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.
Scieur et al. REF interpret acceleration as a multi-step integration method from numerical analysis applied to the gradient flow differential equation.
Integration Methods and Accelerated Optimization Algorithms
arXiv: Optimization and Control
Mathematics