Can Machines Learn the True Probabilities?
This addresses a foundational problem in probabilistic machine learning for AI systems dealing with uncertainty.
The paper investigates whether AI machines can learn true objective probability functions from their environment, proving conditions under which such learning is possible or impossible.
When there exists uncertainty, AI machines are designed to make decisions so as to reach the best expected outcomes. Expectations are based on true facts about the objective environment the machines interact with, and those facts can be encoded into AI models in the form of true objective probability functions. Accordingly, AI models involve probabilistic machine learning in which the probabilities should be objectively interpreted. We prove under some basic assumptions when machines can learn the true objective probabilities, if any, and when machines cannot learn them.