The Enhanced Physics-Informed Kolmogorov-Arnold Networks: Applications of Newton's Laws in Financial Deep Reinforcement Learning (RL) Algorithms

TL;DR

This paper introduces a physics-informed reinforcement learning framework using Kolmogorov-Arnold Networks for portfolio optimization, demonstrating improved stability and performance across diverse financial markets.

Contribution

It integrates physics-informed regularization and Kolmogorov-Arnold Networks into DRL for more interpretable and efficient financial decision-making, outperforming standard methods.

Findings

Higher cumulative and annualized returns across markets

Improved Sharpe and Calmar ratios

More stable training and better generalization in noisy markets

Abstract

Deep Reinforcement Learning (DRL), a subset of machine learning focused on sequential decision-making, has emerged as a powerful approach for tackling financial trading problems. In finance, DRL is commonly used either to generate discrete trade signals or to determine continuous portfolio allocations. In this work, we propose a novel reinforcement learning framework for portfolio optimization that incorporates Physics-Informed Kolmogorov-Arnold Networks (PIKANs) into several DRL algorithms. The approach replaces conventional multilayer perceptrons with Kolmogorov-Arnold Networks (KANs) in both actor and critic components-utilizing learnable B-spline univariate functions to achieve parameter-efficient and more interpretable function approximation. During actor updates, we introduce a physics-informed regularization loss that promotes second-order temporal consistency between observed return dynamics and the action-induced portfolio adjustments. The proposed framework is evaluated across three equity markets-China, Vietnam, and the United States, covering both emerging and developed economies. Across all three markets, PIKAN-based agents consistently deliver higher cumulative and annualized returns, superior Sharpe and Calmar ratios, and more favorable drawdown characteristics compared to both standard DRL baselines and classical online portfolio-selection methods. This yields more stable training, higher Sharpe ratios, and superior performance compared to traditional DRL counterparts. The approach is particularly valuable in highly dynamic and noisy financial markets, where conventional DRL often suffers from instability and poor generalization.