梦想中的机器学习：金融市场强化学习的Lipschitz扩展
Dreaming machine learning: Lipschitz extensions for reinforcement learning on financial markets
摘要：
我们考虑了一个准度量拓扑结构的金融市场的框架下构建一个新的强化学习模型。它基于度量空间中定义的奖励函数的Lipschitz型扩展。具体而言，McShane和惠特尼扩展被认为是一个奖励函数，这是由总的评价所产生的投资决策在给定的时间。我们将度量定义为欧几里得距离和角度量分量的线性组合。从时间间隔开始的关于系统演化的所有信息都用于支持奖励函数的扩展，但此外，通过添加一些人工产生的状态来丰富该数据集。因此，我们的方法的主要新颖之处在于我们产生更多状态的方式-我们称之为“梦”-以丰富学习。利用代表金融市场演化的动力系统的一些已知状态，我们使用我们的技术通过插值真实状态和引入一些随机变量来模拟新的状态。这些新的状态被用来提供学习算法，该学习算法旨在通过遵循典型的强化学习方案来改进投资策略。
英文摘要：
We consider a quasi-metric topological structure for the construction of a new reinforcement learning model in the framework of financial markets. It is based on a Lipschitz type extension of reward functions defined in metric spaces. Specifically, the McShane and Whitney extensions are considered for a reward function which is defined by the total evaluation of the benefits produced by the investment decision at a given time. We define the metric as a linear combination of a Euclidean distance and an angular metric component. All information about the evolution of the system from the beginning of the time interval is used to support the extension of the reward function, but in addition this data set is enriched by adding some artificially produced states. Thus, the main novelty of our method is the way we produce more states -- which we call "dreams" -- to enrich learning. Using some known states of the dynamical system that represents the evolution of the financial market, we use our technique to simulate new states by interpolating real states and introducing some random variables. These new states are used to feed a learning algorithm designed to improve the investment strategy by following a typical reinforcement learning scheme.
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