Adaptive Proximal Gradient Method for Convex Optimization
This work provides incremental improvements to first-order optimization algorithms for convex optimization problems.
The paper tackles the problem of making gradient descent and proximal gradient methods adaptive without added computational cost by using local curvature information, resulting in methods that allow for larger stepsizes than previous suggestions.
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. We propose adaptive versions of GD and ProxGD that are based on observed gradient differences and, thus, have no added computational costs. Moreover, we prove convergence of our methods assuming only local Lipschitzness of the gradient. In addition, the proposed versions allow for even larger stepsizes than those initially suggested in [MM20].