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Distributed optimization is manifesting great potential in multiple fields, e.g., machine learning, control, and resource allocation. Existing decentralized optimization algorithms require sharing explicit state information among the agents, which raises the risk of private information leakage. To ensure privacy security, combining information security mechanisms, such as differential privacy and homomorphic encryption, with traditional decentralized optimization algorithms is a commonly used means. However, this would either sacrifice optimization accuracy or incur heavy computational burden. To overcome these shortcomings, we develop a novel privacy-preserving decentralized optimization algorithm, called PPSD, that combines gradient tracking with a state decomposition mechanism. Specifically, each agent decomposes its state associated with the gradient into two substates. One substate is used for interaction with neighboring agents, and the other substate containing private information acts only on the first substate and thus is entirely agnostic to other agents. For the strongly convex and smooth objective functions, PPSD attains a $R$-linear convergence rate. Moreover, the algorithm can preserve the agents' private information from being leaked to honest-but-curious neighbors. Simulations further confirm the results.

Deep hiding, embedding images with others using deep neural networks, has demonstrated impressive efficacy in increasing the message capacity and robustness of secret sharing. In this paper, we challenge the robustness of existing deep hiding schemes by preventing the recovery of secret images, building on our in-depth study of state-of-the-art deep hiding schemes and their vulnerabilities. Leveraging our analysis, we first propose a simple box-free removal attack on deep hiding that does not require any prior knowledge of the deep hiding schemes. To improve the removal performance on the deep hiding schemes that may be enhanced by adversarial training, we further design a more powerful removal attack, efficient box-free removal attack (EBRA), which employs image inpainting techniques to remove secret images from container images. In addition, to ensure the effectiveness of our attack and preserve the fidelity of the processed container images, we design an erasing phase based on the locality of deep hiding to remove secret information and then make full use of the visual information of container images to repair the erased visual content. Extensive evaluations show our method can completely remove secret images from container images with negligible impact on the quality of container images.

Average consensus is essential for multi-agent systems to achieve specific functions and is widely used in network control, information fusion, etc. In conventional average consensus algorithms, all agents reach an agreement by individual calculations and sharing information with their respective neighbors. Nevertheless, the information interactions that occur in the communication network may make sensitive information be revealed. In this paper, we develop a new privacy-preserving average consensus method for unbalanced digraphs. Specifically, we ensure privacy preservation by carefully embedding randomness in mixing weights to confuse communications and introducing an extra auxiliary parameter to mask the state-updated rule in the initial several iterations. In parallel, we exploit the intrinsic robustness of consensus dynamics to guarantee that the average consensus is precisely achieved. Theoretical results demonstrate that the designed algorithms can converge linearly to the exact average consensus value and can guarantee privacy preservation of agents against both honest-but-curious and eavesdropping attacks. The designed algorithms are fundamentally different compared to differential privacy based algorithms that enable privacy preservation via sacrificing consensus performance. Finally, numerical experiments validate the correctness of the theoretical findings.

We deal with a general distributed constrained online learning problem with privacy over time-varying networks, where a class of nondecomposable objectives are considered. Under this setting, each node only controls a part of the global decision, and the goal of all nodes is to collaboratively minimize the global cost over a time horizon $T$ while guarantees the security of the transmitted information. For such problems, we first design a novel generic algorithm framework, named as DPSDA, of differentially private distributed online learning using the Laplace mechanism and the stochastic variants of dual averaging method. Note that in the dual updates, all nodes of DPSDA employ the noise-corrupted gradients for more generality. Then, we propose two algorithms, named as DPSDA-C and DPSDA-PS, under this framework. In DPSDA-C, the nodes implement a circulation-based communication in the primal updates so as to alleviate the disagreements over time-varying undirected networks. In addition, for the extension to time-varying directed ones, the nodes implement the broadcast-based push-sum dynamics in DPSDA-PS, which can achieve average consensus over arbitrary directed networks. Theoretical results show that both algorithms attain an expected regret upper bound in $\mathcal{O}( \sqrt{T} )$ when the objective function is convex, which matches the best utility achievable by cutting-edge algorithms. Finally, numerical experiment results on both synthetic and real-world datasets verify the effectiveness of our algorithms., Comment: 16 pages, 6 figures

This paper investigates two accelerated primal-dual mirror dynamical approaches for smooth and nonsmooth convex optimization problems with affine and closed, convex set constraints. In the smooth case, an accelerated primal-dual mirror dynamical approach (APDMD) based on accelerated mirror descent and primal-dual framework is proposed and accelerated convergence properties of primal-dual gap, feasibility measure and the objective function value along with trajectories of APDMD are derived by the Lyapunov analysis method. Then, we extend APDMD into two distributed dynamical approaches to deal with two types of distributed smooth optimization problems, i.e., distributed constrained consensus problem (DCCP) and distributed extended monotropic optimization (DEMO) with accelerated convergence guarantees. Moreover, in the nonsmooth case, we propose a smoothing accelerated primal-dual mirror dynamical approach (SAPDMD) with the help of smoothing approximation technique and the above APDMD. We further also prove that primal-dual gap, objective function value and feasibility measure of SAPDMD have the same accelerated convergence properties as APDMD by choosing the appropriate smooth approximation parameters. Later, we propose two smoothing accelerated distributed dynamical approaches to deal with nonsmooth DEMO and DCCP to obtain accelerated and efficient solutions. Finally, numerical experiments are given to demonstrate the effectiveness of the proposed accelerated mirror dynamical approaches.