增强的物理信息柯尔莫戈罗夫-阿诺德网络：牛顿定律在金融深度强化学习（RL）算法中的应用
The Enhanced Physics-Informed Kolmogorov-Arnold Networks: Applications of Newton's Laws in Financial Deep Reinforcement Learning (RL) Algorithms
AI总结：
本文提出了一种结合物理信息柯尔莫戈罗夫-阿诺德网络的强化学习框架，用于金融投资组合优化，通过引入物理信息正则化损失提升模型稳定性与收益表现。
摘要：
深度强化学习（DRL），作为机器学习的一个子集，专注于序列决策制定，已发展为解决金融交易问题的强大方法。在金融领域，DRL通常用于生成离散的交易信号或确定连续的资产组合分配。在本工作中，我们提出了一种新的强化学习框架，用于投资组合优化，该框架将物理信息柯尔莫戈罗夫-阿诺德网络（PIKANs）整合到多个DRL算法中。该方法在actor和critic组件中用柯尔莫戈罗夫-阿诺德网络（KANs）替代传统的多层感知机，利用可学习的B样条单变量函数实现参数高效且更具解释性的函数逼近。在actor更新过程中，我们引入了物理信息正则化损失，以促进观测到的收益动态与动作引起的资产组合调整之间的二次时间一致性。所提出的框架在三个股票市场——中国、越南和美国——上进行了评估，涵盖了新兴市场和发展中国家。在所有三个市场中，基于PIKAN的智能体始终能够提供更高的累计和年化收益，更优越的夏普比率和卡玛比率，以及更有利的回撤特征，与标准DRL基线和经典在线投资组合选择方法相比。这导致了更稳定的训练、更高的夏普比率和优于传统DRL的性能。该方法在高度动态和嘈杂的金融市场中特别有价值，因为传统DRL往往在稳定性和泛化能力方面表现不佳。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
