Nesterov acceleration in optimizing over probability measures
Optimization over probability measures has become an increasingly important paradigm in modern machine learning, scientific computing, and uncertainty quantification. Motivated by Nesterov's accelerated gradient method in Euclidean space, we develop Heavy-ball and Nesterov acceleration methods over the probability measure space $\mathcal{P}_2$ and establish non-asymptotic convergence guarantees that match their Euclidean counterparts. In particular, we derive convergence rates with respect to both the number of iterations and the number of particles used to represent the underlying probability distributions. Extending accelerated optimization from Euclidean space to probability measures i...
| Authors | Jiaqi Tang, Qin Li, Wilfrid Gangbo |
|---|---|
| Primary category | math.OC |
| Published | 25 July 2026 |
| Last updated at source | 25 July 2026 |
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