Related papers: A Split-Client Approach to Second-Order Optimizati…
Federated learning is a machine learning approach where multiple devices collaboratively learn with the help of a parameter server by sharing only their local updates. While gradient-based optimization techniques are widely adopted in this…
We show that, for finite-sum minimization problems, incorporating partial second-order information of the objective function can dramatically improve the robustness to mini-batch size of variance-reduced stochastic gradient methods, making…
This paper studies second-order methods for convex-concave minimax optimization. Monteiro and Svaiter (2012) proposed a method to solve the problem with an optimal iteration complexity of $\mathcal{O}(\epsilon^{-3/2})$ to find an…
We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size.…
We propose a splitting approach to solve the second-order Hamilton--Jacobi equation, reducing it to a heat step and a purely first-order step. The latter is implemented using a gradient value policy iteration algorithm, enabling efficient…
For linear time-invariant (LTI) systems, the design of an optimal controller is a commonly encountered problem in many applications. Among all the optimization approaches available, the linear quadratic regulator (LQR) methodology certainly…
In this article, we consider the problem of unconstrained time-varying convex optimization, where the cost function changes with time. We provide an in-depth technical analysis of the problem and argue why freezing the cost at each time…
Finite-sum optimization problems are ubiquitous in machine learning, and are commonly solved using first-order methods which rely on gradient computations. Recently, there has been growing interest in \emph{second-order} methods, which rely…
The Hessian-vector product has been utilized to find a second-order stationary solution with strong complexity guarantee (e.g., almost linear time complexity in the problem's dimensionality). In this paper, we propose to further reduce the…
Second-order methods are widely adopted to improve the convergence rate of learning algorithms. In federated learning (FL), these methods require the clients to share their local Hessian matrices with the parameter server (PS), which comes…
We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying MDPs controlled by the underlying…
We consider the problem of asynchronous stochastic optimization, where an optimization algorithm makes updates based on stale stochastic gradients of the objective that are subject to an arbitrary (possibly adversarial) sequence of delays.…
Split Learning (SL) is a promising collaborative machine learning approach, enabling resource-constrained devices to train models without sharing raw data, while reducing computational load and preserving privacy simultaneously. However,…
Split learning (SL) enables collaborative training of large language models (LLMs) between resource-constrained edge devices and compute-rich servers by partitioning model computation across the network boundary. However, existing SL…
Stochastic second-order methods achieve fast local convergence in strongly convex optimization by using noisy Hessian estimates to precondition the gradient. However, these methods typically reach superlinear convergence only when the…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
Second-order federated learning (FL) algorithms offer faster convergence than their first-order counterparts by leveraging curvature information. However, they are hindered by high computational and storage costs, particularly for…
Split Federated Learning (SFL) enables collaborative training between resource-constrained edge devices and a compute-rich server. Communication overhead is a central issue in SFL and can be mitigated with auxiliary networks. Yet, the…
Zeroth-order optimization addresses problems where gradient information is inaccessible or impractical to compute. While most existing methods rely on first-order approximations, incorporating second-order (curvature) information can, in…
In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is the classical structural design problems (e.g., compliance minimization and compliant…