Stochastic guarantees under negative comonotonicity

Develop stochastic convergence guarantees for monotone-inclusion methods under negative comonotonicity, extending the deterministic acceleration results available beyond monotonicity.

Background

The theoretical guarantees in the paper rely on monotonicity. The discussion notes that deterministic acceleration is known to extend to negative comonotonicity, a weaker structural condition that includes certain nonmonotone settings. However, the corresponding stochastic theory for the expected squared residual or related criteria is not established, and the paper’s rock-paper-scissors experiment lies outside its formal theory.

References

Although deterministic acceleration extends to negative comonotonicity \citep{lee2021fast,gorbunov2023convergence}, corresponding stochastic guarantees are unknown; the RPS experiment therefore lies outside our theory.

— Accelerated Algorithms for Stochastic Monotone Inclusions with Fixed Queries  (2609.35631 - Lee et al., 28 Sep 2026) in Section 5, Discussion