Curiosity Meets Cooperation: A Game-Theoretic Approach to Long-Tail Multi-Label Learning

TL;DR

This paper tackles long-tail imbalances in multi-label learning by formulating the problem as a differentiable cooperative potential game, CD-GTMLL. It partitions the label space into overlapping subsets managed by multiple predictors that share a global accuracy payoff while receiving curiosity bonuses that emphasize tail labels and encourage peer disagreement. The authors prove that gradient best-response updates ascend a differentiable potential, leading to tail-aware equilibria, and they demonstrate state-of-the-art Rare-F1 and P@k gains on conventional and extreme-scale benchmarks. Ablation analyses reveal emergent specialization among players and faster consensus on rare classes, validating the proposed division-of-labor and curiosity mechanism as a scalable route to long-tail robustness in multi-label prediction.

Abstract

Long-tail imbalance is endemic to multi-label learning: a few head labels dominate the gradient signal, while the many rare labels that matter in practice are silently ignored. We tackle this problem by casting the task as a cooperative potential game. In our Curiosity-Driven Game-Theoretic Multi-Label Learning (CD-GTMLL) framework, the label space is split among several cooperating players that share a global accuracy payoff yet earn additional curiosity rewards that rise with label rarity and inter-player disagreement. These curiosity bonuses inject gradient on under-represented tags without hand-tuned class weights. We prove that gradient best-response updates ascend a differentiable potential and converge to tail-aware stationary points that tighten a lower bound on the expected Rare-F1. Extensive experiments on conventional benchmarks and three extreme-scale datasets show consistent state-of-the-art gains, delivering up to +4.3% Rare-F1 and +1.6% P@3 over the strongest baselines, while ablations reveal emergent division of labour and faster consensus on rare classes. CD-GTMLL thus offers a principled, scalable route to long-tail robustness in multi-label prediction.

Figures (10)

• Figure 1: Real-world multi-label scenes are long-tailed: a few frequent classes (e.g., car, pedestrian, traffic light) dominate while many rare classes (e.g., power pole, aerial work platform) appear sparsely (left). A conventional single model may score well overall yet often overlooks these rare labels (top-right). Our approach replaces the monolith with a small set of cooperative experts that divide the work and then fuse their opinions into a single consensus prediction (bottom-right), improving tail coverage without sacrificing head performance.
• Figure 2: CD--GTMLL pipeline. Long-tailed data are encoded by a shared Backbone into features $h(x)$. In the forward path (black arrows), $h(x)$ is sent to multiple Players, each specializing on an overlapping label subset $\mathcal{L}_i$ and producing posteriors $\pi_i$. A label-wise Fusion $g(\{\pi_i\})$ yields $\hat{\mathbf p}$, which is Thresholded to predictions $\hat{\mathbf y}$. In the training path (red arrows), each player receives a Curiosity signal-rarity bonus (focus on tail labels) plus disagreement with peers-producing $C_i(x)$. A Global utility $R$ scores $(\hat{\mathbf y},\mathbf y)$; the Per-player objective $J_i=R+\alpha\,\mathbb{E}[C_i]$ drives a cyclic best-response update of $\theta_i$. The cooperative game encourages division of labor across overlapping subsets and improves tail coverage while preserving head performance.
• Figure 3: Precision-recall curves on Pascal VOC-R.
• Figure 4: Ablation on Pascal VOC-2007 (left) and MS-COCO-2014 (right). Bars show mean $\pm$ std over three seeds; numbers above non-full variants indicate the absolute gap to the full model.
• Figure 5: Absolute Rare-F1 degradation under label noise and occlusion.

Theorems & Definitions (7)

• Theorem 1: Existence and tail-awareness
• proof : Proof sketch
• Proposition 1: Curiosity prioritizes tail labels
• proof : Proof sketch
• Theorem 2: Convergence of cyclic block ascent
• proof : Proof sketch
• Theorem 3: Lower bound on micro Rare--F1