DAK-UCB: Diversity-Aware Prompt Routing for LLMs and Generative Models

Recent years have seen explosive growth in generative AI, including models like GANs, VAEs, diffusion models, and large language models, with applications spanning image synthesis, text generation, and video creation. Early efforts prioritized improving fidelity metrics such as FID and Inception Score, but these metrics often failed to capture output diversity, leading to mode collapse and homogenized outputs. To counter this, researchers introduced diversity metrics like Maximum Mean Discrepancy (MMD), kernel entropy, and coverage scores, which better quantify distributional differences and sample variety. Despite these advances, model selection methods still largely focus on single metrics, neglecting the importance of balancing quality and diversity. Reinforcement learning and contextual bandits have been explored for adaptive scheduling, but most lack explicit diversity considerations, limiting their effectiveness in producing rich, varied outputs. This gap motivates the development of algorithms that can dynamically optimize multiple objectives simultaneously.

Current model selection techniques predominantly optimize for fidelity scores, such as CLIP-Score, ignoring the diversity of generated outputs. This leads to homogenized results, reducing the utility and fairness of AI systems, especially in sensitive applications like biased data generation or creative arts. The core challenge is designing an online, scalable framework that can incorporate multiple, often conflicting, objectives—fidelity and diversity—while providing theoretical guarantees. Additionally, existing diversity metrics are computationally expensive and difficult to estimate in real-time, complicating their integration into adaptive algorithms. Balancing these factors requires novel score decompositions, efficient online estimation, and a principled decision-making process that can adapt to prompt-specific variations.

The paper introduces several key innovations: 1) defining joint kernel distance and kernel entropy scores with two-sample expectation structures suitable for online estimation; 2) extending the kernelized UCB algorithm to incorporate these scores with confidence bounds, ensuring theoretical regret guarantees; 3) designing prompt-dependent model mixture strategies to optimize diversity dynamically. These innovations enable the algorithm to balance fidelity and diversity effectively, leveraging kernel methods' flexibility and theoretical robustness. The approach is novel in embedding diversity metrics directly into the online decision framework, moving beyond single-objective optimization to a multi-faceted, adaptive scheduling paradigm.

• �� Define diversity metrics (kernel distance, kernel entropy) as two-sample expectations over prompt-output pairs, enabling online estimation.
• �� Extend kernel ridge regression to estimate these scores with confidence bounds, ensuring reliable online updates.
• �� Incorporate fidelity metrics (e.g., CLIP-Score) and diversity scores into a combined UCB policy, balancing quality and variety.
• �� Use prompt as context, updating per-arm models with each generated sample, and selecting models via optimistic bounds.
• �� Introduce prompt-dependent model mixtures, optimizing mixture weights through quadratic programming to enhance diversity.
• �� Theoretical analysis guarantees sublinear regret bounds, ensuring convergence and robustness.
• �� Implement algorithms with efficient kernel approximations for scalability.

The evaluation uses MS-COCO prompts, comparing DAK-UCB against baselines like random, oracle, and diversity-unaware PAK-UCB. Three generative models (e.g., SDXL, GigaGAN, Kandinsky) are tested over 2000 iterations, with metrics including CLIP-Score, kernel distance, and kernel entropy. The experiments assess the ability to balance fidelity and diversity, analyze parameter sensitivity, and validate theoretical guarantees. Results show DAK-UCB achieves over 15% improvement in diversity scores while maintaining comparable fidelity, with the mixture strategy further boosting diversity by 20%. The robustness across prompt categories and convergence behavior are also examined.

DAK-UCB outperforms traditional methods, with kernel distance scores improved by 15%, and CLIP-Score maintained above 0.75. The mixture approach enhances diversity by 20%, demonstrating adaptability. The confidence bounds derived from kernel ridge regression ensure stable online estimation, with regret bounds confirmed theoretically. These results validate the effectiveness of integrating diversity metrics into the online selection process, enabling more varied and representative outputs without sacrificing quality.

This framework can be applied in personalized content creation, virtual assistants, and multi-modal AI systems, where diverse outputs enhance user engagement and fairness. It enables dynamic, prompt-dependent scheduling of models, improving the richness of generated content in real-time. The approach is suitable for industries requiring high variability, such as entertainment, advertising, and education, especially when fairness and inclusivity are priorities.

Computational complexity of kernel methods may limit scalability, especially with large datasets or high-dimensional features. Parameter tuning (e.g., λ, kernel bandwidths) remains sensitive and task-specific. The current validation is primarily on image generation; extending to text and video modalities requires further work. Future efforts should focus on kernel approximation techniques, multi-modal adaptation, and user preference integration to address these challenges.