CoGameReg: Cooperative-Game-Based Collaborative Semi-Supervised Regression for Seismic Reservoir Property Prediction

arXiv:2610.12884 · cs.LG · Submitted 2026-10-09 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Today's paper: "CoGameReg: Cooperative-Game-Based Collaborative Semi-Supervised Regression for Seismic Reservoir Property Prediction".

Jane: The gist Accurate estimation of reservoir properties from seismic data remains challenging when well-log labels are sparse but three-dimensional seismic observations are abundant,

Tom: First, who's behind it and why it matters.

Title and authors: Tom: We're talking about the title and authors of CoGameReg today. The authors are Zhiyu Guo, Jiwei Jia, Lei Li, and they are from Jilin University and also have affiliations with AI for Science and Engineering Center in Shenzhen <ref:2610.12884#pg1>.

Jane: It's interesting that the title emphasizes the cooperative game-based approach; it tells us right away this isn't just a simple ensemble method, but something structured around how different models interact <ref:2610.12884#pg2>.

Lu: The authors are focused on moving beyond just individual model performance and into designing the structure of how those models contribute to the final output, which is what they call contribution-aware weighting <ref:2610.12884#pg1>.

Meng: So they're trying to figure out which parts of the input data matter most for each model, and then using that knowledge to create better labels for the unlabeled data <ref:2610.12884#pg3>.

Lalam: The authors introduce the Tri-Game mechanism, which combines a rank–MSE performance game with a pairwise consistency game to estimate these nonnegative regressor weights from labeled training data <ref:2610.12884#pg1>.

The paper's summary: Tom: So the summary boils down to this framework that treats different regressors as players and estimates their contribution-aware weights once from the labeled training data <ref:2610.12884#pg1>. These weights are then reused for final prediction fusion, which is a big deal because it means you don't have to recalculate everything every time you make a new prediction <ref:2610.12884#pg1>.

Jane: Basically, they create shared pseudolabels by using these contribution-weighted predictions from the heterogeneous regressors, and they do this through an iterative process where models get better as they get more labels <ref:2610.12884#pg3>.

Lu: What's important is that the Tri-Game mechanism gives them a way to balance two things: how well the individual models perform, which involves rank and MSE utilities, and how much their predictions agree with each other, which is the consistency component <ref:2610.12884#pg1>.

Meng: They use this initial weighting vector w(zero) derived from these components to generate a pseudo-label y-bar u at each iteration t, and then they use a local error-reduction principle to decide which samples to accept <ref:2610.12884#pg3>.

Lalam: The iterative steps involve initializing an ensemble with weights on the probability simplex, applying the Tri-Game Shapley valuation mechanism to get w(zero), and then in each step, generating a pseudo-label y-bar u from the fixed weighted ensemble <ref:2610.12884#pg1>.

The paper's improvements: Tom: One of the main improvements they highlight is that they explicitly make each regressor’s influence visible in the learning targets generated for unlabeled seismic samples under sparse well control <ref:2610.12884#pg1>. This is something I like, making the mechanics transparent.

Jane: They also focus on local candidate screening, which they say is important alongside this weighting because pseudo-label quality depends not only on individual accuracy but also on how the different regressors interact <ref:2610.12884#pg3>.

Lu: The improvement lies in using a common local error-reduction criterion on each regressor’s current augmented training set to decide which samples to accept, which they call Candidate admission <ref:2610.12884#pg3>. This is a refinement over just accepting or rejecting based on one model's error <ref:2610.12884#pg3>.

Meng: From an engineering standpoint, having that local criterion helps manage the quality of the pseudo-label pool P(t) by selecting only the best candidates to retrain each regressor independently <ref:2610.12884#pg3>. That sounds like a manageable way to handle model drift or noise.

Lalam: The final improvement they show is that each regressor maintains its own augmented training set DL union P(t), and it retrains independently, which is what allows the system to evolve the label pool iteratively <ref:2610.12884#pg3>.

Conclusion: Tom: So to wrap up, CoGameReg uses a fixed initial weight vector w(zero) derived from a Tri-Game mechanism—combining rank–MSE performance and pairwise consistency—to construct shared pseudolabels for reservoir property prediction <ref:2610.12884#pg1>.

Jane: The results show that on ten public regression datasets, CoGameReg achieved the lowest average RMSE of zero point one zero nine eight across thirty dataset-ratio settings, and it even yielded the joint-lowest or lowest RMSE in eighteen of them <ref:2610.12884#pg2>.

Lu: The ablation study confirms that having contribution-aware weighting within the pseudo-labeling loop is what leads to the best average performance across all their variants, and it outperforms both SSR-Decoupled Shapley Weighting and purely supervised Shapley Weighted Ensemble <ref:2610.12884#pg3>.

Meng: For deployment, they show that in a field application on three blind wells, CoGameReg achieved a pooled coefficient of determination of zero point five nine four two and a root mean square error of five point seven four four one percentage points <ref:2610.12884#pg3>.

Lalam: The paper notes that the field results show CoGameReg reproduces major water-saturation trends, but they also point out that the variable performance among the blind wells means these are data-driven reservoir-property estimates <ref:2610.12884#pg3>.

Tom: It sounds like this framework is particularly strong because it combines multi-model ensemble diversity with that multi-component Tri-Game Shapley valuation and fixed initial weight semi-supervised collaborative training <ref:2610.12884#pg3>.

Jane: It seems like a very solid approach for when you have abundant seismic data but are severely limited by the cost of collecting well logs, suggesting that this method could be really useful in the exploration phase <ref:2610.12884#pg2>.

Lu: Yeah, it addresses the interaction structure issue that plagues co-training regression when you're dealing with unlabeled data <ref:2610.12884#pg3>.

Meng: I'm just thinking about what happens when you have to run this at scale; the fact that each regressor retrains independently is good for modularity but adds overhead on the training pipeline <ref:2610.12884#pg3>.

Lalam: The overall bias for CoGameReg is zero point seven six nine three percentage points, and their macro-average R2 is zero point five zero three four plus or minus zero point two zero nine four <ref:2610.12884#pg3>.

Tom: This whole process of using contribution-aware weighting to build shared labels is a really clean way to handle the heterogeneity of the inputs <ref:2610.12884#pg1>.

Jane: We've covered CoGameReg, but we'll keep an eye on how this cooperative game concept applies to other types of data learning next time <ref:2610.12884#pg3>.

Zhiyu Guo, Jiwei Jia, Lei Li

School of Mathematics, Jilin University · AI for Science and Engineering Center, Shenzhen Loop Area Institute · BGP Inc. · China National Petroleum Corporation · National Engineering Research Center of Oil & Gas Exploration Computer Software

cs.LG

Submitted: 2026-10-09

Updated: 2026-10-09

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 86/100

The gist: The gist Accurate estimation of reservoir properties from seismic data remains challenging when well-log labels are sparse but three-dimensional seismic observations are abundant, and CoGameReg

Key concepts

Cooperative Game
The framework models different regression components (regressors) as players in a game. The goal is to find a way for these players to cooperate and reach an optimal outcome, which helps determine how important each predictor is for the final prediction.
Tri-Game Shapley Mechanism
This mechanism estimates the importance (weights) of each regressor by combining three types of games: one based on performance (Rank-MSE), one based on pairwise consistency, and a consensus component. This provides a robust way to assign non-negative weights from labeled data.
Pseudo-label Construction
The framework uses the contribution-weighted predictions from the ensemble to generate 'shared pseudo-labels' for unlabeled seismic samples. These shared labels are then used iteratively to retrain and improve the model, effectively leveraging limited well data to guide predictions on dense seismic data.

Summary

The gist Accurate estimation of reservoir properties from seismic data remains challenging when well-log labels are sparse but three-dimensional seismic observations are abundant, and CoGameReg presents a cooperativegame-based semi-supervised regression framework that uses contributionweighted predictions of heterogeneous regressors to construct shared pseudolabels

How it works

CoGameReg is a framework that treats heterogeneous regressors as players and estimates their contribution-aware weights once from the labeled training data. The Tri-Game mechanism combines a coalition-level rank–MSE performance game with a pairwise consistency game to estimate nonnegative regressor weights from labeled training data. These weights remain fixed during collaborative training and are reused for final prediction fusion.

The framework operates iteratively through the following steps:

  1. Initialization involves constructing a pool of N regressors S = M i, i=1 to N, and initializing a weighted ensemble predictor whose weight vector lies on the probability simplex fw(x) = X N i=1 w i M(x), w ∈ ∆N−1.

  2. The Tri-Game Shapley valuation mechanism is applied once to estimate an initial contribution-aware weight vector w(0) ∈ ∆N−1.

  3. At each iteration t, a pseudo-label is generated by the fixed weighted ensemble: y¯u = X N i=1 w(0) i M(t−1) i (xu), where xu ∈ U′ t−1.

  4. Candidate admission is model-indexed because the same local gain functional is evaluated separately on each L(t−1) i.

  5. The local error-reduction principle of COREG is used to estimate the local mean squared error reduction resulting from accepting (xu, y¯u) by δ(i) xu = 1/omegau X j∈omegau yj − h temp i(xj)2 − yj − h temp'i(xj)2.

  6. Candidate admission is determined by selecting the top ρ proportion of C(t) i, ranked by δ(i) xu.

  7. The accepted subset A(t) i is selected to update the pseudo-label pool P(t) i = P(t−1) i ∪ A(t) i.

  8. Each regressor Mi maintains its own augmented training set DL ∪ P(t) i and is retrained independently.

Tri-Game Shapley Valuation Mechanism

The Tri-Game mechanism is defined by three conceptual valuation games—ordinal, accuracy, and consensus. The performance component combines Rank and MSE utilities into a mixed characteristic function vPerf(G) = α · vRank(G) + β · vMSE(G), G ̸= ∅. The consistency component evaluates cross-regressor consensus using the consistency utility of a coalition G as vCon(G) = 1/2 X Mi∈G X Mj∈G j̸=i exp − yˆi − yˆj2 / 2σ2.

The fixed initial ensemble weight vector w(0) is obtained by aggregating these normalized components into the unified ensemble weight w(0) i = (α + β)ϕ˜Perf,i + γϕ˜Con,i. The performance component utilizes Spearman’s rank correlation coefficient for Rank utility vRank(G) = 1 + ρs(yL, y¯G)2, while the MSE utility is defined using an exponential transformation of the mean squared error: vMSE(G) = exp − MSE(yL, y¯G)2/bMSE.

Experimental Evaluation and Results

CoGameReg was evaluated on 10 public regression datasets, a synthetic three-dimensional P-wave velocity prediction task, and a field water-saturation application. On the 10 public benchmark regression datasets, CoGameReg achieved the lowest average RMSE (0.1098) across the 30 dataset-ratio settings and yields the lowest or joint-lowest RMSE in 18 of them. The comparison with classical collaborative and self-training baselines is particularly informative, showing that CoGameReg achieves lower RMSE than Self-KNN, COREG, and Avg. Ensemble on most datasets and labeled-data ratios.

In the field application, predictions clipped to 0–100% yield a pooled coefficient of determination of 0.5942, a root mean square error of 5.7441 percentage points, and a Pearson correlation of 0.8265 across three blind wells. CoGameReg has the highest Pearson correlation among the four field methods. In the synthetic experiment, CoGameReg achieves an RMSE of 0.4137, an R2 of 0.5065, and an SRC of 0.5747, yielding the best values among the methods reported in Table 5.

Ablation Study Insights

The ablation study results show that the final CoGameReg variant achieves the lowest average RMSE (0.1098) among all ablation variants and attains the best or tied-best result in 12 of the 30 dataset-ratio settings. The results support placing contribution-aware weighting within the pseudo-labeling loop. Furthermore, the final CoGameReg variant reduces the average RMSE to 0.1098 and outperforms both SSR-Decoupled Shapley Weighting and purely supervised Shapley Weighted Ensemble in this comparison.

The field results demonstrate that CoGameReg reproduces major water-saturation trends at the three blind wells and yields the highest pooled Pearson correlation among the four compared methods. However, the variable performance among the blind wells indicates that the field results should be interpreted as data-driven reservoir-property estimates.

The study concludes that no single-component or intermediate variant matches the average RMSE of the complete CoGameReg configuration. The overall ablation results suggest that the best average performance is obtained when multi-model ensemble diversity, multi-component Tri-Game Shapley valuation, and fixed-initial weight semi-supervised collaborative training are combined.

The source code for CoGameReg is available at https://github.com/ACE020215/CoGameReg. The public benchmark data sets and the Stanford VI-E synthetic reservoir data are available from the cited sources. The proprietary field seismic and well-log data are confidential and cannot be released. All four methods use the same five input volumes and training/validation/blindtest well partition. The predicted values were post-processed according to the physical definition of water saturation, specifically clipped to the valid range of 0–100% before visualization and quantitative evaluation on the validation and blind-test wells. The overall bias for CoGameReg is 0.7693 percentage points. The macro-average R2 is 0.5034± 0.2094, and the macro-average RMSE is 5.5573 ± 1.8027 percentage points. The final CoGameReg variant achieves a lower average RMSE (0.1098) than all single-component and purely supervised variants. The field results therefore support applicability under the evaluated conditions, with performance depending on the metric and well location. This work was supported by CNPC Science and Technology Major Project (No. SG0023Z0010050100111) and CNPC Youth Science and Technology Special Project ”Research on Rock Physics and Facies-Driven Intelligent Seismic Reservoir Characterization Methods” (No.

Improvements for AI systems

  1. Bold header: Fixed Contribution-Aware Weight Initialization

This mechanism utilizes the Tri-Game mechanism combines a rank–MSE performance game with a pairwise consistency game to estimate nonnegative regressor weights from labeled training data, which are fixed throughout collaborative training and are reused for final prediction fusion. This explicitly makes each regressor’s influence explicit in the learning targets generated for unlabeled seismic samples under sparse well control.

  1. Bold header: Tri-Game Valuation Mechanism

The framework employs a valuation mechanism where the ensemble weight is determined by combining components, such as a mixed rank–MSE performance characteristic function with a pairwise consistency game, resulting in weights calculated as w(0)i = (α + β)ϕ˜Perf,i + γϕ˜Con,i. This allows the system to balance predictive accuracy and cross-model agreement.

  1. Bold header: Local Candidate Screening Integration

Candidate admission is controlled by a criterion derived from the fixed weights: Candidate admission is evaluated using a common local error-reduction criterion on each regressor’s current augmented training set, specifically when evaluating the difference between the pre- and post-inclusion neighborhood MSE to determine if "δ(i)xu > θ."

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