Changing a deployment policy can invalidate a world model's uncertainty while leaving the physical transition mechanism and predictor unchanged.
One-step prediction and policy-controlled dynamics
For one-step prediction, if source and target laws share the conditional mechanism $P(Y|X)=Q(Y|X)$, then the intervention is identified by the pre-outcome change of measure $w(X)=dQ_X/dP_X$. For policy-controlled dynamics this ratio factors into state-occupancy and action-propensity terms.
Weighted conformal calibration transports marginal coverage to the target law; with an estimated ratio $\hat w$, $P_Q\{Y \in C_{\hat w}(X)\} \ge 1-α-TV(Q,\hat Q) \ge 1-α-E_P|w-\hat w|$.
Population log-loss regret and ratio error
Population log-loss regret for a source-versus-target domain classifier bounds the same ratio error. If $h$ is its clipped target posterior, $ρ$ is the target-domain prior, and $Δ(h)$ is population log-loss regret, then $E_P|w-\hat w_h| \le (1/(ργ))\sqrt{Δ(h)/2}$. An exact cancellation improves the dependence from a generic odds-map bound of order $γ^{-2}$ to $(ργ)^{-1}$.
Experiments
- Our experiments use a released DINO-feature world model and physical Franka trajectories.
- Under the strongest controlled state-action shift, ordinary 90% conformal sets cover 55.0%, whereas oracle and learned-ratio calibration cover 91.0% and 90.9%.
- The learned surrogate remains within 0.9% total variation of the target law.
Calibration and deployment law
Calibration is relative to the deployment law: the model can remain fixed while calibration follows the intervention.
We machine-check in Lean 4 the finite-support algebraic and causal identities used in the classifier-regret argument, including its coverage-composition step.