Adaptivity via a Parallel Architecture for Stochastic Gradient Methods

Abstract:We develop a parallel framework that assembles static gradient methods to achieve better adaptivity. A static gradient method, denoted by $\mathrm{GD}(x_0,T)$, takes as input an initial point $x_0\in\mathbb{R}^n$ and $T\in \mathbb{R}^+$ specifying the number $\floor{T}$ of iterations. The step size is chosen as $s=S(T)$, where $S(\cdot)$ is a predetermined function of $T$. The method then performs the iterations $ x_{i+1}=x_i-\frac{\eta}{s}\cdot g_i,$ where $g_i$ is a stochastic gradient evaluated at $x_i$, and $\eta$ is a scaling factor. For an integer $p\ge1$, the $p$ processors in the proposed parallel framework search for an appropriate value of $T$ according to a geometric sequence so that the resulting gradient descent satisfies the desired convergence conditions. Each processor executes an infinite sequence of stages indexed by $i=1,2,\ldots$. At stage $i$, processor $j$ is assigned $ T_{j,i}=h(j,i),$ where $h:\mathbb{N}\times\mathbb{N} \rightarrow\mathbb{R}^{+}$ is a prescribed function. Processor $j$ $(j=0,1,\ldots,p-1)$ executes $\mathrm{GD}(x_0, T_{j,i})$ at stage $i$.

Machine Learning (cs.LG); Hardware Architecture (cs.AR); Optimization and Control (math.OC)

arXiv:2607.28902 [cs.LG]

(or arXiv:2607.28902v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.28902 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.