# CFR without Unbiasedness: Deterministic Guarantees for Persistent Public-Chance Schedules

arXiv: https://arxiv.org/abs/2608.14761 · HTML: https://mlsanity.com/paper/2608.14761/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 14 Aug 2026.

## Builds on (most cited first, 15 of 15)

- [Online Learning under Delayed Feedback](https://mlsanity.com/paper/1306.0686/) (2013)
- [Solving Large Imperfect Information Games Using CFR+](https://mlsanity.com/paper/1407.5042/) (2014)
- [Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games using Baselines](https://mlsanity.com/paper/1809.03057/) (2018)
- [Revisiting CFR+ and Alternating Updates](https://mlsanity.com/paper/1810.11542/) (2018)
- [GraB: Finding Provably Better Data Permutations than Random Reshuffling](https://mlsanity.com/paper/2205.10733/) (2022)
- [Stochastic Regret Minimization in Extensive-Form Games](https://mlsanity.com/paper/2002.08493/) (2020)
- [Characterizing & Finding Good Data Orderings for Fast Convergence of Sequential Gradient Methods](https://mlsanity.com/paper/2202.01838/) (2022)
- [Solving Games with Functional Regret Estimation](https://mlsanity.com/paper/1411.7974/) (2014)
- [Online Learning with Local Permutations and Delayed Feedback](https://mlsanity.com/paper/1703.04274/) (2017)
- [Sampling without Replacement Leads to Faster Rates in Finite-Sum Minimax Optimization](https://mlsanity.com/paper/2206.02953/) (2022)
- [Lazy-CFR: fast and near optimal regret minimization for extensive games with imperfect information](https://mlsanity.com/paper/1810.04433/) (2018)
- [Correlated Chance Sampling for Monte Carlo Counterfactual Regret Minimization](https://mlsanity.com/paper/2607.27035/) (2026)
- [Stochastic Extragradient with Random Reshuffling: Improved Convergence for Variational Inequalities](https://mlsanity.com/paper/2403.07148/) (2024)
- [Small Nash Equilibrium Certificates in Very Large Games](https://mlsanity.com/paper/2006.16387/) (2020)
- [Bounds for Approximate Regret-Matching Algorithms](https://mlsanity.com/paper/1910.01706/) (2019)

## Abstract (arXiv)

At a finite public-chance cut, counterfactual regret minimization (CFR) must choose how many outcomes to evaluate before each regret update. Exact evaluation processes the full cut at one strategy profile; persistent partial evaluation processes a fixed without-replacement order across evolving profiles. The latter covers every outcome once per epoch, yet its feedback is generally conditionally biased because earlier batches influence the profiles seen by later batches. We establish a deterministic target-transfer theorem for uniform, nonnested additive public cuts. The theorem bounds full-cut exploitability by regret on the delivered feedback and a public-debit term that couples prefix coverage discrepancy with motion along the realized strategy path. Consecutively balanced schedules consequently converge for additive signed regret matching (RM) and RM+ under predetermined averaging weights, while a fixed RM+ construction proves that the discrepancy--path product is necessary in general. A component-resolved form of the theorem converts an execution trace into a numerical exploitability certificate. On two released heads-up no-limit hold'em turn endgames, persistent order improves substantially over fresh reshuffling despite identical epochwise coverage, and partial coverage wins every registered shallow matched-budget comparison. A depth study locates a crossover between 32 and 64 full-cut outcome budgets, after which complete coverage dominates. These results characterize public-chance width and order as learning variables and provide a deterministic basis for designing and auditing persistent CFR schedules.