Off-Policy Residual Identifiability

Abstract

Behavior laws identify a target policy exactly when no model pair remains ambiguous.

Theorem 1.1 (An empty off-policy residual characterizes identifiability).

$$\mathrm{IdentifiableFromBehaviorLaw}\left(behaviorLaw,targetPolicyLaw\right)\iff \mathrm{offPolicyResidual}\left(behaviorLaw,targetPolicyLaw\right)=EmptySet$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/Experiment/OffPolicyResidualIdentifiability.target_policy_identifiable_iff_off_policy_residual_empty (✓ std3). ∎

Source. Repository-derived.

Commentary.

A behavior law and a target-policy law are readouts on the same model class. Identifiability means that any two models with the same behavior law have the same target-policy law.

The off-policy residual consists exactly of model pairs with equal behavior laws and unequal target-policy laws. Fiber constancy is therefore equivalent to emptiness of this residual, including for an empty model class.

References

• Truth anchor: D5/S3/ConceptDynamics/Experiment/OffPolicyResidualIdentifiability.target_policy_identifiable_iff_off_policy_residual_empty
• Dependency: D5/S3/ConceptDynamics/Experiment/ExperimentValueIsKernelReduction