# SUCAG: Stochastic Unbiased Curvature-aided Gradient Method for Distributed Optimization

arXiv: https://arxiv.org/abs/1803.08198 · HTML: https://mlsanity.com/paper/1803.08198/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2018.

## Built on by (most cited first, 4 of 4)

- [The Entrapment Problem in Random Walk Decentralized Learning](https://mlsanity.com/paper/2407.20611/) (2024)
- [Distributed saddle point problems for strongly concave-convex functions](https://mlsanity.com/paper/2202.05812/) (2022)
- [Self-Regulating Random Walks for Resilient Decentralized Learning on Graphs](https://mlsanity.com/paper/2407.11762/) (2024)
- [Decentralized Learning via Random Walk with Jumps](https://mlsanity.com/paper/2604.12260/) (2026)

## Abstract (arXiv)

We propose and analyze a new stochastic gradient method, which we call Stochastic Unbiased Curvature-aided Gradient (SUCAG), for finite sum optimization problems. SUCAG constitutes an unbiased total gradient tracking technique that uses Hessian information to accelerate con- vergence. We analyze our method under the general asynchronous model of computation, in which each function is selected infinitely often with possibly unbounded (but sublinear) delay. For strongly convex problems, we establish linear convergence for the SUCAG method. When the initialization point is sufficiently close to the optimal solution, the established convergence rate is only dependent on the condition number of the problem, making it strictly faster than the known rate for the SAGA method. Furthermore, we describe a Markov-driven approach of implementing the SUCAG method in a distributed asynchronous multi-agent setting, via gossiping along a random walk on an undirected communication graph. We show that our analysis applies as long as the graph is connected and, notably, establishes an asymptotic linear convergence rate that is robust to the graph topology. Numerical results demonstrate the merits of our algorithm over existing methods.