# A Robust Accelerated Optimization Algorithm for Strongly Convex Functions

arXiv: https://arxiv.org/abs/1710.04753 · HTML: https://mlsanity.com/paper/1710.04753/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2017.

## Built on by (most cited first, 14 of 14)

- [On the fast convergence of minibatch heavy ball momentum](https://mlsanity.com/paper/2206.07553/) (2022)
- [DiSK: Differentially Private Optimizer with Simplified Kalman Filter for Noise Reduction](https://mlsanity.com/paper/2410.03883/) (2024)
- [MomentumSMoE: Integrating Momentum into Sparse Mixture of Experts](https://mlsanity.com/paper/2410.14574/) (2024)
- [On the Convergence of mSGD and AdaGrad for Stochastic Optimization](https://mlsanity.com/paper/2201.11204/) (2022)
- [Analytical Study of Momentum-Based Acceleration Methods in Paradigmatic High-Dimensional Non-Convex Problems](https://mlsanity.com/paper/2102.11755/) (2021)
- [Tuning Stochastic Gradient Algorithms for Statistical Inference via Large-Sample Asymptotics](https://mlsanity.com/paper/2207.12395/) (2022)
- [Convex Programs and Lyapunov Functions for Reinforcement Learning: A Unified Perspective on the Analysis of Value-Based Methods](https://mlsanity.com/paper/2202.06922/) (2022)
- [Transient growth of accelerated optimization algorithms](https://mlsanity.com/paper/2103.08017/) (2021)
- [Increasing Batch Size Improves Convergence of Stochastic Gradient Descent with Momentum](https://mlsanity.com/paper/2501.08883/) (2025)
- [Tradeoffs between convergence rate and noise amplification for momentum-based accelerated optimization algorithms](https://mlsanity.com/paper/2209.11920/) (2022)
- [Accelerated Gradient Methods with Biased Gradient Estimates: Risk Sensitivity, High-Probability Guarantees, and Large Deviation Bounds](https://mlsanity.com/paper/2509.13628/) (2025)
- [Accelerating Perturbed Stochastic Iterates in Asynchronous Lock-Free Optimization](https://mlsanity.com/paper/2109.15292/) (2021)
- [A Selective Review on Statistical Methods for Massive Data Computation: Distributed Computing, Subsampling, and Minibatch Techniques](https://mlsanity.com/paper/2403.11163/) (2024)
- [From Inexact Gradients to Byzantine Robustness: Acceleration and Optimization under Similarity](https://mlsanity.com/paper/2602.03329/) (2026)

## Abstract (arXiv)

This work proposes an accelerated first-order algorithm we call the Robust Momentum Method for optimizing smooth strongly convex functions. The algorithm has a single scalar parameter that can be tuned to trade off robustness to gradient noise versus worst-case convergence rate. At one extreme, the algorithm is faster than Nesterov's Fast Gradient Method by a constant factor but more fragile to noise. At the other extreme, the algorithm reduces to the Gradient Method and is very robust to noise. The algorithm design technique is inspired by methods from classical control theory and the resulting algorithm has a simple analytical form. Algorithm performance is verified on a series of numerical simulations in both noise-free and relative gradient noise cases.