MCRNR: fast computing of restricted Nash responses by means of sampling
Bibliographic record
Abstract
This paper presents a sample-based algorithm for the computation of restricted Nash strategies in complex extensive form games. Recent work indicates that regret-minimization algorithms using selective sampling, such as Monte-Carlo Counterfactual Regret Minimization (MCCFR), converge faster to Nash equilibrium (NE) strategies than their non-sampled counterparts which perform a full tree traversal. In this paper, we show that MCCFR is also able to establish NE strategies in the complex domain of Poker. Although such strategies are defensive (i.e. safe to play), they are oblivious to opponent mistakes. We can thus achieve better performance by using (an estimation of) opponent strategies. The Restricted Nash Response (RNR) algorithm was proposed to learn robust counter-strategies given such knowledge. It solves a modified game, wherein it is assumed that opponents play according to a fixed strategy with a certain probability, or to a regret-minimizing strategy otherwise. We improve the rate of convergence of the RNR algorithm using sampling. Our new algorithm, MCRNR, samples only relevant parts of the game tree. It is therefore able to converge faster to robust bestresponse strategies than RNR. We evaluate our algorithm on a variety of imperfect information games that are small enough to solve yet large enough to be strategically interesting, as well as a large game, Texas Hold’em Poker.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".