Analogous benefits of alternation for regret-matching dynamics

Establish whether regret-matching-type dynamics, including counterfactual regret minimization with regret matching+ updates, enjoy benefits from alternating updates analogous to those proved for mirror-descent and gradient-descent-ascent dynamics.

Background

The paper contrasts established results for alternating mirror descent and alternating gradient descent-ascent with the comparatively limited theory for alternating regret-matching procedures. Although alternation is empirically important in counterfactual regret minimization, the authors state that an analogous theoretical benefit for regret-matching-type dynamics has not been established.

References

All concern mirror-descent or gradient-descent-ascent updates; whether regret-matching-type dynamics enjoy analogous benefits remains open.

— Why Alternation Speeds Up Counterfactual Regret Minimization?  (2610.21970 - Li et al., 15 Oct 2026) in Section 2, Related Work

Whether alternating + enjoys an $O(1/T)$ guarantee of the kind proved for the algorithm class of \citet{tao2026optimalalternatingregretonline} is open; our exponents are local measurements, not rates.

— Why Alternation Speeds Up Counterfactual Regret Minimization?  (2610.21970 - Li et al., 15 Oct 2026) in Section 6, “Experiments,” subsection “Horizon dependence”

Establishing the required growth rate of $S_t$ is itself open, and the program is a paper-sized undertaking that still would not touch the os-prm-side difficulty.

— Why Alternation Speeds Up Counterfactual Regret Minimization?  (2610.21970 - Li et al., 15 Oct 2026) in Appendix, Section “Registration,” subsection “Three proof routes, honestly accounted”