FastAdaBelief: Improving Convergence Rate for Belief-based Adaptive Optimizer by Strong Convexity
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The AdaBelief algorithm demonstrates superior generalization ability to the Adam algorithm by viewing the exponential moving average of observed gradients. AdaBelief is proved to have a data-dependent O(√(T)) regret bound when objective functions are convex, where T is a time horizon. However, it remains to be an open problem on how to exploit strong convexity to further improve the convergence rate of AdaBelief. To tackle this problem, we present a novel optimization algorithm under strong convexity, called FastAdaBelief. We prove that FastAdaBelief attains a data-dependant O(log T) regret bound, which is substantially lower than AdaBelief. In addition, the theoretical analysis is validated by extensive experiments performed on open datasets (i.e., CIFAR-10 and Penn Treebank) for image classification and language modeling.
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