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A key example of an optimal stopping problem is the secretary problem. Optimal stopping problems can often be written in the form of a Bellman equation , and are therefore often solved using dynamic programming .
In decision theory, the odds algorithm (or Bruss algorithm) is a mathematical method for computing optimal strategies for a class of problems that belong to the domain of optimal stopping problems. Their solution follows from the odds strategy, and the importance of the odds strategy lies in its optimality, as explained below.
The optimal policy for the problem is a stopping rule. Under it, the interviewer rejects the first r − 1 applicants (let applicant M be the best applicant among these r − 1 applicants), and then selects the first subsequent applicant that is better than applicant M. It can be shown that the optimal strategy lies in this class of strategies.
In probability theory, the optional stopping theorem (or sometimes Doob's optional sampling theorem, for American probabilist Joseph Doob) says that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected value. Since martingales can be used to model the wealth of a gambler participating ...
A simple suboptimal rule, which performs almost as well as the optimal rule within the class of memoryless stopping rules, was proposed by Krieger & Samuel-Cahn. [7] The rule stops with the smallest i {\displaystyle i} such that R i < i c / ( n + i ) {\displaystyle R_{i}<ic/(n+i)} for a given constant c, where R i {\displaystyle R_{i}} is the ...
Example of a stopping time: a hitting time of Brownian motion.The process starts at 0 and is stopped as soon as it hits 1. In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or optional time [1]) is a specific type of “random time”: a random variable whose value is interpreted as the time at ...
The regularization term, or penalty, imposes a cost on the optimization function to make the optimal solution unique. Implicit regularization is all other forms of regularization. This includes, for example, early stopping, using a robust loss function, and discarding outliers.
More recently, in 2011, an extension of the SPRT method called Maximized Sequential Probability Ratio Test (MaxSPRT) [7] was introduced. The salient feature of MaxSPRT is the allowance of a composite, one-sided alternative hypothesis, and the introduction of an upper stopping boundary. The method has been used in several medical research ...