Engagement Process: Modeling Agents and Environments Evolving in Time

In real-world interaction, computation, action execution, and environmental events overlap across different timescales. Synchronous observation–action loops bind computation and interaction to shared decision boundaries, obscuring their distinct temporal structure. We introduce Engagement Process (EP), a new interaction paradigm that explicitly represents agent execution state and models the agent and environment as two processes evolving on a shared physical timeline. This makes computational progress and duration explicit while removing the one-to-one coupling between observations and actions. We formalize EP, analyze the utility of timely observations and access to computational progress, and present basic value-learning and policy-gradient methods. Guided by EP, we augment LLMs with TimeRoPE for temporal awareness and an EP interaction protocol that coordinates agent–environment interaction as both evolve in physical time. Experiments show that EP agents can learn when to compute, wait, and act, enabling more effective interaction under deadlines and asynchronous events.