2018
DOI: 10.1109/tcns.2016.2614100
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Differentially Private Distributed Convex Optimization via Functional Perturbation

Abstract: We study a class of distributed convex constrained optimization problems where a group of agents aim to minimize the sum of individual objective functions while each desires that any information about its objective function is kept private. We prove the impossibility of achieving differential privacy using strategies based on perturbing the inter-agent messages with noise when the underlying noise-free dynamics are asymptotically stable. This justifies our algorithmic solution based on the perturbation of indi… Show more

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Cited by 138 publications
(106 citation statements)
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“…To secure the data and operate on ciphertext space, a homomorphic encryption method is discussed in [20]. Privacy preservation in Machine Learning (ML) is addressed using a differential privacy paradigm, which deals with adding a statistically-designed noise to the exchanged functions or states to protect the sensitive data [21]. Alternatively, in [22], a cryptographic image classification algorithm is proposed on a multi-layer extreme learning system that is capable of specifically classifying encrypted images without decryption.…”
Section: Related Workmentioning
confidence: 99%
“…To secure the data and operate on ciphertext space, a homomorphic encryption method is discussed in [20]. Privacy preservation in Machine Learning (ML) is addressed using a differential privacy paradigm, which deals with adding a statistically-designed noise to the exchanged functions or states to protect the sensitive data [21]. Alternatively, in [22], a cryptographic image classification algorithm is proposed on a multi-layer extreme learning system that is capable of specifically classifying encrypted images without decryption.…”
Section: Related Workmentioning
confidence: 99%
“…To solve the optimization problem (20), f αk i (x) was set to f αk i (x) = 1 2x Tx + (b k i ) Tx for our approach in the simulations, where b k i was set to b k i = 1 k+1 c i + d i with c i ∈ R n and d i ∈ R n being constants private to agent i. Fig.…”
Section: A Evaluation Of Our Approachmentioning
confidence: 99%
“…One widely used approach to enabling privacypreservation in decentralized optimization is differential privacy [18]- [21] which protects sensitive information by adding carefully-designed noise to exchanged states or objective functions. However, adding noise also compromises the accuracy of optimization results and causes a fundamental trade-off between privacy and accuracy [18]- [20]. In fact, approaches based on differential privacy may fail to converge to the accurate optimization result even without noise perturbation [20].…”
Section: Introductionmentioning
confidence: 99%
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“…While secure multi-party computation also deals with scenarios where no trust exists among agents, the maximum number of agents that can collude (without the privacy of others being breached) is bounded, whereas using differential privacy provides immunity against arbitrary collusions [Kairouz et al, 2015, Pettai andLaud, 2015]. As a result, differential privacy has been adopted by recent works in a number of areas pertaining to networked systems, such as control [Huang et al, 2012, estimation [Ny and Pappas, 2014], and optimization [Han et al, 2014, Huang et al, 2015, Nozari et al, 2017. Of relevance to our present work, the paper [Huang et al, 2012] studies the average consensus problem with differentially privacy guarantees and proposes an adjacency-based distributed algorithm with decaying Laplace noise and mean-square convergence.…”
Section: Introductionmentioning
confidence: 99%