A Robust Accelerated Optimization Algorithm for Strongly Convex Functions
For practitioners in optimization, this work provides a tunable algorithm that balances speed and noise robustness, though the improvement is incremental over existing methods.
This paper introduces the Robust Momentum Method for smooth strongly convex optimization, which trades off between convergence speed and robustness to gradient noise via a single parameter. The algorithm can be faster than Nesterov's Fast Gradient Method in noise-free settings but more fragile, or reduce to the Gradient Method for high robustness.
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.