Adaptive compressed sensing (CS) aims to select the most informative measurements sequentially, which is crucial for many modern imaging systems. This task can be formulated as a Bayesian sequential optimal experimental design (sOED) problem, where each new acquisition is chosen to maximally reduce uncertainty about the unknown image given prior information and subsequent data provided by acquisitions. However, in single-pixel imaging (SPI), the large design space consists of all possible binary illumination patterns. Directly optimizing the Bayesian sOED objective over this space using conventional methods is generally challenging. In this work, we reformulate sOED for SPI as a reinforcement learning (RL) problem. In RL, an agent learns a policy through repeated experimental trials to maximize a reward, here given as the expected information gain, the most complete measure of uncertainty reduction in Bayesian OED. This avoids the need to directly optimize complex information-theoretic objectives during a measurement to obtain the next design. Instead, the result is a learned policy function that directly maps the current posterior belief about the image to the next optimal binary measurement pattern, in a computationally efficient way. Using a simple yet representative SPI imaging scenario, this work evaluates the scalability of the learned policy under two different policy parameterizations. Furthermore, we investigate how performance deteriorates when only approximate posterior information is available or the measurements are impaired by noise, and propose several strategies to introduce additional design constraints motivated by biomedical applications. The numerical experiments demonstrate that the proposed Bayesian sOED-RL framework remains robust and can be extended to more complex, large-scale SPI scenarios.

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