Can Machines Learn the True Probabilities?

TL;DR

This paper investigates the conditions under which AI machines can accurately learn true objective probabilities, clarifying the limitations and possibilities of probabilistic learning in uncertain environments.

Contribution

It provides theoretical proofs delineating when machines can or cannot learn true objective probabilities under certain assumptions.

Findings

Identifies conditions enabling machines to learn true probabilities.

Establishes scenarios where learning true probabilities is impossible.

Clarifies the role of assumptions in probabilistic machine learning.

Abstract

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.