Papers › Stochastic Composition Optimization of Functions without Lipschitz Continuous Gradient
Stochastic Composition Optimization of Functions without Lipschitz Continuous Gradient
Yin Liu, Sam Davanloo Tajbakhsh
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
In this paper, we study stochastic optimization of two-level composition of functions without Lipschitz continuous gradient. The smoothness property is generalized by the notion of relative smoothness which provokes the Bregman gradient method. We propose three Stochastic Composition Bregman Gradient algorithms for the three possible relatively smooth compositional scenarios and provide their sample complexities to achieve an ϵ-approximate stationary point. For the smooth of relatively smooth composition, the first algorithm requires O(ϵ⁻²) calls to the stochastic oracles of the inner function value and gradient as well as the outer function gradient. When both functions are relatively smooth, the second algorithm requires O(ϵ⁻³) calls to the inner function value stochastic oracle and O(ϵ⁻²) calls to the inner and outer functions gradients stochastic oracles. We further improve the second algorithm by variance reduction for the setting where just the inner function is smooth. The resulting algorithm requires O(ϵ^(-5/2)) calls to the inner function value stochastic oracle, O(ϵ^(-3/2)) calls to the inner function gradient and O(ϵ⁻²) calls to the outer function gradient stochastic oracles. Finally, we numerically evaluate the performance of these three algorithms over two different examples.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections