## Control Systems and Computers, N1, 2019, Article 2

##### https://doi.org/10.15407/usim.2019.01.011

Upr. sist. maš., 2019, Issue 1 (279), pp. 11-21.

UDC 65.01:62-505

L.S. Fainzilberg, Doctor (Eng.), Professor, Head of the department, International Research and Training Center for Information Technologies and Systems of the NAS and MES of Ukraine, Glushkov ave., 40, Kyiv, 03187, Ukraine, fainzilberg@gmail.com

### MODIFIED OPTIMAL STOPING METHOD IN THE PROBLEM OF A SEQUENTIAL ALTERNATIVES ANALYSIS

Introduction. The traditional formulation of the optimal stopping problem is aimed at choosing the moment of making a decision about the appearance of the best option during the sequential viewing of ranked alternatives in a random order. A distinctive feature of the proposed method generalization is that the decision on an applicant appearance, which by some criterion differs from the absolute leader by no more than a specified amount (assignment), is considered correct.

The purpose of the article is to explore the possibilities of a modified optimal stopping method based on a statistical experiment.

Methods. The statistical experiment is based on the Monte Carlo method and provides for the multiple generation of the arrays of independent identically distributed random variables that mimic the values of the super alternative criterion, which the person observes at the current step. Based on a series of multiple tests, the probability of an applicant selecting, which differs by a given amount from the absolute leader, is estimated. The dependence probability analysis of the correct decisions on the assignment value is done.

Result. It is established that already at a value of 4% assignment, the required amount of experimental sampling for making a final decision decreases from 37% (the classical method) to 15%. At the same time, the probability of right decision increases to  (when is concession of 10%) compared with the probability  of the right decision, achieved by the classical method.

Conclusion. By introducing an insignificant concession to the deviations of the chosen applicant from the absolute leader, the possibilities of the optimal stopping method are expanded to solve the practical problems.

Keywords: optimal stopping, alternative, probability of correct decision.

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