Stochastic Gradient Descent (SGD) has played a central role in machine learning. However, it requires a carefully hand-picked stepsize for fast convergence, which is notoriously tedious and time-consuming to tune. Over the last several years, a plethora of adaptive gradient-based algorithms have emerged to ameliorate this problem. In this paper, we propose new surrogate losses to cast the problem of learning the optimal stepsizes for the stochastic optimization of a non-convex smooth objective function onto an online convex optimization problem. This allows the use of no-regret online algorithms to compute optimal stepsizes on the fly. In turn, this results in a SGD algorithm with self-tuned stepsizes that guarantees convergence rates that are automatically adaptive to the level of noise.
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Stochastic modified equations for the asynchronous stochastic gradient descent
We propose stochastic modified equations (SMEs) for modelling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more information about the ASGD dynamics and elucidates the relationship between different types of stochastic gradient algorithms. We show the convergence of ASGD to the SME in the continuous time limit, as well as the SME’s precise prediction to the trajectories of ASGD with various forcing terms. As an application, we propose an optimal mini-batching strategy for ASGD via solving the optimal control problem of the associated SME.
more » « less- NSF-PAR ID:
- 10124648
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Information and Inference: A Journal of the IMA
- ISSN:
- 2049-8764
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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