THEORY-1344: Empowerment is the channel capacity from an agent's next n actions to its sensor n steps later, an open-loop, interventional measure of how many perceptibly different futures the agent can bring about, which counts no control the agent cannot perceive; given side information about the channel's state it is never lower, so it is ordered by what the agent can read, from full state through its own sensor history to none

Source

Klyubin, Polani and Nehaniv (2005), LIT-1965, eq. 3; (2008), LIT-1951, eqs. 1–3. Read in NOTE-1511 and NOTE-1514.

What was actually shown

Definition. ℰ = max_{p(aⁿ)} I(Aⁿ_t; S_{t+n}), with the actions drawn from an independent source so the channel p(s_{t+n} | âⁿ) is the causal effect (2008, pp. 2–3). Open-loop: actions are not chosen on sensor feedback.

Perceived control only. “We define what an agent does solely in terms of what it perceives” (2005, p. 129); control visible to an outside observer but not to the agent’s sensors adds nothing.

Contextual empowerment. ℰ(· | C) = Σ_c p(c) ℰ(· | C = c), the capacity with side information at sender and receiver; never below the context-free value (2008, eq. 3). Re-derived: with A independent of C, I(A; S | C) = I(A; S, C) ≥ I(A; S). The best context is the global state; the agent’s own history “constitutes an upper limit on what the agent can possibly know” (2008, p. 4).

What this does not say

• That a high-empowerment state is reachable or sustainable: in the cart-pole the maxima are not (THEORY-1336).
• That it measures cost, viability or closed-loop control.
• That it is a universal drive in organisms.