10.4 Three targets for every DIAL-X method

The word target has three meanings that should remain separate. For a base system \(X\), define

Operational target \(Y_X\).

The deployable object: a policy, adapter composite, causal model, workflow, preference representation, recommendation, database instance, or reasoning trace.

Structural target \(\mathbb S_X\).

The declaration that types the operational object: its objects, arrows, factorizations, equations, support restrictions, observers, and allowed interventions.

Epistemic target \(\mathcal C_X\).

The certificate required to call the result admitted: held-out return, interventional prediction, descent, proof, safety constraint, simulator test, or a calibrated decision to abstain.

A scalar objective may help construct \(Y_X\), but it does not by itself specify \(\mathbb S_X\) or \(\mathcal C_X\). This is why the DIAL-2 experiments reported policy regret and structural-action accuracy separately. A method could lower regret by refitting every regime while changing the declaration when no structural change was warranted.