Empowerment is an intrinsic motivation signal that measures the agent's ability to influence its future sensory states — defined as the channel capacity (maximum mutual information) between the agent's actions and its future states: $I^*(A_t; S_{t+k})$.

Empowerment Formulation

• Mutual Information: $mathfrak{E}(s) = max_{p(a|s)} I(A_t; S_{t+k} | S_t = s)$ — maximize over all action distributions.
• Channel Capacity: Empowerment is the information-theoretic channel capacity of the action → future state channel.
• High Empowerment: States where the agent's actions have the most diverse consequences — the agent has maximum control.
• Low Empowerment: States where actions have little effect — the agent is "stuck" or "powerless."

Why It Matters

• Task-Independent: Empowerment is a universal intrinsic motivation — no task-specific reward needed.
• Meaningful Behavior: Empowerment-seeking agents naturally move to states of high influence — homeostasis, tool use, position maintenance.
• Safety: Empowerment can keep agents in controllable, recoverable states — useful for safe RL.

Empowerment is seeking maximum influence — moving to states where the agent's actions have the greatest impact on its future.