We introduce a locally differentially private (LDP) algorithm for online federated learning that employs temporally correlated noise to improve utility while preserving privacy. To address challenges posed by the correlated noise and local updates with streaming non-IID data, we develop a perturbed iterate analysis that controls the impact of the noise on the utility. Moreover, we demonstrate how the drift errors from local updates can be effectively managed for several classes of nonconvex loss functions. Subject to an (ε, δ)-LDP budget, we establish a dynamic regret bound that quantifies the impact of key parameters and the intensity of changes in the dynamic environment on the learning performance. Numerical experiments confirm the efficacy of the proposed algorithm.

We propose a novel algorithm, termed soft quasi-Newton (soft QN), for optimization in the presence of bounded noise. Traditional quasi-Newton algorithms are vulnerable to such noise-induced perturbations. To develop a more robust quasi-Newton method, we replace the secant condition in the matrix optimization problem for the Hessian update with a penalty term in its objective and derive a closed-form update formula. A key feature of our approach is its ability to maintain positive definiteness of the Hessian inverse approximation throughout the iterations. Furthermore, we establish the following properties of soft QN: it recovers the BFGS method under specific limits, it treats positive and negative curvature equally, and it is scale invariant. Collectively, these features enhance the efficacy of soft QN in noisy environments. For strongly convex objective functions and Hessian approximations obtained using soft QN, we develop an algorithm that exhibits linear convergence toward a neighborhood of the optimal solution even when gradient and function evaluations are subject to bounded perturbations. Through numerical experiments, we demonstrate that soft QN consistently outperforms state-of-the-art methods across a range of scenarios.

We propose a novel algorithm for solving the composite Federated Learning (FL) problem. This algorithm manages non-smooth regularization by strategically decoupling the proximal operator and communication, and addresses client drift without any assumptions about data similarity. Moreover, each worker uses local updates to reduce the communication frequency with the server and transmits only a d-dimensional vector per communication round. We prove that our algorithm converges linearly to a neighborhood of the optimal solution and demonstrate the superiority of our algorithm over state-of-the-art methods in numerical experiments.

We introduce a novel differentially private algorithm for online federated learning that employs temporally correlated noise to enhance utility while ensuring privacy of continuously released models. To address challenges posed by DP noise and local updates with streaming non-iid data, we develop a perturbed iterate analysis to control the impact of the DP noise on the utility. Moreover, we demonstrate how the drift errors from local updates can be effectively managed under a quasi-strong convexity condition. Subject to an (, δ) DP budget, we establish a dynamic regret bound over the entire time horizon, quantifying the impact of key parameters and the intensity of changes in dynamic environments. Numerical experiments confirm the efficacy of the proposed algorithm.

This paper proposes a locally differentially private federated learning algorithm for strongly convex but possibly nonsmooth problems that protects the gradients of each worker against an honest but curious server. The proposed algorithm adds artificial noise to the shared information to ensure privacy and dynamically allocates the time-varying noise variance to minimize an upper bound of the optimization error subject to a predefined privacy budget constraint. This allows for an arbitrarily large but finite number of iterations to achieve both privacy protection and utility up to a neighborhood of the optimal solution, removing the need for tuning the number of iterations. Numerical results show the superiority of the proposed algorithm over state-of-the-art methods.

Fast charging of electric vehicles remains a compromise between charging time and degradation penalty. Conventional battery management systems use experience-based charging protocols that are expected to meet vehicle lifetime goals. Novel electrochemical model-based battery fast charging uses a model to observe internal battery states. This enables control of charging rates based on states such as the lithium-plating potential but relies on an accurate model as well as accurate model parameters. However, the impact of battery degradation on the model's accuracy and therefore the fitness of the estimated optimal charging procedure is often not considered. In this work, we therefore investigate electrochemical model-based aging-adaptive fast charging of automotive lithium-ion cells. First, an electrochemical model is identified at the beginning of life for 6 automotive prototype cells and the electrochemically constrained fast-charge is designed. The model parameters are then periodically re-evaluated during a cycling study and the charging procedure is updated to account for cell degradation. The proposed method is compared with two reference protocols to investigate both the effectiveness of selected electrochemical constraints as well as the benefit of aging-adaptive usage. Finally, post-mortem characterization is presented to highlight the benefit of aging-adaptive battery utilization.

Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for manifold optimization in the centralized setting, there are currently very few works addressing the federated setting. In this paper, we consider nonconvex federated learning over a compact smooth submanifold in the setting of heterogeneous client data. We propose an algorithm that leverages stochastic Riemannian gradients and a manifold projection operator to improve computational efficiency, uses local updates to improve communication efficiency, and avoids client drift. Theoretically, we show that our proposed algorithm converges sub-linearly to a neighborhood of a first-order optimal solution by using a novel analysis that jointly exploits the manifold structure and properties of the loss functions. Numerical experiments demonstrate that our algorithm has significantly smaller computational and communication overhead than existing methods.

This paper proposes a prediction-based gradient compression method for distributed learning with event-triggered communication. Our goal is to reduce the amount of information transmitted from the distributed agents to the parameter server by exploiting temporal correlation in the local gradients. We use a linear predictor that combines past gradients to form a prediction of the current gradient, with coefficients that are optimized by solving a least-square problem. In each iteration, every agent transmits the predictor coefficients to the server such that the predicted local gradient can be computed. The difference between the true local gradient and the predicted one, termed the prediction residual, is only transmitted when its norm is above some threshold. When this additional communication step is omitted, the server uses the prediction as the estimated gradient. This proposed design shows notable performance gains compared to existing methods in the literature, achieving convergence with reduced communication costs.

We present an adaptive mechanism for hyperparameter selection in differentially private optimization that addresses the inherent trade-off between utility and privacy. The mechanism eliminates the often unstructured and time-consuming manual effort of selecting hyperpa-rameters and avoids the additional privacy costs that hyperparameter selection otherwise incurs on top of that of the actual algorithm. We instantiate our mechanism for noisy gradient descent on non-convex, convex and strongly convex loss functions, respectively, to derive schedules for the noise variance and step size. These schedules account for the properties of the loss function and adapt to convergence metrics such as the gradient norm. When using these schedules, we show that noisy gradient descent converges at essentially the same rate as its noise-free counterpart. Numerical experiments show that the schedules consistently perform well across a range of datasets without manual tuning.

We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony impacts the convergence rates of the iterates. Our results shorten, streamline and strengthen existing convergence proofs for several asynchronous optimization methods and allow us to establish convergence guarantees for popular algorithms that were thus far lacking a complete theoretical under-standing. Specifically, we use our results to derive better iteration complexity bounds for proximal incremental aggregated gradient methods, to obtain tighter guarantees depending on the average rather than maximum delay for the asynchronous stochastic gradient descent method, to provide less conservative analyses of the speedup conditions for asynchronous block-co ordinate implementations of Krasnosel'skii-Mann iterations, and to quantify the convergence rates for totally asynchronous iterations under various assumptions on communication delays and update rates.