Analysis Of Thompson Sampling For Controlling Unknown Linear Diffusion Processes

Abstract

Linear diffusion processes serve as canonical continuous-time models for dynamic decision-making under uncertainty. These systems evolve according to drift matrices that specify the instantaneous rates of change in the expected system state, while also experiencing continuous random disturbances modeled by Brownian noise. For instance, in medical applications such as artificial pancreas systems, the drift matrices represent the internal dynamics of glucose concentrations. Classical results in stochastic control provide optimal policies under perfect knowledge of the drift matrices. However, practical decision-making scenarios typically feature uncertainty about the drift; in medical contexts, such parameters are patient-specific and unknown, requiring adaptive policies for efficiently learning the drift matrices while ensuring system stability and optimal performance. We study the Thompson sampling (TS) algorithm for decision-making in linear diffusion processes with unknown drift ma

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