Writing study: Deep (Predictive) Discounted Counterfactual Regret Minimization
← AAAI 2026 oral writing corpus
Hang Xu, Kai Li, Haobo Fu, Qiang Fu, Junliang Xing, Jian Cheng · Official AAAI 2026 oral record
Figure, table and section ledger
Editorial contribution type: Training, objectives & optimization (primary).
Layout extraction, not a required paper template. Counts are distinct caption labels; a multi-panel figure counts once. Section spans are estimated from heading positions, including floats and whitespace. Method and limitations.
- Canonical PDF
- 9 physical pages
- Before references / appendix
- ≈ 7.09 page-equivalents
- Main figures / tables
- 2 / 0
- Attached appendix figures / tables
- 0 / 0
- Attached appendix span
- No boundary detected; not assumed zero
Extraction notes: No attached appendix boundary detected. Zero means no recognized caption, not independently verified absence.
Source-bound correction: Checked 2026-10-25. Physical p.7 raster shows two genuine figure labels and no table. A left-column line starting Figure 2. Final average rewards is prose, while the actual Figure 2 caption is in the right column. Exclude both same-page label candidates and restore only the source-verified right-column caption. Unnumbered main headings are source-bound. No attached appendix is present in the publisher PDF.
Section-by-section lengths and source pages
The title/abstract/front matter precede the first numbered heading. A span ends at the next detected top-level heading, not at the last sentence; end-page whitespace is included. References and statements are listed separately. These are not measurements of text-only or artwork area.
| Top-level heading | Starts on PDF page | Estimated span | Share of entire PDF |
|---|---|---|---|
| Introduction | 1 | ≈ 1.11 pp. | 12.33% |
| Preliminaries | 2 | ≈ 1.5 pp. | 16.67% |
| Related Work | 3 | ≈ 0.44 pp. | 4.89% |
| Deep (Predictive) Discounted CFR | 4 | ≈ 2.23 pp. | 24.78% |
| Experiments | 6 | ≈ 1.24 pp. | 13.78% |
| Conclusions and Future Research | 7 | ≈ 0.22 pp. | 2.44% |
| Acknowledgments | 8 | ≈ 0.05 pp. | 0.56% |
| References | 8 | ≈ 1.91 pp. | 21.22% |
All detected figure and table locations
Main text
Attached appendix
No recognized caption labels.
Argument and organization
- Introduction; Preliminaries; Related Work
Limits the problem to model-free two-player zero-sum imperfect-information games and establishes the tabular, sampling and neural CFR ingredients needed to explain the approximation difficulty.
- Deep (Predictive) Discounted CFR
Uses expected-target statements to motivate bootstrapped advantages, then adds discounting, clipping and a baseline value network; separate algorithm boxes describe training and sampled traversal.
- Experiments; Conclusions and Future Research
Separates exploitability on eight tractable games from average reward against five rule-based agents in a larger poker game, with main-text pointers to ablations and implementation detail.
Problem, claim and contribution
The introduction defines model-free access explicitly: the algorithm samples episodes rather than using a perfect simulator. It then isolates why existing neural CFR fits do not directly reproduce advanced tabular updates. This prevents the reader from treating comparisons against simulator-dependent methods as matched information-access comparisons.
Abstract and Introduction, physical pp.1-2; Monte Carlo CFR and DeepCFR, p.3 · Main paper
Argument and section order
Definitions of information sets, reach probabilities and exploitability precede the new update. Theorems 1-2 explain a change in the expected supervised target; the implementation discussion then explains bootstrapping, prediction and variance reduction. Training and traversal are split into two algorithms so persistent buffers and within-episode recursion are not mixed.
Preliminaries, pp.2-3; Theorems 1-2 and Algorithms 1-2, pp.4-5; variance reduction, p.6 · Main paper
Figures, captions and visual explanation
Algorithm 1 is a full-width display with explicit input, initialization, buffer clearing, player/iteration loops and final strategy output. Figure 1 uses a shared method legend across eight game panels, sampled episodes on the horizontal axis and log exploitability vertically. Figure 2 changes the vertical quantity to average reward and must be read as a different evaluation, not another exploitability plot.
Algorithm 1, physical p.4; Figures 1-2, p.7; rendered pages inspected · Main paper
Tables, comparisons and evidence
The small-game protocol gives four seeds and identifies shaded bands as 95% confidence intervals. It specifies similar three-layer networks and normalized utilities across methods. The larger game instead uses 20,000 matches against five rule-based styles and a larger sampling/network budget, so reward gains establish that opponent-set result rather than an equilibrium certificate.
Experimental setup and Convergence to Equilibrium, p.6; Head-to-Head Evaluation, p.7 · Main paper
Appendix and reproducibility
The paper routes proofs, game definitions, configurations, opponent construction and ablations to distinct appendices A-E. This is an inspectable claim-to-detail plan, but the actual appendices are outside the proceedings PDF used here. The main-text ablation conclusion cannot substitute for reading its omitted plots and controls.
Proof pointer, p.4; games/configuration pointers, p.6; opponent/ablation pointers, p.7; extended-version link, p.1 · Main paper
Clarity and writing conventions
The method keeps cumulative and instantaneous advantage networks distinct and names which variant needs the extra predictor. Conclusions retain the two-player zero-sum setting and identify improved next-advantage prediction as future work. Use similarly bounded language: the displayed theoretical statements concern expected targets, not a blanket convergence guarantee for a finite neural implementation.
Algorithms 1-2 and Theorems 1-2, pp.4-5; Approximating Advanced CFR Variants, pp.5-6; Conclusion, p.7 · Main paper
What to reuse—and what not to infer
Transferable lesson: For a theory-informed learning algorithm, connect each formal statement to the changed training target, then show the executable update order. Separate sample-efficiency curves, wall-clock claims and opponent-specific outcomes, each with its own denominator and uncertainty description.
Boundary: The proof appendices were not inspected, and empirical convergence plots are not a proof of neural convergence. Sampled episodes are not elapsed time. Stronger rewards against five rule-based poker opponents do not establish exploitability or superiority against arbitrary opponents, and the larger-game setup differs from the small-game setup.
Apply this lesson using the argument and evidence worksheet.
Inspection record and sources
- Checked
- 2026-10-25
- Reading status
- Writing-focused manuscript scan + selected visuals inspected
- Main text
- Writing-focused text scan of physical PDF pp.1-7, including the model-free game setting, formal preliminaries, target-estimation arguments, algorithms, convergence plots, head-to-head evaluation and appendix routing. Physical pp.4 and 7 were rendered and visually inspected; the acknowledgments/reference boundary on p.8 was checked. Theorems were read for their role and stated scope, not independently proved.
- Appendix / supplement
- The main paper points to Appendix A for proofs, B for games, C for configurations, D for rule-based opponents and E for ablations. These appendices are not attached to the inspected nine-page proceedings PDF. The first-page extended-version link was recorded but that version and its appendices were not retrieved or inspected in this study.
- Visually inspected PDF pages
- 4, 7
This is a writing-focused scan of the manuscript and the stated supplementary scope: framing, organization, visual explanation, evidence presentation and wording. It is not a line-by-line proof audit, reproduction of results or exhaustive scientific review.