  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.
