Related papers: ADAHESSIAN: An Adaptive Second Order Optimizer for…

Despite the popularity of the Adam optimizer in practice, most theoretical analyses study Stochastic Gradient Descent (SGD) as a proxy for Adam, and little is known about how the solutions found by Adam differ. In this paper, we show that…

Deep neural networks are usually trained with stochastic gradient descent (SGD), which minimizes objective function using very rough approximations of gradient, only averaging to the real gradient. Standard approaches like momentum or ADAM…

A new, fast second-order method is proposed that achieves the optimal $\mathcal{O}\left(|\log(\epsilon)|\epsilon^{-3/2}\right)$ complexity to obtain first-order $\epsilon$-stationary points. Crucially, this is deduced without assuming the…

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…

We provide new adaptive first-order methods for constrained convex optimization. Our main algorithms AdaACSA and AdaAGD+ are accelerated methods, which are universal in the sense that they achieve nearly-optimal convergence rates for both…

We consider the minimization of a continuous function over the intersection of a regular cone with an affine set via a new class of adaptive first- and second-order optimization methods, building on the Hessian-barrier techniques introduced…

The integration of an ensemble of deep learning models has been extensively explored to enhance defense against adversarial attacks. The diversity among sub-models increases the attack cost required to deceive the majority of the ensemble,…

Adam-type algorithms have become a preferred choice for optimisation in the deep learning setting, however, despite success, their convergence is still not well understood. To this end, we introduce a unified framework for Adam-type…

We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization…

Atomistic foundation models constitute a paradigm shift in computational materials science by providing universal machine-learned interatomic potentials with broad transferability across chemical spaces. Although fine-tuning is essential…

The value of second-order methods lies in the use of curvature information. Yet, this information is costly to extract and once obtained, valuable negative curvature information is often discarded so that the method is globally convergent.…

Differentially private (stochastic) gradient descent is the workhorse of DP private machine learning in both the convex and non-convex settings. Without privacy constraints, second-order methods, like Newton's method, converge faster than…

Deep neural network models, though very powerful and highly successful, are computationally expensive in terms of space and time. Recently, there have been a number of attempts on binarizing the network weights and activations. This greatly…

In this paper we propose several adaptive gradient methods for stochastic optimization. Unlike AdaGrad-type of methods, our algorithms are based on Armijo-type line search and they simultaneously adapt to the unknown Lipschitz constant of…

Despite their popularity in the field of continuous optimisation, second-order quasi-Newton methods are challenging to apply in machine learning, as the Hessian matrix is intractably large. This computational burden is exacerbated by the…

Adaptive optimization methods, which perform local optimization with a metric constructed from the history of iterates, are becoming increasingly popular for training deep neural networks. Examples include AdaGrad, RMSProp, and Adam. We…

Second-order optimization methods offer superior convergence rates but are often bottlenecked by the wall-clock cost of Hessian computation and factorization. In the moderate-dimensional regime where the full Hessian fits in memory,…

Many popular first-order optimization methods (e.g., Momentum, AdaGrad, Adam) accelerate the convergence rate of deep learning models. However, these algorithms require auxiliary parameters, which cost additional memory proportional to the…

Despite their overwhelming capacity to overfit, deep neural networks trained by specific optimization algorithms tend to generalize well to unseen data. Recently, researchers explained it by investigating the implicit regularization effect…

Fine-tuning LLMs is necessary for various dedicated downstream tasks, but classic backpropagation-based fine-tuning methods require substantial GPU memory. To this end, a recent work, MeZO, which relies solely on forward passes to fine-tune…