2024-06-30-asi24a.md

title	section	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Universally Instance-Optimal Mechanisms for Private Statistical Estimation	Original Papers	We consider the problem of instance-optimal statistical estimation under the constraint of differential privacy where mechanisms must adapt to the difficulty of the input dataset. We prove a new instance specific lower bound using a new divergence and show it characterizes the local minimax optimal rates for private statistical estimation. We propose two new mechanisms that are universally instance-optimal for general estimation problems up to logarithmic factors. Our first mechanism, the total variation mechanism, builds on the exponential mechanism with stable approximations of the total variation distance, and is universally instance-optimal in the high privacy regime $\epsilon \leq 1/\sqrt{n}$. Our second mechanism, the T-mechanism, is based on the T-estimator framework (Birg{é}, 2006) using the clipped log likelihood ratio as a stable test: it attains instance-optimal rates for any $\epsilon \leq 1$ up to logarithmic factors. Finally, we study the implications of our results to robust statistical estimation, and show that our algorithms are universally optimal for this problem, characterizing the optimal minimax rates for robust statistical estimation.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	asi24a	0	Universally Instance-Optimal Mechanisms for Private Statistical Estimation	221	259	221-259	221	false	Asi, Hilal and Duchi, John C. and Haque, Saminul and Li, Zewei and Ruan, Feng	given family Hilal Asi given family John C. Duchi given family Saminul Haque given family Zewei Li given family Feng Ruan	2024-06-30		Proceedings of Thirty Seventh Conference on Learning Theory	247	inproceedings	date-parts 2024 6 30	https://proceedings.mlr.press/v247/asi24a/asi24a.pdf