Expert's evaluation is like a beis din & witnesses

Igros Moshe(Y.D. 2:103): Concerning the matter of a teacher who wants to punish a student that he has warned (Makkos 8b)… Certainly a teacher needs to punish a student for that which he clearly did - but not for mere suspicions. This is also true even if the teacher thinks that there is clearly circumstantial evidence that the student committed the prohibited act. It is not permitted for any person in the world to rely on his own opinion in order to punish even the slightest – unless he has clear knowledge and witnesses. Even for a matter which is only worth pennies (peruta) it is necessary to have witnesses and surely for corporal punishment which is worth more than money. In fact the teacher’s right to punish is not any different then a beis din for which mere suspicion is irrelevant to punish. However there is an apparent contradiction found in Makkos (8b) that even though a student has learned his lesson it is still permitted to punish him? But that is only if according to the student’s ability he is able to learn more Torah than he does because he is lazy and doesn’t work hard. In such a case he can be punished even though the student in fact had learned his lesson and doesn’t waste his time. But if the student does not look deeply into the matter because of his laziness then it is appropriate to punish him. This action is based only on the evaluation of the teacher because his expertise makes this something obvious to him and it is within his competence to judge these matters and it is impossible to go to beis din to judge this matter. There are obviously other matters that occur regularly to either a rav or a teacher and his students that they judge according to their understanding without bringing in witnesses and judges. These judgments that a rav or a teacher make without testimony of witnesses before a beis din is similar to what we find in Shulchan Aruch (C.M. 35:14) that in circumstances where men don’t typically go – there is an ancient decree to believe women. And similarly a rav or a teacher and his students, it is a very common that he is forced to rely on his expert opinion alone in deciding what actions to take. Nevertheless this knowledge has to be something that is clear to him and not mere suspicions. Furthermore if there are any doubt or suspicions concerning one of his students in a matter that is improper, it is necessary to first speak to him in a way that draws him closer to Torah and keeps him away from the suspected behavior. However if it clearly known to the teacher that it is necessary for the student to be punished, then it is proper to punish him calmly and not with anger or upset….