Most existing decentralized learning methods with differential privacy (DP) guarantee rely on constant gradient clipping bounds and fixed-level DP Gaussian noises for each node throughout the training process, leading to a significant accuracy degradation compared to non-private counterparts. In this paper, we propose a new Dynamic Differentially Private Decentralized learning approach (termed Dyn-D^2P) tailored for general time-varying directed networks. Leveraging the Gaussian DP (GDP) framework for privacy accounting, Dyn-D^2P dynamically adjusts gradient clipping bounds and noise levels based on gradient convergence. This proposed dynamic noise strategy enables us to enhance model accuracy while preserving the total privacy budget. Extensive experiments on benchmark datasets demonstrate the superiority of Dyn-D^2P over its counterparts employing fixed-level noises, especially under strong privacy guarantees. Furthermore, we provide a provable utility bound for Dyn-D^2P that establishes an explicit dependency on network-related parameters, with a scaling factor of 1/sqrt{n} in terms of the number of nodes n up to a bias error term induced by gradient clipping. To our knowledge, this is the first model utility analysis for differentially private decentralized non-convex optimization with dynamic gradient clipping bounds and noise levels.

Collaborative learning enhances the performance and adaptability of multi-robot systems in complex tasks but faces significant challenges due to high communication overhead and data heterogeneity inherent in multi-robot tasks. To this end, we propose CoCoL, a Communication efficient decentralized Collaborative Learning method tailored for multi-robot systems with heterogeneous local datasets. Leveraging a mirror descent framework, CoCoL achieves remarkable communication efficiency with approximate Newton-type updates by capturing the similarity between objective functions of robots, and reduces computational costs through inexact sub-problem solutions. Furthermore, the integration of a gradient tracking scheme ensures its robustness against data heterogeneity. Experimental results on three representative multi-robot collaborative learning tasks show that the proposed CoCoL can significantly reduce both the number of communication rounds and total bandwidth consumption while maintaining state-of-the-art accuracy. These benefits are particularly evident in challenging scenarios involving non-IID (non-independent and identically distributed) data distribution, streaming data, and time-varying network topologies.

This paper considers solving a class of nonconvex-strongly-convex distributed stochastic bilevel optimization (DSBO) problems with personalized inner-level objectives. Most existing algorithms require computational loops for hypergradient estimation, leading to computational inefficiency. Moreover, the impact of data heterogeneity on convergence in bilevel problems is not explicitly characterized yet. To address these issues, we propose LoPA, a loopless personalized distributed algorithm that leverages a tracking mechanism for iterative approximation of inner-level solutions and Hessian-inverse matrices without relying on extra computation loops. Our theoretical analysis explicitly characterizes the heterogeneity across nodes (denoted by $b$), and establishes a sublinear rate of $\mathcal{O}( {\frac{1}{{{{\left( {1 - \rho } \right)}}K}}\!+ \!\frac{{(\frac{b}{\sqrt{m}})^{\frac{2}{3}} }}{{\left( {1 - \rho } \right)^{\frac{2}{3}} K^{\frac{2}{3}} }} \!+ \!\frac{1}{\sqrt{ K }}( {\sigma _{\operatorname{p} }} + \frac{1}{\sqrt{m}}{\sigma _{\operatorname{c} }} ) } )$ without the boundedness of local hypergradients, where ${\sigma _{\operatorname{p} }}$ and ${\sigma _{\operatorname{c} }}$ represent the gradient sampling variances associated with the inner- and outer-level variables, respectively. We also integrate LoPA with a gradient tracking scheme to eliminate the impact of data heterogeneity, yielding an improved rate of ${{\mathcal{O}}}(\frac{{1}}{{ (1-\rho)^2K }} \!+\! \frac{1}{{\sqrt{K}}}( \sigma_{\rm{p}} \!+\! \frac{1}{\sqrt{m}}\sigma_{\rm{c}} ) )$. The computational complexity of LoPA is of ${{\mathcal{O}}}({\epsilon^{-2}})$ to an $\epsilon$-stationary point, matching the communication complexity due to the loopless structure, which outperforms existing counterparts for DSBO. Numerical experiments validate the effectiveness of the proposed algorithm.

In this paper, we show that applying adaptive methods directly to distributed minimax problems can result in non-convergence due to inconsistency in locally computed adaptive stepsizes. To address this challenge, we propose D-AdaST, a Distributed Adaptive minimax method with Stepsize Tracking. The key strategy is to employ an adaptive stepsize tracking protocol involving the transmission of two extra (scalar) variables. This protocol ensures the consistency among stepsizes of nodes, eliminating the steady-state error due to the lack of coordination of stepsizes among nodes that commonly exists in vanilla distributed adaptive methods, and thus guarantees exact convergence. For nonconvex-strongly-concave distributed minimax problems, we characterize the specific transient times that ensure time-scale separation of stepsizes and quasi-independence of networks, leading to a near-optimal convergence rate of $\tilde{\mathcal{O}} \left( \epsilon ^{-\left( 4+\delta \right)} \right)$ for any small $\delta > 0$, matching that of the centralized counterpart. To our best knowledge, D-AdaST is the *first* distributed adaptive method achieving near-optimal convergence without knowing any problem-dependent parameters for nonconvex minimax problems. Extensive experiments are conducted to validate our theoretical results.

We develop a general framework unifying several gradient-based stochastic optimization methods for empirical risk minimization problems both in centralized and distributed scenarios. The framework hinges on the introduction of an augmented graph consisting of nodes modeling the samples and edges modeling both the inter-device communication and intra-device stochastic gradient computation. By designing properly the topology of the augmented graph, we are able to recover as special cases the renowned Local-SGD and DSGD algorithms, and provide a unified perspective for variance-reduction (VR) and gradient-tracking (GT) methods such as SAGA, Local-SVRG and GT-SAGA. We also provide a unified convergence analysis for smooth and (strongly) convex objectives relying on a proper structured Lyapunov function, and the obtained rate can recover the best known results for many existing algorithms. The rate results further reveal that VR and GT methods can effectively eliminate data heterogeneity within and across devices, respectively, enabling the exact convergence of the algorithm to the optimal solution. Numerical experiments confirm the findings in this paper.