Description: Optimal stopping is a strategy used in decision-making that seeks to determine the most appropriate moment to stop data collection in a sampling process. This concept is based on the idea that, in situations where one must decide when to stop searching for additional information, it is crucial to find a balance between the cost of continuing to collect data and the benefit of obtaining more accurate information. Optimal stopping is applied in various fields, such as statistics, economics, and operations research, and is grounded in mathematical and probabilistic principles. By implementing this strategy, decision-makers can minimize the risk of making decisions based on incomplete or biased information, thereby optimizing the outcomes of their analyses. The key to optimal stopping lies in establishing clear criteria that guide the decision of when to stop, considering factors such as time, available resources, and the variability of the collected data. In summary, optimal stopping is a valuable tool that helps analysts maximize efficiency in data collection and improve the quality of decisions based on that data.
History: The concept of optimal stopping has its roots in decision theory and probability theory, with significant contributions from mathematicians such as John von Neumann and others in the 20th century. One of the most well-known problems related to optimal stopping is the ‘secretary problem,’ which was formalized in the 1950s. This problem illustrates how to select the best option from a set of candidates as they are presented and has been the subject of study in various disciplines, including economics and game theory.
Uses: Optimal stopping is used in various applications, such as sample selection in surveys, decision-making in financial investments, and in search and optimization algorithms. It is also applied in areas like artificial intelligence, where the right moment to stop searching for solutions in complex problems is sought.
Examples: A classic example of optimal stopping is the secretary problem, where the goal is to hire the best candidate from a group. Another example is found in stock investment, where an investor may decide when to sell a stock to maximize profits, evaluating the performance up to that point and the risk of holding it further.
