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Entropy

On Laws of Thought—A Quantum-like Machine Learning Approach

Lizhi Xin, Kevin Z. Xin, Houwen Xin

Published Aug 15, 2023• 4 citations
Publisher

Abstract

Incorporating insights from quantum theory, we propose a machine learning-based decision-making model, including a logic tree and a value tree; a genetic programming algorithm is applied to optimize both the logic tree and value tree. The logic tree and value tree together depict the entire decision-making process of a decision-maker. We applied this framework to the financial market, and a "machine economist" is developed to study a time series of the Dow Jones index. The "machine economist" will obtain a set of optimized strategies to maximize profits, and discover the efficient market hypothesis (random walk).

DOI
10.3390/e25081213

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Incorporating insights from quantum theory, we propose a machine learning-based decision-making model, including a logic tree and a value tree; a genetic programming algorithm is applied to optimize both the logic tree and value tree. The logic tree and value tree together depict the entire decision-making process of a decision-maker. We applied this framework to the financial market, and a "machine economist" is developed to study a time series of the Dow Jones index. The "machine economist" will obtain a set of optimized strategies to maximize profits, and discover the efficient market hypothesis (random walk).
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.
Abstract A macroscopic particle obeys Newton's law, and a microscopic particle obeys the principles of quantum mechanics - so where is the sharp boundary between the macroscopic and microscopic worlds? It was this "interpretation problem" that prompted Schrödinger to propose his famous thought experiment (a cat that is simultaneously both dead and alive) and sparked a great debate about the quantum measurement problem, and there is still no satisfactory answer yet. This is precisely the inadequacy of rigorous mathematical models in describing the laws of nature. We propose a computational model to describe and understand the laws of nature based on Darwin's natural selection. In fact, whether it's a macro particle, a micro electron or a security, they can all be considered as an entity, the change of this entity over time can be described by a data series composed of states and values. An observer can learn from this data series to construct theories (usually consisting of functions and differential equations). We don't model with the usual functions or differential equations, but with a state Decision Tree (determines the state of an entity) and a value Function Tree (determines the distance between two points of an entity). A state Decision Tree and a value Function Tree together can reconstruct an entity's trajectory and make predictions about its future trajectory. Our proposed algorithmic model discovers laws of nature by only learning observed historical data (sequential measurement of observables) based on maximizing the observer's expected value. There is no differential equation in our model; our model has an emphasis on machine learning, where the observer builds up his/her experience by being rewarded or punished for each decision he/she makes, and eventually leads to rediscovering Newton's law, the Born rule (quantum mechanics) and the efficient market hypothesis (financial market).
Quantum Machine Learning (QML) prediction of stock values is on the verge of changing the financial market and particularly enhancing HFT techniques. This is an attempt at quantum computing-machine learning hybrid aimed at enhancing the accuracy and efficiency of trading decisions. The historical machine learning-based stock price prediction models are incapable of processing large volumes of data, executing trades faster, and modeling complex market dynamics in real-time. The challenges result in ineffective trading decisions and trade lags at high frequencies. These problems are solved by HFT Optimization and Quantum Machine Learning. Because quantum computing capability is processing large amounts of data simultaneously, the proposed architecture enhances prediction accuracy and speed while reducing latency of decision-making. Quantum Neural Networks (QNNs) and quantum-optimized algorithms are useful to boost the modeling of market behavior. This technology will enhance stock price forecasting and optimization of trading strategies, which increases profit and minimize risk. Initial evidence indicates that quantum-based HFT systems are faster in execution speed and market flexibility than conventional techniques, which is essential to the future of automated trading.
Quantum Machine Learning (QML) has emerged as a promising field, offering the potential to revolutionize various computational tasks, including machine learning. This paper investigates the application of QML to decision tree algorithms, specifically focusing on the development of a novel non-linear decision tree model designed for optimized decision-solving. We explore how quantum computation can enhance the optimization process inherent in decision tree construction, leading to improved efficiency and accuracy. The core claim is that leveraging quantum mechanics allows for automatic parameter adjustment within the decision tree, significantly increasing its effectiveness. This work introduces a framework where quantum algorithms are employed to refine the decision tree structure, addressing limitations of traditional methods. The research also investigates the potential benefits of this approach in complex decision scenarios, highlighting the advantages over conventional techniques. The paper concludes with a discussion of future research directions and the expected impact of QML on the field of decision tree learning.
In order to know if the Schrodinger's cat is alive or dead without opening the box, observers have to play a game with nature. The observers have to "guess" (with degrees of belief) the state of the cat due to incomplete information; in other words, the observers' decision has to be made under uncertainty. We propose a quantum expected value theory for decision-making under uncertainty. Value operator is proposed to guide observers to choose corresponding actions based on their subjective beliefs through objective quantum world by maximizing the value from the measured historical results. The value operator, as a quantum decision tree, can be constructed from both quantum gates and logic operations. Genetic programming is applied to optimize quantum decision trees.
The relentless quest for optimized financial portfolios has led to the exploration of advanced computational techniques capable of navigating financial markets’ complex and dynamic landscape. This dissertation presents a solution for portfolio optimization by harnessing the synergistic potential of quantum computing and machine learning. We propose a hybrid framework that integrates quantum algorithms’ optimization capabilities with machine learning’s predictive accuracy to address the multifaceted challenges of portfolio management. The study begins with a comprehensive review of traditional and contemporary portfolio optimization methods and an in-depth analysis of quantum computing principles relevant to optimization problems. Next, we examine machine learning models commonly used for forecasting financial time series, which serve as critical inputs for the quantum optimization process. The proposed solution is evaluated through simulations and real-world financial data to demonstrate its efficacy in achieving optimized asset allocations with enhanced risk-adjusted returns. This research contributes to the theoretical advancement of financial optimization techniques and provides practical insights for investors and portfolio managers seeking to leverage emerging technologies for strategic decision-making.