2022/12/07 by Baranwal, Mayank, Budhraja, Param, Raj, Vishal +1
#Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2212.03765
Gradient-based first-order convex optimization algorithms find widespread applicability in a variety of domains, including machine learning tasks. Motivated by the recent advances in fixed-time stability theory of continuous-time dynamical systems, we introduce a generalized framework for designing accelerated optimization algorithms with strongest convergence guarantees that further extend to a subclass of non-convex functions. In particular, we introduce the GenFlow algorithm and its momentum variant that provably converge to the optimal solution of objective functions satisfying the Polyak-Łojasiewicz (PL) inequality in a fixed time. Moreover, for functions that admit non-degenerate saddle-points, we show that for the proposed GenFlow algorithm, the time required to evade these saddle-points is uniformly bounded for all initial conditions. Finally, for strongly convex-strongly concave minimax problems whose optimal solution is a saddle point, a similar scheme is shown to arrive at the optimal solution again in a fixed time. The superior convergence properties of our algorithm are validated experimentally on a variety of benchmark datasets.