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Adaptive gradient methods like Adagrad and its variants are widespread in large-scale optimization. However, their use of diagonal preconditioning matrices limits the ability to capture parameter correlations. Full-matrix adaptive methods,…

Knowledge Tracing (KT) aims to model a student's learning trajectory and predict performance on the next question. A key challenge is how to better represent the relationships among students, questions, and knowledge concepts (KCs).…

In deep learning, different kinds of deep networks typically need different optimizers, which have to be chosen after multiple trials, making the training process inefficient. To relieve this issue and consistently improve the model…

Adaptive gradient methods, such as Adam and LAMB, have demonstrated excellent performance in the training of large language models. Nevertheless, the need for adaptivity requires maintaining second-moment estimates of the per-parameter…

Adaptive gradient optimizers like Adam(W) are the default training algorithms for many deep learning architectures, such as transformers. Their diagonal preconditioner is based on the gradient outer product which is incorporated into the…

Vanilla gradient methods are often highly sensitive to the choice of stepsize, which typically requires manual tuning. Adaptive methods alleviate this issue and have therefore become widely used. Among them, AdaGrad has been particularly…

Reducing the variance of the gradient estimator is known to improve the convergence rate of stochastic gradient-based optimization and sampling algorithms. One way of achieving variance reduction is to design importance sampling strategies.…

Adaptive gradient methods for stochastic optimization adjust the learning rate for each parameter locally. However, there is also a global learning rate which must be tuned in order to get the best performance. In this paper, we present a…

Adaptive gradient methods (AGMs) have become popular in optimizing the nonconvex problems in deep learning area. We revisit AGMs and identify that the adaptive learning rate (A-LR) used by AGMs varies significantly across the dimensions of…

Adaptive Random Testing (ART) has faced criticism, particularly for its computational inefficiency, as highlighted by Arcuri and Briand. Their analysis clarified how ART requires a quadratic number of distance computations as the number of…

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…

Although adaptive optimization algorithms such as Adam show fast convergence in many machine learning tasks, this paper identifies a problem of Adam by analyzing its performance in a simple non-convex synthetic problem, showing that Adam's…

Low-rank adaption (LoRA) is a widely used parameter-efficient finetuning method for LLM that reduces memory requirements. However, current LoRA optimizers lack transformation invariance, meaning the actual updates to the weights depends on…

We provide a new adaptive method for online convex optimization, MetaGrad, that is robust to general convex losses but achieves faster rates for a broad class of special functions, including exp-concave and strongly convex functions, but…

Adaptive gradient-based optimizers such as Adagrad and Adam are crucial for achieving state-of-the-art performance in machine translation and language modeling. However, these methods maintain second-order statistics for each parameter,…

A number of recent adaptive optimizers improve the generalisation performance of Adam by essentially reducing the variance of adaptive stepsizes to get closer to SGD with momentum. Following the above motivation, we suppress the range of…

Variance reduction (VR) methods for finite-sum minimization typically require the knowledge of problem-dependent constants that are often unknown and difficult to estimate. To address this, we use ideas from adaptive gradient methods to…

Adaptive methods like Adam have become the $\textit{de facto}$ standard for large-scale vector and Euclidean optimization due to their coordinate-wise adaptation with a second-order nature. More recently, matrix-based spectral optimizers…

We propose a new, more general approach to the design of stochastic gradient-based optimization methods for machine learning. In this new framework, optimizers assume access to a batch of gradient estimates per iteration, rather than a…

Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD)…