# Accelerated Stochastic Optimization Methods under Quasar-convexity

arXiv: https://arxiv.org/abs/2305.04736 · HTML: https://mlsanity.com/paper/2305.04736/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2023.

## Built on by (most cited first, 6 of 6)

- [Aiming towards the minimizers: fast convergence of SGD for overparametrized problems](https://mlsanity.com/paper/2306.02601/) (2023)
- [Nesterov acceleration in benignly non-convex landscapes](https://mlsanity.com/paper/2410.08395/) (2024)
- [Expected Variational Inequalities](https://mlsanity.com/paper/2502.18605/) (2025)
- [Minimisation of Quasar-Convex Functions Using Random Zeroth-Order Oracles](https://mlsanity.com/paper/2505.02281/) (2025)
- [Mean-field underdamped Langevin dynamics and its spacetime discretization](https://mlsanity.com/paper/2312.16360/) (2023)
- [Smooth Quasar-Convex Optimization with Constraints](https://mlsanity.com/paper/2510.01943/) (2025)

## Abstract (arXiv)

Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is quasar-convexity, a non-convex generalization of convexity that subsumes convex functions. Existing algorithms for minimizing quasar-convex functions in the stochastic setting have either high complexity or slow convergence, which prompts us to derive a new class of stochastic methods for optimizing smooth quasar-convex functions. We demonstrate that our algorithms have fast convergence and outperform existing algorithms on several examples, including the classical problem of learning linear dynamical systems. We also present a unified analysis of our newly proposed algorithms and a previously studied deterministic algorithm.