Asynchronous stochastic gradient descent (ASGD) is a standard way to exploit heterogeneous compute resources in distributed learning: instead of forcing fast workers to wait for slow ones, the server updates the model whenever a gradient arrives. Vanilla ASGD applies each arriving gradient with the same weight. When local data distributions are heterogeneous, this becomes problematic: faster workers contribute more updates, and we show theoretically that the method is biased toward a frequency-weighted average of the local objectives rather than the desired global objective. Existing remedies typically move away from the simple ASGD template by introducing gathering phases, buffering, or extra memory. We show that this is unnecessary. Keeping the standard ASGD mechanism, we recover the correct objective by rescaling worker-specific stepsizes in proportion to their computation times, so that each worker contributes the same aggregate learning rate over a cycle. In the non-convex setting, under smoothness and bounded heterogeneity assumptions, we prove that the resulting method, Rescaled ASGD, converges to stationary points of the correct global objective in the fixed-computation model. Its time complexity matches the known lower bound in the leading term, while the effects of staleness and data heterogeneity appear only in lower-order terms. Experiments confirm that the method converges to the correct objective and is competitive with state-of-the-art baselines.

The existing analysis of asynchronous stochastic gradient descent (SGD) degrades dramatically when any delay is large, giving the impression that performance depends primarily on the delay. On the contrary, we prove much better guarantees for the same asynchronous SGD algorithm regardless of the delays in the gradients, depending instead just on the number of parallel devices used to implement the algorithm. Our guarantees are strictly better than the existing analyses, and we also argue that asynchronous SGD outperforms synchronous minibatch SGD in the settings we consider. For our analysis, we introduce a novel recursion based on "virtual iterates" and delay-adaptive stepsizes, which allow us to derive state-of-theart guarantees for both convex and non-convex objectives.

We consider nonconvex stochastic optimization problems in the asynchronous centralized distributed setup where the communication times from workers to a server can not be ignored, and the computation and communication times are potentially different for all workers.

We study the asynchronous stochastic gradient descent algorithm, for distributed training over $n$ workers that might be heterogeneous. In this algorithm, workers compute stochastic gradients in parallel at their own pace and return them to the server without any synchronization.Existing convergence rates of this algorithm for non-convex smooth objectives depend on the maximum delay $\tau_{\max}$ and reach an $\epsilon$-stationary point after $O\!\left(\sigma^2\epsilon^{-2}+ \tau_{\max}\epsilon^{-1}\right)$ iterations, where $\sigma$ is the variance of stochastic gradients.

We consider nonconvex stochastic optimization problems in the asynchronous centralized distributed setup where the communication times from workers to a server can not be ignored, and the computation and communication times are potentially different for all workers.

"virtual iterates" and delay-adaptive stepsizes, which allow us to derive state-of-the-art guarantees for both convex and non-convex objectives.