Correct-by-Construction Reinforcement Learning of Cardiac Pacemakers from Duration Calculus Requirements

Summary

Dole et al. formalize dual-chamber pacemaker requirements in Duration Calculus, compile bounded-time requirements into executable stopwatch automata, and use the resulting safety-game region as a shield for reinforcement learning. The case study is an adaptive DDD pacemaker for heart-block rhythms: the learner can tune pacing timing for patient comfort, while the shield rejects actions that would violate formal pacemaker safety requirements.

This is a partial ingest based on the full extracted text, emphasizing the DC-to-automata construction, shield-RL interface, and pacemaker evidence.

Key Claims

• Natural-language pacemaker requirements from the Boston Scientific specification can be formalized in Duration Calculus, which can express accumulated duration constraints that ordinary timed automata may not capture directly.
• Because pacemaker-heart interaction is cyclic and each relevant timing obligation is bounded, the requirements fall into a bounded-time fragment of DC.
• Bounded DC formulae can be compiled into acyclic timed or stopwatch automata, making satisfiability, reachability, and safety-game computations decidable for the compiled artifacts.
• The computed safety region gives a maximally permissive action set for the pacemaker and can be used as an RL shield.
• Shielding allows an adaptive pacemaker learner to explore a more permissive design space while still blocking actions that violate non-permissive timing requirements.

Methods / Formalism

• Duration Calculus is used as an interval logic over timed traces, with interval length constraints, accumulated-duration constraints, counting constraints, and the chop operator for sequential composition.
• A DC formula under bounded semantics is evaluated over a finite timed trace sigma=(s_0,tau_0)...(s_n,tau_n) and an interval [b,e].
• For a bounded DC formula D, the construction builds automata for subformulae over bounded intervals. A duration constraint such as “the accumulated duration of proposition P satisfies a comparison with c” uses a stopwatch variable that runs while P is true and is checked at the accepting transition.
• The compiled automata are acyclic. Reachability and satisfiability can be encoded as quantifier-free linear real arithmetic constraints and are decidable for this bounded construction.
• When signals are partitioned into controllable pacemaker actions and uncontrollable environment/heart signals, the automata induce a two-player safety game. A controllable-predecessor computation gives the safe region and maximally permissive pacemaker actions.
• The RL agent is given the safety region, and candidate actions outside the permissive set are blocked. See Duration Calculus Pacemaker Shields for the formal routing.

Evidence / Experiments

• The authors implement DC-to-stopwatch-automata construction by extending DCVALID, which uses MONA and provides validation/visualization for DC formulae.
• They write the DDD pacemaker requirements in DC and validate compiled automata on two scenarios: Ventricular Safety Pacing and Upper Rate Hold-off.
• For adaptive pacing, they relax one timing choice so a ventricular pace may occur anywhere inside the AV interval, then shield an RL agent against actions that would violate the remaining pacemaker requirements.
• In a simple heart model with 3:2 heart block and stochastic acceleration/deceleration, the learner adapts pacing to match intrinsic rhythm while the shield blocks unsafe attempts, including actions during blanking periods and actions that would violate upper-rate limits.
• The reported experiments are proof-of-concept and simulation-based; the paper does not claim clinical deployment readiness.

Connections

• Extends Shielding with a real-time medical-device specification pipeline: natural-language requirements → DC formulae → stopwatch automata → safety game → RL shield.
• Adds Duration Calculus to the Temporal Logic and Formal Methods clusters as a duration-sensitive specification language.
• Connects to Safe Reinforcement Learning because safety is enforced by an external shield rather than learned from reward penalties.
• Relates to Runtime Verification because the compiled executable specifications support simulation, monitoring, validation, verification, and synthesis.
• Touches Control Theory through pacemaker-heart closed-loop timing and the design of a controller constrained by hard real-time requirements.

Open Questions

• How scalable is the bounded DC-to-stopwatch-automata pipeline when more pacemaker features and sensors are included?
• How permissive is the shield after multiple requirements are implicitly conjoined, and when does shield conservatism prevent useful adaptation?
• Can the same pattern support other safety-critical medical or cyber-physical controllers with patient-specific adaptation?
• How should clinical validation handle the gap between a simple heart model and real physiological variability?

Citation

Dole, Kalyani, Ashutosh Gupta, John Komp, Shankaranarayanan Krishna, and Ashutosh Trivedi. 2023. “Correct-by-Construction Reinforcement Learning of Cardiac Pacemakers from Duration Calculus Requirements.” AAAI-23.