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DTEND:20230316T120000Z
UID:e5e9b0445e29a02820fcd0c6fd513412-432
DTSTAMP:19700101T120010Z
DESCRIPTION:Private Convex Optimization via Exponential Mechanism
URL;VALUE=URI:https://www.csa.iisc.ac.in/newweb/event/432/private-convex-optimization-via-exponential-mechanism/
SUMMARY:We study differentially private optimization of (non-smooth) convex functions F(x)=E_i[f_i(x)]. The classic exponential mechanism minimizes F(x) by sampling from pi(x) ~ exp(-kF(x)), but achieves a suboptimal privacy vs utility tradeoff. We show that modifying the exponential mechanism by adding an ell_2^2 regularizer to F(x) and sampling from pi(x) ~ exp(-k(F(x)+mu ||x||_2^2/2)) recovers both optimal empirical risk and population loss under (eps,delta)-DP. We also give an algorithm to efficiently sample from the exponential mechanism using optimal number of oracle queries to f_i(x).
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We prove that the regularized exponential mechanism satisfies Gaussian Differential Privacy; our privacy bound is optimal (with tight constants), as it includes the analysis of Gaussian mechanism as a special case. The privacy proof uses isoperimetric inequality for strongly log-concave measures.
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Joint work with Yin Tat Lee and Daogao Liu. The link to the paper is at https://arxiv.org/pdf/2203.00263.pdf.
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Speaker Website: https://www.microsoft.com/en-us/research/people/sigopi/
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Microsoft teams link:
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https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZGE3NDg5NzktMWQ0Zi00MzFmLTg5OTgtMTMyYWM4MWQyYjI2%40thread.v2/0?context=%7b%22Tid%22%3a%226f15cd97-f6a7-41e3-b2c5-ad4193976476%22%2c%22Oid%22%3a%227c84465e-c38b-4d7a-9a9d-ff0dfa3638b3%22%7d
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We are grateful to the Kirani family for generously supporting the theory seminar series
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Hosts: Rahul Madhavan, Rameesh Paul, Aditya Subramanian and Aditya Abhay Lonkar
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