TY - GEN
T1 - Schrödinger Mechanisms
T2 - 2023 IEEE International Symposium on Information Theory, ISIT 2023
AU - Alghamdi, Wael
AU - Asoodeh, Shahab
AU - Calmon, Flavio P.
AU - Felipe Gomez, Juan
AU - Kosut, Oliver
AU - Sankar, Lalitha
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - We consider the problem of designing optimal differential privacy mechanisms with a favorable privacy-utility tradeoff in the limit of a large number n of compositions (i.e., sequential queries). Here, utility is measured by the average distance between the mechanism's input and output, evaluated by a cost function c. We show that if n is sufficiently large and the sensitivities of all queries are small, then the optimal additive noise mechanism has probability density function fully characterized by the ground-state eigenfunction of the Schrödinger operator with potential c. This leads to a family of optimal mechanisms, dubbed the Schrödinger mechanisms, depending on the choice of the cost function. Instantiating this result, we demonstrate that for c(x) = x2 the Gaussian mechanism is optimal, and for c(x) = |x|, the optimal mechanism is obtained by the Airy function, thereby leading to the Airy mechanism.
AB - We consider the problem of designing optimal differential privacy mechanisms with a favorable privacy-utility tradeoff in the limit of a large number n of compositions (i.e., sequential queries). Here, utility is measured by the average distance between the mechanism's input and output, evaluated by a cost function c. We show that if n is sufficiently large and the sensitivities of all queries are small, then the optimal additive noise mechanism has probability density function fully characterized by the ground-state eigenfunction of the Schrödinger operator with potential c. This leads to a family of optimal mechanisms, dubbed the Schrödinger mechanisms, depending on the choice of the cost function. Instantiating this result, we demonstrate that for c(x) = x2 the Gaussian mechanism is optimal, and for c(x) = |x|, the optimal mechanism is obtained by the Airy function, thereby leading to the Airy mechanism.
UR - http://www.scopus.com/inward/record.url?scp=85171482036&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85171482036&partnerID=8YFLogxK
U2 - 10.1109/ISIT54713.2023.10206616
DO - 10.1109/ISIT54713.2023.10206616
M3 - Conference contribution
AN - SCOPUS:85171482036
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2201
EP - 2206
BT - 2023 IEEE International Symposium on Information Theory, ISIT 2023
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 25 June 2023 through 30 June 2023
ER -