Faster Stochastic Optimization with Arbitrary Delays via Asynchronous Mini-Batching
This work addresses optimization in distributed systems with delayed gradients, offering improved convergence guarantees for machine learning practitioners dealing with asynchronous updates.
The paper tackles the problem of asynchronous stochastic optimization with arbitrary delays by developing a method that transforms any standard stochastic first-order algorithm into an asynchronous one, achieving convergence rates that depend on quantile delays, such as O(τ_q/qT + σ/√(qT)) for non-convex problems, improving over prior results based on average delays.
We consider the problem of asynchronous stochastic optimization, where an optimization algorithm makes updates based on stale stochastic gradients of the objective that are subject to an arbitrary (possibly adversarial) sequence of delays. We present a procedure which, for any given $q \in (0,1]$, transforms any standard stochastic first-order method to an asynchronous method with convergence guarantee depending on the $q$-quantile delay of the sequence. This approach leads to convergence rates of the form $O(τ_q/qT+σ/\sqrt{qT})$ for non-convex and $O(τ_q^2/(q T)^2+σ/\sqrt{qT})$ for convex smooth problems, where $τ_q$ is the $q$-quantile delay, generalizing and improving on existing results that depend on the average delay. We further show a method that automatically adapts to all quantiles simultaneously, without any prior knowledge of the delays, achieving convergence rates of the form $O(\inf_{q} τ_q/qT+σ/\sqrt{qT})$ for non-convex and $O(\inf_{q} τ_q^2/(q T)^2+σ/\sqrt{qT})$ for convex smooth problems. Our technique is based on asynchronous mini-batching with a careful batch-size selection and filtering of stale gradients.