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Approximating Stochastic Gradient Descent (SGD) as a Stochastic Differential Equation (SDE) has allowed researchers to enjoy the benefits of studying a continuous optimization trajectory while carefully preserving the stochasticity of SGD.…

The choice of batch sizes in minibatch stochastic gradient optimizers is critical in large-scale model training for both optimization and generalization performance. Although large-batch training is arguably the dominant training paradigm…

Autonomous robot exploration (ARE) is the process of a robot autonomously navigating and mapping an unknown environment. Recent Reinforcement Learning (RL)-based approaches typically formulate ARE as a sequential decision-making problem…

Adversarial training has become one of the most effective methods for improving robustness of neural networks. However, it often suffers from poor generalization on both clean and perturbed data. In this paper, we propose a new algorithm,…

We consider the problem of estimating the learning rate in adaptive methods, such as AdaGrad and Adam. We propose Prodigy, an algorithm that provably estimates the distance to the solution $D$, which is needed to set the learning rate…

We study the implicit bias of AdaGrad on separable linear classification problems. We show that AdaGrad converges to a direction that can be characterized as the solution of a quadratic optimization problem with the same feasible set as the…

A new paradigm to estimate the gradient of a black-box scalar function is introduced, considering it as a member of a set of admissible gradients that are computed using existing function samples. Results on gradient estimate accuracy,…

Despite superior training outcomes, adaptive optimization methods such as Adam, Adagrad or RMSprop have been found to generalize poorly compared to Stochastic gradient descent (SGD). These methods tend to perform well in the initial portion…

Stochastic methods with coordinate-wise adaptive stepsize (such as RMSprop and Adam) have been widely used in training deep neural networks. Despite their fast convergence, they can generalize worse than stochastic gradient descent. In this…

Many popular adaptive gradient methods such as Adam and RMSProp rely on an exponential moving average (EMA) to normalize their stepsizes. While the EMA makes these methods highly responsive to new gradient information, recent research has…

In this paper, we propose a new, simplified high probability analysis of AdaGrad for smooth, non-convex problems. More specifically, we focus on a particular accelerated gradient (AGD) template (Lan, 2020), through which we recover the…

Adaptive gradient optimizers (AdaGrad), which dynamically adjust the learning rate based on iterative gradients, have emerged as powerful tools in deep learning. These adaptive methods have significantly succeeded in various deep learning…

Adaptive optimization algorithms -- such as Adagrad, Adam, and their variants -- have found widespread use in machine learning, signal processing and many other settings. Several methods in this family are not rotationally equivariant,…

Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second…

Adaptive gradient methods, such as AdaGrad, have become fundamental tools in deep learning. Despite their widespread use, the asymptotic convergence of AdaGrad remains poorly understood in non-convex scenarios. In this work, we present the…

Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving…

Training deep learning models on limited data while maintaining generalization is one of the fundamental challenges in molecular property prediction. One effective solution is transferring knowledge extracted from abundant datasets to those…

We are faced with convex quadratic programing in many contexts related to control theory, economy and robotics. In this paper, we introduce a new active set algorithm for solving such problems and analyze its possible advantages. The…

Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic…

Simulating differential equations on classical computers becomes an intractable problem if the grid size is extremely large. Quantum computers are believed to achieve a possibly exponential speedup in the matrix operation. In this paper, we…