# Second-order Online Nonconvex Optimization

arXiv: https://arxiv.org/abs/2001.10114 · HTML: https://mlsanity.com/paper/2001.10114/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2020.

## Built on by (most cited first, 9 of 9)

- [Non-Convex Bilevel Optimization with Time-Varying Objective Functions](https://mlsanity.com/paper/2308.03811/) (2023)
- [Online Decision-Focused Learning](https://mlsanity.com/paper/2505.13564/) (2025)
- [Distributionally Time-Varying Online Stochastic Optimization under Polyak-Lojasiewicz Condition with Application in Conditional Value-at-Risk Statistical Learning](https://mlsanity.com/paper/2309.09411/) (2023)
- [A Survey on Distributed Online Optimization and Game](https://mlsanity.com/paper/2205.00473/) (2022)
- [Augmented Lagrangian Methods for Time-varying Constrained Online Convex Optimization](https://mlsanity.com/paper/2205.09571/) (2022)
- [Online Dynamic Submodular Optimization](https://mlsanity.com/paper/2306.10835/) (2023)
- [Online Non-convex Optimization with Long-term Non-convex Constraints](https://mlsanity.com/paper/2311.02426/) (2023)
- [Online Non-Stationary Stochastic Quasar-Convex Optimization](https://mlsanity.com/paper/2407.03601/) (2024)
- [Optimistic Gradient Learning with Hessian Corrections for High-Dimensional Black-Box Optimization](https://mlsanity.com/paper/2502.04829/) (2025)

## Abstract (arXiv)

We present the online Newton's method, a single-step second-order method for online nonconvex optimization. We analyze its performance and obtain a dynamic regret bound that is linear in the cumulative variation between round optima. We show that if the variation between round optima is limited, the method leads to a constant regret bound. In the general case, the online Newton's method outperforms online convex optimization algorithms for convex functions and performs similarly to a specialized algorithm for strongly convex functions. We simulate the performance of the online Newton's method on a nonlinear, nonconvex moving target localization example and find that it outperforms a first-order approach.