Machine learning for decision-making under uncertainty

TL;DR

This paper introduces a novel decision-making model under uncertainty that combines quantum theory, genetic programming, and machine learning to learn decision laws from data without relying on traditional probability or utility functions.

Contribution

It proposes a new quantum decision tree framework that learns decision strategies from historical data using genetic programming, diverging from classical probability-based models.

Findings

The model successfully learns decision strategies from data.

It does not rely on differential equations or transition probabilities.

The approach emphasizes experiential learning through rewards and punishments.

Abstract

We live in a world brimming with uncertainty, where we constantly have to make a lot of decisions under incomplete information. We are firm believers that our subjective belief cannot be computed by rigorous mathematical formula; instead based on Darwin's natural selection (the evolution process is simulated by machine learning with genetic programming), a proposed computational model that incorporates insights from quantum theory to describe and explain decision-making under uncertainty. Unlike other decision-making theories that explain the decision-making process through probability theory, our proposed decision theory discovers "laws" of thought by learning observed historical data. There is no differential equation and no transition probability in our decision theory, our decision model has an emphasis on machine learning, where decision-makers build-up their experience by being rewarded or punished for each decision they make and prepare them for making better decisions in the future. We do not model with the usual utility function, but with quantum decision tree that simulates people's decision process. Each quantum decision tree includes a set of strategies; every time a decision is made, the decision-maker first chooses a strategy from the quantum decision tree's strategy pool, and then chooses an action based on the degree of belief which is obtained by genetic programming based on maximizing expected value.