Early stopping behavior of discrete dual algorithms under strong monotonicity

Determine whether discrete dual algorithms, including Dual Fast Extragradient and Dual Optimal Halpern Method, exhibit early stopping or fast approach to terminal accuracy under strongly monotone operators analogous to the Dual-Anchor ODE, and characterize the conditions and rates for such behavior.

Background

The experiments show that dual algorithms tend to approach terminal accuracy earlier than primal methods in strongly monotone settings, and Appendix subsection 8 provides continuous-time analysis demonstrating early stopping for the Dual-Anchor ODE.

The authors state that they expect similar behavior in discrete-time algorithms and explicitly leave the investigation of this phenomenon to future work.