Active Measuring in Reinforcement Learning With Delayed Negative Effects

Measuring states in reinforcement learning (RL) can be costly in real-world settings and may negatively influence future outcomes. We introduce the Actively Observable Markov Decision Process (AOMDP), where an agent not only selects control actions but also decides whether to measure the latent state. The measurement action reveals the true latent state but may have a negative delayed effect on the environment. We show that this reduced uncertainty enables sample-efficient learning and may increase the value of the optimal policy despite these costs. We formulate an AOMDP as a periodic partially observable MDP and propose an online RL algorithm based on belief states. To approximate the belief states, we further propose a sequential Monte Carlo method to jointly approximate the posterior of unknown static environment parameters and unobserved latent states. We evaluate the proposed algorithm in a digital health application, where the agent decides when to deliver digital interventions and when to assess users' psychological status through surveys.