Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimization
Optimizing functionals over the space of probability measures is now ubiquitous in machine learning. A widely used approach is to perform the optimization directly over the Wasserstein space, but many objective functionals of practical interest are non-convex along Wasserstein geodesics, making the analysis of standard first-order methods challenging. In this work, we study a class of objectives over the Wasserstein space that admit a difference-of-convex (DC) decomposition and we lift the classical convex-concave procedure (CCCP) to this setting. Under smoothness and strong convexity assumptions on the convex components of the decomposition, we prove almost stationarity along the iterate...
| Authors | Clément Bonet, Pierre-Cyril Aubin-Frankowski, Youssef Mroueh |
|---|---|
| Primary category | cs.LG |
| Published | 26 June 2026 |
| Last updated at source | 26 June 2026 |
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