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TRiCo: Triadic Game-Theoretic Co-Training for Robust Semi-Supervised Learning

Hongyang He, Xinyuan Song, Yangfan He, Zeyu Zhang, Yanshu Li, Haochen You, Lifan Sun, Wenqiao Zhang

TL;DR

TRiCo rethinks semi-supervised learning by embedding two frozen-view students, a meta-learned teacher, and an adversarial embedding perturbation generator into a Stackelberg game.Pseudo-labels are selected by mutual information rather than confidence, and the teacher adaptively tunes MI thresholds and loss weights to maximize validation generalization.An entropy-driven perturbation module and end-to-end meta-gradients enable hard-sample mining and robust curriculum-style supervision, yielding state-of-the-art results on CIFAR-10, SVHN, STL-10, and ImageNet with limited labels.The framework is theoretically grounded (Nash equilibrium existence) and empirically versatile, compatible with frozen backbones, and effective under few-shot and distribution-shift scenarios.

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.Code:https://github.com/HoHongYeung/NeurIPS25-TRiCo.

TRiCo: Triadic Game-Theoretic Co-Training for Robust Semi-Supervised Learning

TL;DR

TRiCo rethinks semi-supervised learning by embedding two frozen-view students, a meta-learned teacher, and an adversarial embedding perturbation generator into a Stackelberg game.Pseudo-labels are selected by mutual information rather than confidence, and the teacher adaptively tunes MI thresholds and loss weights to maximize validation generalization.An entropy-driven perturbation module and end-to-end meta-gradients enable hard-sample mining and robust curriculum-style supervision, yielding state-of-the-art results on CIFAR-10, SVHN, STL-10, and ImageNet with limited labels.The framework is theoretically grounded (Nash equilibrium existence) and empirically versatile, compatible with frozen backbones, and effective under few-shot and distribution-shift scenarios.

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.Code:https://github.com/HoHongYeung/NeurIPS25-TRiCo.

Paper Structure

This paper contains 28 sections, 1 theorem, 37 equations, 10 figures, 25 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Method
  3. Overview of TRiCo
  4. View-wise Co-Training
  5. Meta-Learned Teacher Strategy
  6. Unified Objective Function and Training Procedure
  7. Theoretical guarantee
  8. Experiments
  9. TRiCo Results
  10. Ablation Studies
  11. Few-Shot and Out-of-Distribution Generalization
  12. Few-Shot Semi-Supervised Learning
  13. Out-of-Distribution Generalization
  14. Related Works
  15. Conclusion
  16. ...and 13 more sections

Key Result

Theorem 1

Under Assumptions assump:compact_strategy_spaces and assump:payoff_continuity, there exists a Nash equilibrium $(\pi_T^*, f_1^*, f_2^*, G^*) \in \Pi_T \times \Pi_S \times \Pi_G$ in the TRiCo framework such that:

Figures (10)

  • Figure 1:
  • Figure 2:
  • Figure 3:
  • Figure 5: Overview of the TRiCo framework. Two student models $f_1$ and $f_2$ learn from different frozen views $V_1$ and $V_2$. Each view is passed through an entropy-guided generator to produce adversarial inputs, which are then filtered by a meta-learned teacher $\pi_T$ to generate pseudo-labels based on MI and confidence thresholds. All components interact via game-theoretic objectives to optimize robustness and generalization.
  • Figure 6: T-SNE visualization on STL-10. Left (a) : Meta Co-Training (MCT); Right (b) : TRiCo. Each color denotes a semantic class. TRiCo leads to more compact and well-separated clusters in the embedding space, highlighting its superior representation quality.
  • ...and 5 more figures

Theorems & Definitions (2)

  • Theorem 1: Existence of Nash Equilibrium in Triadic Game
  • proof