A critical factor for expanding the adoption of networked solutions is ensuring local data privacy of in-network agents implementing a distributed algorithm. In this paper, we consider privacy preservation in the distributed optimization problem in the sense that local cost parameters should not be revealed. Current approaches to privacy preservation normally propose methods that sacrifice exact convergence or increase communication overhead. We propose PrivOpt, an intrinsically private distributed optimization algorithm that converges exponentially fast without any convergence error or using extra communication channels. We show that when the number of the parameters of the local cost is greater than the dimension of the decision variable of the problem, no malicious agent, even if it has access to all transmitted-in and -out messages in the network, can obtain local cost parameters of other agents. As an application study, we show how our proposed PrivOpt algorithm can be used to solve an optimal resource allocation problem with the guarantees that the local cost parameters of all the agents stay private.
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This content will become publicly available on March 1, 2025
Optimal querying for communication-efficient ADMM using Gaussian process regression
In distributed optimization schemes consisting of a group of agents connected to a central coordinator, the optimization algorithm often involves the agents solving private local sub-problems and exchanging data frequently with the coordinator to solve the global distributed problem. In those cases, the query-response mechanism usually causes excessive communication costs to the system, necessitating communication reduction in scenarios where communication is costly. Integrating Gaussian processes (GP) as a learning component to the Alternating Direction Method of Multipliers (ADMM) has proven effective in learning each agent’s local proximal operator to reduce the required communication exchange. A key element for integrating GP into the ADMM algorithm is the querying mechanism upon which the coordinator decides when communication with an agent is required. In this paper, we formulate a general querying decision framework as an optimization problem that balances reducing the communication cost and decreasing the prediction error. Under this framework, we propose a joint query strategy that takes into account the joint statistics of the query and ADMM variables and the total communication cost of all agents in the presence of uncertainty caused by the GP regression. In addition, we derive three different decision mechanisms that simplify the general framework by making the communication decision for each agent individually. We integrate multiple measures to quantify the trade-off between the communication cost reduction and the optimization solution’s accuracy/optimality. The proposed methods can achieve significant communication reduction and good optimization solution accuracy for distributed optimization, as demonstrated by extensive simulations of a distributed sharing problem.
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- Award ID(s):
- 2238296
- NSF-PAR ID:
- 10514299
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Franklin Open
- Volume:
- 6
- Issue:
- C
- ISSN:
- 2773-1863
- Page Range / eLocation ID:
- 100080
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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