用强化学习自动调参，加速投资组合与期权定价的计算
Accelerated Portfolio Optimization and Option Pricing with Reinforcement Learning
- 用强化学习动态调整块预条件子大小以提升求解速度
- 在真实投资组合数据上实现收敛速度显著加快、计算成本降低
- 适合需要快速决策的量化交易和实时期权定价场景
我们提出一种基于强化学习（RL）的框架，用于优化投资组合优化和期权定价中迭代求解器的块预条件子大小。投资组合中的协方差矩阵或期权定价模型中微分算子的离散化会导致大规模线性系统 $\mathbf{A}\textbf{x}=\textbf{b}$。高维投资组合或细网格期权定价直接求逆会带来巨大计算开销，因此实际应用中通常采用迭代方法。然而，病态系统收敛缓慢。传统预处理技术常需针对问题调参。为此，我们利用强化学习动态调节块预条件子大小，加速迭代求解器收敛。在一系列真实世界投资组合优化矩阵上的评估表明，该RL框架能有效调整预处理策略，显著加速收敛并降低计算成本。所提出的加速求解器支持更快速的动态投资组合配置和实时期权定价。
原文摘要 · Abstract (English)
We present a reinforcement learning (RL)-driven framework for optimizing block-preconditioner sizes in iterative solvers used in portfolio optimization and option pricing. The covariance matrix in portfolio optimization or the discretization of differential operators in option pricing models lead to large linear systems of the form $\mathbf{A}\textbf{x}=\textbf{b}$. Direct inversion of high-dimensional portfolio or fine-grid option pricing incurs a significant computational cost. Therefore, iterative methods are usually used for portfolios in real-world situations. Ill-conditioned systems, however, suffer from slow convergence. Traditional preconditioning techniques often require problem-specific parameter tuning. To overcome this limitation, we rely on RL to dynamically adjust the block-preconditioner sizes and accelerate iterative solver convergence. Evaluations on a suite of real-world portfolio optimization matrices demonstrate that our RL framework can be used to adjust preconditioning and significantly accelerate convergence and reduce computational cost. The proposed accelerated solver supports faster decision-making in dynamic portfolio allocation and real-time option pricing.
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