An Accelerated DFO Algorithm for Finite-sum Convex Functions
This addresses the need for faster optimization in machine learning where gradients are inaccessible, offering a solution to instability issues in existing methods.
The paper tackles the problem of designing a stable accelerated derivative-free optimization algorithm for finite-sum convex functions, achieving provable accelerated convergence rates for both smooth convex and strongly-convex cases, with empirical validation on tasks and datasets.
Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given to the concept of acceleration in the DFO literature, existing stochastic algorithms for objective functions with a finite-sum structure have not been shown theoretically to achieve an accelerated rate of convergence. Algorithms that use acceleration in such a setting are prone to instabilities, making it difficult to reach convergence. In this work, we exploit the finite-sum structure of the objective in order to design a variance-reduced DFO algorithm that provably yields acceleration. We prove rates of convergence for both smooth convex and strongly-convex finite-sum objective functions. Finally, we validate our theoretical results empirically on several tasks and datasets.