Information-Driven Active Perception for k-step Predictive Safety Monitoring

This work studies the synthesis of active perception policies for predictive safety monitoring in partially observable stochastic systems. Operating under strict sensing and communication budgets, the proposed monitor dynamically schedules sensor queries to maximize information gain about the safety of future states. The underlying stochastic dynamics are captured by a labeled hidden Markov model (HMM), with safety requirements defined by a deterministic finite automaton (DFA). To enable active information acquisition, we introduce minimizing k-step Shannon conditional entropy of the safety of future states as a planning objective, under the constraint of a limited sensor query budget. Using observable operators, we derive an efficient algorithm to compute the k-step conditional entropy and analyze key properties of the conditional entropy gradient with respect to policy parameters. We validate the effectiveness of the method for predictive safety monitoring through a dynamic congestion game example.