Engagement Process: Rethinking the Temporal Interface of Action and Observation

Task completion in digital and physical environments increasingly involves complex temporal interaction, where actions and observations unfold over different time scales rather than align with fixed observation--action steps. To model such interactions, we propose \emph{Engagement Process} (EP), an interaction formalism that inherits the decision-theoretic structure of POMDPs while making time explicit in the action--observation interface. EP represents actions and observations as decoupled event streams along time, rather than updates paired at fixed decision steps. This interface captures single-agent timing issues such as deliberation latency, delayed feedback, and persistent actions, while supporting richer agent-side organization, multi-rate coordination, and compositional interaction among subsystems. Across toy, LLM-agent, and learning experiments, EP exposes temporal behaviors hidden by step-based interfaces and enables policies to adapt under explicit time costs.