Accelerating Perturbed Stochastic Iterates in Asynchronous Lock-Free Optimization
This provides a theoretical and algorithmic advancement for distributed optimization systems where asynchronous updates are common.
The paper tackles the problem of accelerating asynchronous lock-free optimization for finite-sum objectives, achieving optimal incremental gradient complexity while maintaining the same linear speed-up condition as non-accelerated methods.
We show that stochastic acceleration can be achieved under the perturbed iterate framework (Mania et al., 2017) in asynchronous lock-free optimization, which leads to the optimal incremental gradient complexity for finite-sum objectives. We prove that our new accelerated method requires the same linear speed-up condition as the existing non-accelerated methods. Our core algorithmic discovery is a new accelerated SVRG variant with sparse updates. Empirical results are presented to verify our theoretical findings.