where it is applied in Reinforcement Learning, Deep Learning, and Natural Language Processing. By using Optimal Stopping, AI systems can make better decisions and learn more efficiently from data.