Title: TRiCo: Triadic Game-Theoretic Co-Training for Robust Semi-Supervised Learning
Venue: NeurIPS 2025
Accepted: yes
Keywords: Semi-supervised learning
Abstract: We introduce TRiCo, a novel triadic game-theoretic co-training framework that rethinks the structure of semi-supervised learning by incorporating a teacher, two students, and an adversarial generator into a unified training paradigm. Unlike existing co-training or teacher-student approaches, TRiCo formulates SSL as a structured interaction among three roles: (i) two student classifiers trained on frozen, complementary representations, (ii) a meta-learned teacher that adaptively regulates pseudo-label selection and loss balancing via validation-based feedback, and (iii) a non-parametric generator that perturbs embeddings to uncover decision boundary weaknesses. Pseudo-labels are selected based on mutual information rather than confidence, providing a more robust measure of epistemic uncertainty. This triadic interaction is formalized as a Stackelberg game, where the teacher leads strategy optimization and students follow under adversarial perturbations. By addressing key limitations in existing SSL frameworks—such as static view interactions, unreliable pseudo-labels, and lack of hard sample modeling—TRiCo provides a principled and generalizable solution. Extensive experiments on CIFAR-10, SVHN, STL-10, and ImageNet demonstrate that TRiCo consistently achieves state-of-the-art performance in low-label regimes, while remaining architecture-agnostic and compatible with frozen vision backbones.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces a semi-supervised learning (SSL) method that is based on a game-theoretic interaction among models. This paper observes how existing methods select pseduo-labels based on the models' confidence, which is susceptible to calibration error and can be detrimental. The proposed solution uses mutual information as an alternative to pseudo-label selection. It is shown that across a wide range of standard SSL benchmarks, the proposed method outperforms not only existing SSL methods but also fully-supervised methods despite using only 25% of the dataset.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n* The proposed method is tested on many image classification benchmarks. This is convincing, as many SSL methods are tested on fewer datasets due to the higher compute requirements. \n\n* This paper demonstrates various benefits to the proposed method, including feature clustering and CAM visualizations. \n\n**Weaknesses**\n* Complexity: This is a limitation that exists not only in the proposed method, but also in existing semi-supervised learning methods. The proposed method uses two encoders that are trained using different methods, several additional models, and adversarially-robust training, in addition to the many details. Such multi-stage training methods and those that combine various modules are hard to apply to new problems due to development costs and potentially requiring a whole new set of hyperparameters to tune.\n\n* It's unclear what the role of each stage plays. Can some of the components be removed yet achieve similar performance? While Section 2 motivates each component, it's unclear that the intended effects are the cause for enhanced performance. For example, describing the teacher-student training as a Stackelberg game doesn't seem to use anything from game theory. Existence of a Nash equilibrium often doesn't say much about the quality of the equilibrium or convergence to equilibrium. While the teacher-student training is described as a bi-level (Stackelberg) game, the students/teacher are updated iteratively instead of being solved at different time scales. \n\nOverall, the practical benefits seem to outweigh the limitations as an off-the-shelf method. My main concern is that the method seems to be a bit ad-hoc, and therefore may have limited applicability outside of the considered benchmarks. \n\n\n**Minor Comments**\n\n* The figures should have thicker curves; they are hard to read, for example Figure 1.a.\n\n* It seems unnecessary to put the results figure in page 1. I recommend moving this to the experiments/results sections.\n\nQUESTIONS:\nIs there any part of the method that can be removed or combined with others and yet retain the high performance?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-26"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces TriCO, a new framework of semi-supervised learning based on Pseudo-labeling strategy, involving three (sets of) agents: Students, Teacher, and Generator.\nWith Teacher being the leader in the Stackelberg Game, students and teacher balance each other to find a solution that is very competitive, sometimes even SOTA, in the standard SSL task, as well as in OOD task. \nThe paper also provides the guarantee that there is a nash equilibrium in the three-player game.\n\nSTRENGTHS AND WEAKNESSES:\n## Strength\n\n This paper is clearly strong in two aspects : first, it brings in “game theory” into  the challenging problem of interacting systems in the setting of SSL, and backs it up with a formal guarantee. “Three” player game is something that I have never encountered before in this genre, and strikes as a fundamental novelty.  \nSecond, the efficacy of the method is demonstrated on a strong basis. Ablations are also conducted thoroughly.  While I am committed not to evaluate the research based merely on “the depth of the experiments”, I believe that this thoroughness solidly supports the significance of the proposition. \n\n\n## Weaknesses \n\n- Several parts are difficult to read and some fix would greatly help conveying the idea. \nFor example, several definitions seems missing.  From the context, $p_i$ in (1) seems like the ensemble average, but this has never been explicitly stated in the main manuscript.  $H(p(y))$ is also confusing, since $p(y)$ is a scaler ;  I believe this is $p_Y$.    It also seems that $L_sup$ stands for $E_{i, X, Y}[ CE (f_i (v_i(X), Y) ]$, but I do not see it explicitly defined. \nThe same goes for $Accuracy_{val}(f_1, f_2)$.   Theorem 1, I believe, is supposed to be followed by “for all $f_i, G, \\pi_T$.  \n\n- Lastly, although the existence of Nash Equilibrium is wonderful and inspiring, I believe this problem is a Stackelberg game, and I believe Stackelberg Equilbrium and Nash Equilbrium are not always the same?   If I am not missing some lines, I believe some explanation in this aspect is warranted. I believe that if the paper can provide the existence of  Stackelberg Equilbrium, this work is irrefutable.\nI'm very much open to increasing the score when these subtlties and questions below are resolved to a degree.\n\nQUESTIONS:\n- Please see the second weakness section;  I wonder that Stackelberg Equilbrium is difficult in this context because the Generator is non-parametric?  Can this problem be resolved if we can impose some structural assumptions here? I believe that the result of Stackelberg Equilibrium would be beneficial to the community even if it requires additional (even possibly, a little unrealistic) assumption.\n\n\n- Also, I was a little worried that mentions were not made so much regarding the stability of the learning in the main manuscript, other than at the theorem section (Fig 5 in the Appendix and Table 15 are acknowledged).   As an devil's advocate, I would also like to know if there are any implicit hyperparameters (or the parameters of the training) that one must be particularly careful about in training TriCO,  because \"training multi-agents system\" has always been a challenge---this information would definitely benefit the researchers that would follow this study.\n\nLIMITATIONS:\nAs claimed \"Limitations are implicitly discussed in Section 4\", regarding limited supervision and drastic distributional shift. I believe this should be explicitly stated, and this will not hurt the work's credibility.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes TRiCo, a game-theoretic co-training approach for semi-supervised learning. As in other co-training approaches, TRiCo uses two student models which predict pseudo-labels on differently-augmented views of the same input data. The pseudo-labels are then used as supervision for the opposite student model. In conjunction with the complementary pseudo-label loss, an adversarial loss is also added to the training objective, computed through applying PGD to the input samples, to encourage the model to produce accurate predictions even against highly-adversarial examples. To filter the pseudo-labels, instead of the normal softmax output, the metric of mutual information is used, computed through measuring the empirical prediction distribution $p(y|x)$ through using monte carlo dropout. To determine the MI threshold for maintaining pseudo-labels, and for determining the relative weighting of the unsupervised and adversarial losses, a teacher model is maintained during training to predict these quantities. The teacher model is trained on the meta-objective of the student model performance on a held out labeled validation set, with its updated computed using a first-order approximation from unrolling the student model gradient update. The authors evaluate TRiCo on both the standard SSL setting, as well as a few-shot learning setting, and demonstrate state-of-the-art performance.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- The paper is well-written and easy to understand.\n- The idea is quite novel and represents a departure from the currently popular self-training paradigm in SSL.\n- The authors provide sound theoretical backing to support the use of TRiCo.\n- Experiments are extensive, and demonstrate consistent improvement across a variety of dataset and task settings.\n\nWeaknesses:\n- Although achieving state-of-the-art results, compared to competing approaches on Imagenet, TRiCo's improvement is quite marginal (only +0.1 in the 10% labeled setting, -0.4 in the 1% setting).\n- A key aspect of the method, leveraging mutual information to filter pseudo-labels, seems to only be weakly-supported by experimental evidence. In the ablation studies, MI filtering is only better by +0.1 when compared to a well-tuned confidence threshold. This makes me skeptical that the mutual information filtering is at all critical to the success of the method.\n- TRiCo's time and space complexity is greater than those of competing SSL approaches, and although not insurmountable, is definitely a hurdle to be overcome for practical usage.\n\nQUESTIONS:\n1. Have you performed any experiments using a meta-learned strategy with confidence thresholding, as opposed to MI thresholding? Given that MI thresholding with the teacher strategy is only +0.1 points better, I am suspicious that simply using a meta-learned confidence thresholding strategy will actually produce better results.\n2. Have you considered alternate approaches to monte carlo dropout to estimate the empirical predictive distribution, such as through directly predicting the distribution parameters as outputs of your model?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces TRiCo (Triadic Game-Theoretic Co-Training), a novel semi-supervised learning framework that extends traditional co-training by incorporating three interacting components: two student classifiers, a meta-learned teacher, and an adversarial generator. The approach addresses key limitations in existing SSL methods through (1) mutual information-based pseudo-label filtering instead of confidence thresholds, (2) a meta-learned teacher that adaptively regulates training dynamics via validation feedback, and (3) a non-parametric generator that creates adversarial perturbations to expose decision boundary weaknesses. The framework is formulated as a Stackelberg game where the teacher leads strategy optimization while students and generator follow. Experiments on CIFAR-10, SVHN, STL-10, and ImageNet demonstrate consistent improvements over strong baselines, with TRiCo achieving competitive performance with fully-supervised models using only 25% labeled data.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The paper introduces an original approach that reformulates co-training as a structured three-player game with theoretical guarantees (Nash equilibrium existence). This represents a meaningful departure from existing binary co-training methods and provides a principled framework for multi-agent SSL.\n2. The use of mutual information instead of confidence-based thresholds is theoretically well-motivated and addresses calibration issues that plague existing methods. The MI-based approach better captures epistemic uncertainty and shows improved reliability in low-confidence regions.\n3. The method demonstrates robust improvements across multiple benchmarks (CIFAR-10, SVHN, STL-10, ImageNet) and various label regimes.\n\nWeaknesses:\n1. The connection between game-theoretic equilibria and actual SSL performance remains unclear, and the theoretical assumptions are quite standard.\n2. The method incurs 2-3× runtime overhead and 1.5-2× memory usage due to MI estimation via multiple dropout passes, adversarial perturbation generation, and meta-gradient computation. This computational cost may limit practical adoption, especially in resource-constrained settings.\n3. The mutual information estimation via dropout may be noisy early in training, the first-order meta-gradient approximation may be too crude.\n\nQUESTIONS:\nCan you provide a more detailed computational analysis breaking down the cost of each component (MI estimation, adversarial generation, meta-gradients)?\n\nLIMITATIONS:\nno.\nThe method introduces several hyperparameters (MI threshold, loss weights, perturbation budget) that require careful tuning. The authors should discuss the sensitivity to these choices and the expertise required for proper implementation.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

comments: SUMMARY:
TRiCo is a semi-supervised learning framework that integrates a teacher, two student classifiers, and an adversarial generator. It filters pseudo-labels using mutual information to avoid overconfidence errors. The teacher adjusts pseudo-label selection and loss balancing through meta-learning, while the generator creates adversarial samples to improve robustness. TRiCo is tested across various low-label scenarios and demonstrates effectiveness in handling limited labeled data, while being compatible with different model architectures.

STRENGTHS AND WEAKNESSES:
Strengths:

1. The TriCo framework demonstrates competitive results when compared to baseline methods and is supported by theoretical foundations.

2. The paper is well-written and easy to follow.

Weaknesses:

1. Line 78 claims good performance under class imbalance, but no experimental results support this.

2. Semi-supervised learning is unstable with few samples, and the experimental results should include standard deviation values.

3. The DINOv2 model offers superior representation ability compared to other pre-trained models, which raises concerns about the fairness of the comparison if it is solely used in the proposed method.

4. The TriCo seems overly complex, which improves performance by using an ensemble-like approach and the stronger data perturbation mechanism.

QUESTIONS:
Please see the above weaknesses.

LIMITATIONS:
The experimental section of this paper may need to be carefully organized by the authors, as it feels somewhat disorganized.
TITLE: Official Review
CLARITY: 2
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-07-02