We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the differential equation considered here is the basic gradient flow and we show that multi-step schemes allow integration of this differential equation using larger step sizes, thus intuitively explaining acceleration results.
From a different perspective, Scieur et al. REF use multi-step methods from numerical analysis to discretize the gradient flow equation.
Integration Methods and Accelerated Optimization Algorithms
arXiv: Optimization and Control
Mathematics