Dynamic Memory Based Adaptive Optimization

Define an optimizer as having memory $k$ if it stores $k$ dynamically changing vectors in the parameter space. Classical SGD has memory $0$, momentum SGD optimizer has $1$ and Adam optimizer has $2$. We address the following questions: How can optimizers make use of more memory units? What information should be stored in them? How to use them for the learning steps? As an approach to the last question, we introduce a general method called "Retrospective Learning Law Correction" or shortly RLLC. This method is designed to calculate a dynamically varying linear combination (called learning law) of memory units, which themselves may evolve arbitrarily. We demonstrate RLLC on optimizers whose memory units have linear update rules and small memory ($\leq 4$ memory units). Our experiments show that in a variety of standard problems, these optimizers outperform the above mentioned three classical optimizers. We conclude that RLLC is a promising framework for boosting the performance of known optimizers by adding more memory units and by making them more adaptive.