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.

💡 Research Summary

The paper addresses the problem of predictive safety monitoring for autonomous systems that operate under strict sensing and communication constraints. Traditional runtime verification assumes full observability, which is unrealistic for mobile robots or edge infrastructure that must contend with sensor blind spots and limited bandwidth. To overcome this, the authors propose an active perception framework that actively schedules sensor queries so as to reduce uncertainty about whether a safety violation will occur within a future horizon of k steps.

The system is modeled as a labeled hidden Markov model (Labeled‑HMM) whose states are annotated with atomic propositions. Safety specifications expressed in Linear Temporal Logic over finite traces (LTL_f) are compiled into a deterministic finite automaton (DFA) that recognizes violating traces. By taking the product of the HMM and the DFA, a product HMM is obtained whose state space consists of pairs (physical state, DFA state). Failure states correspond to DFA accepting states, and the set F_Z contains all product states that represent a safety violation.

The core predictive quantity is a binary random variable Wₖₜ that equals 1 if a failure state is visited at any time between t and t + k, and 0 otherwise. The conditional Shannon entropy H(Wₖₜ | Y₀:ₜ) (where Y₀:ₜ includes all past observations and chosen perception actions) quantifies the monitor’s uncertainty about future safety. Minimizing this entropy directly encourages the monitor to acquire the most informative observations for the safety prediction task.

An observation‑based policy π maps the observation history to a distribution over perception actions (sensor queries). The policy is parameterized by θ, and the authors derive the gradient of the conditional entropy with respect to θ. A crucial insight (Lemma 1) is that for a fixed observation/action history, the probability P(Wₖₜ = 0 | y) and thus the entropy are independent of the policy parameters; the only dependence on θ comes through the likelihood of the observed history, log P_θ(y). This leads to a clean policy‑gradient expression: ∇θ H(Wₖₜ | Y) = E{y∼π_θ}