Stochastic Multi-armed Bandits with Non-stationary Rewards Generated by a Linear Dynamical System
This addresses the challenge of adapting bandit algorithms to dynamic environments, specifically for quantitative finance applications, representing an incremental extension of existing methods.
The paper tackles the problem of decision-making in stochastic multi-armed bandits with non-stationary rewards modeled by a linear dynamical system, proposing a strategy that learns the model and selects optimal actions, applied to high-frequency trading to maximize returns.
The stochastic multi-armed bandit has provided a framework for studying decision-making in unknown environments. We propose a variant of the stochastic multi-armed bandit where the rewards are sampled from a stochastic linear dynamical system. The proposed strategy for this stochastic multi-armed bandit variant is to learn a model of the dynamical system while choosing the optimal action based on the learned model. Motivated by mathematical finance areas such as Intertemporal Capital Asset Pricing Model proposed by Merton and Stochastic Portfolio Theory proposed by Fernholz that both model asset returns with stochastic differential equations, this strategy is applied to quantitative finance as a high-frequency trading strategy, where the goal is to maximize returns within a time period.