Finding a stationary point of a stochastic convex problem
We consider the problem of finding stationary points for stochastic convex optimization problems. Rather than surrogates to stationarity, such as a proximity-to-stationarity guarantee or small gradient of the Moreau envelope, we ask for a stronger notion: that the subdifferential of the objective actually contains a small element. This criterion is non-trivial, because subdifferentials of convex functions fail to converge uniformly, even in arbitrarily small neighborhoods of the optimum. Our convergence guarantees rely on dimension theory to decompose the graph of the subdifferential of a convex function, showing how stochastic sampling preserves "pieces" of these graphs, and allowing eff...
| Authors | Felipe Areces, John Duchi, Malo Sommers |
|---|---|
| Primary category | stat.ML |
| Published | 8 July 2026 |
| Last updated at source | 27 July 2026 |
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