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

Trang Thoi, Hung Tran, Tram Thoi, Huaiyang Zhong

TL;DR

A novel reinforcement learning framework for portfolio optimization that incorporates Physics-Informed Kolmogorov-Arnold Networks (PIKANs) into several DRL algorithms and introduces a physics-informed regularization loss that promotes second-order temporal consistency between observed return dynamics and the action-induced portfolio adjustments.

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.

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

TL;DR

A novel reinforcement learning framework for portfolio optimization that incorporates Physics-Informed Kolmogorov-Arnold Networks (PIKANs) into several DRL algorithms and introduces a physics-informed regularization loss that promotes second-order temporal consistency between observed return dynamics and the action-induced portfolio adjustments.

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.
Paper Structure (33 sections, 19 equations, 6 figures, 5 tables, 4 algorithms)

This paper contains 33 sections, 19 equations, 6 figures, 5 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Machine Learning in Portfolio Optimization
  4. Deep Reinforcement Learning
  5. Physics-Informed Neural Network Design
  6. Problem Formulation
  7. State Space
  8. Action Space
  9. Reward Function
  10. Trading Procedure
  11. Post-price drift.
  12. Transaction costs.
  13. Portfolio value update.
  14. Model Design
  15. Deep Deterministic Policy Gradient (DDPG)
  16. ...and 18 more sections

Figures (6)

  • Figure 1: Portfolio wealth trajectories for CSI 300 (China) during the test period. The physics-informed variants show stronger resilience in volatile market conditions.
  • Figure 2: Portfolio wealth trajectories for Vietnam market during the test period. Physics-informed DRL agents maintain higher stability and superior cumulative returns compared with non-physics models.
  • Figure 3: Portfolio wealth trajectories for S&P 100 (U.S.) during the test period. A2C_PINN and TD3_PINN outperform other DRL and rule-based methods in both return and risk control.
  • Figure 4: Evolution of portfolio weights across training episodes for A2C_PINN (U.S. market).
  • Figure 5: Evolution of portfolio weights across training episodes for A2C (U.S. market).
  • ...and 1 more figures