Double Robustness Is Not a Privacy Certificate: Sensitivity Spillover in Private Policy Selection

TMLR Paper8879 Authors

Abstract: Doubly robust (DR) scores are a standard method in causal inference and policy evaluation: they make policy-value estimates insensitive to global nuisance estimation error. Differential privacy (DP), however, requires a different form of robustness: the released output must be stable under the replacement of any one individual. This paper shows that these two notions of robustness can differ significantly in private policy selection. We study the problem of selecting a high-value policy from a finite public library using learned DR utilities and the exponential mechanism. Although fixed or frozen-nuisance utilities have constant sensitivity, we identify a sensitivity spillover effect: replacing one record in the nuisance-training block can change the learned score map, and that changed score map is then evaluated on all records in the scoring block. We prove a separation showing that double robustness, vanishing nuisance error, and even zero DR population bias can coexist with order-$n$ realized utility sensitivity, invalidating the usual fixed-utility privacy calibration. We then give a sufficient certification route based on deterministic replace-one prediction stability of the nuisance learners, which yields a valid pure-DP exponential mechanism and a regret bound separating library approximation, concentration, DR product remainder, and certified privacy cost. Semi-synthetic experiments confirm that spillover can be large even when DR statistical diagnostics look benign, and that stability-oriented regularization controls the privacy-relevant movement. The investigations in this paper highlight an important future need that the private causal policy selection method requires both orthogonality for statistical robustness and algorithmic stability for individual replacement robustness.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Juba_Ziani1

Submission Number: 8879