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On the SDEs and Scaling Rules for Adaptive Gradient Algorithms
Sadhika Malladi · Kaifeng Lyu · Abhishek Panigrahi · Sanjeev Arora

Sat Jul 23 11:50 AM -- 12:00 PM (PDT) @

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. Analogous study of adaptive gradient methods, such as RMSprop and Adam, has been challenging because there were no rigorously proven SDE approximations for these methods. This paper derives the SDE approximations for RMSprop and Adam, giving theoretical guarantees of their correctness as well as experimental validation of their applicability to common large-scaling vision and language settings. A key practical result is the derivation of a square root scaling rule to adjust the optimization hyperparameters of RMSprop and Adam when changing batch size, and its empirical validation in deep learning settings.

Author Information

Sadhika Malladi (Princeton University)
Kaifeng Lyu (Princeton University)
Abhishek Panigrahi (Princeton University)
Sanjeev Arora (Princeton University)

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