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 Gradient Descent




On the Convergence to a Global Solution of Shuffling-Type Gradient Algorithms Lam M. Nguyen

Neural Information Processing Systems

Stochastic gradient descent (SGD) algorithm is the method of choice in many machine learning tasks thanks to its scalability and efficiency in dealing with large-scale problems. In this paper, we focus on the shuffling version of SGD which matches the mainstream practical heuristics. We show the convergence to a global solution of shuffling SGD for a class of non-convex functions under over-parameterized settings.


Adaptive Proximal Gradient Method for Convex Optimization

Neural Information Processing Systems

In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local curvature information of smooth functions.


Resetting the Optimizer in Deep RL: An Empirical Study

Neural Information Processing Systems

We focus on the task of approximating the optimal value function in deep reinforcement learning. This iterative process is comprised of solving a sequence of optimization problems where the loss function changes per iteration. The common approach to solving this sequence of problems is to employ modern variants of the stochastic gradient descent algorithm such as Adam. These optimizers maintain their own internal parameters such as estimates of the first-order and the second-order moments of the gradient, and update them over time. Therefore, information obtained in previous iterations is used to solve the optimization problem in the current iteration. We demonstrate that this can contaminate the moment estimates because the optimization landscape can change arbitrarily from one iteration to the next one. To hedge against this negative effect, a simple idea is to reset the internal parameters of the optimizer when starting a new iteration. We empirically investigate this resetting idea by employing various optimizers in conjunction with the Rainbow algorithm. We demonstrate that this simple modification significantly improves the performance of deep RL on the Atari benchmark.


Trajectory Alignment: Understanding the Edge of Stability Phenomenon via Bifurcation Theory

Neural Information Processing Systems

Cohen et al. (2021) empirically study the evolution of the largest eigenvalue of the loss Hessian, also known as sharpness, along the gradient descent (GD) trajectory and observe the Edge of Stability (EoS) phenomenon.


Tight Risk Bounds for Gradient Descent on Separable Data

Neural Information Processing Systems

Recently, there has been a marked increase in interest regarding the generalization capabilities of unregularized gradient-based learning methods.


Tight Risk Bounds for Gradient Descent on Separable Data

Neural Information Processing Systems

Recently, there has been a marked increase in interest regarding the generalization capabilities of unregularized gradient-based learning methods.



Parameter Symmetry and Noise Equilibrium of Stochastic Gradient Descent Liu Ziyin Massachusetts Institute of Technology, NTT Research

Neural Information Processing Systems

Symmetries are prevalent in deep learning and can significantly influence the learning dynamics of neural networks. In this paper, we examine how exponential symmetries - a broad subclass of continuous symmetries present in the model architecture or loss function - interplay with stochastic gradient descent (SGD). We first prove that gradient noise creates a systematic motion (a "Noether flow") of the parameters θ along the degenerate direction to a unique initialization-independent fixed point θ