Language Model Prompt Selection via Simulation Optimization (2404.08164v2)

Abstract: With the advancement in generative LLMs, the selection of prompts has gained significant attention in recent years. A prompt is an instruction or description provided by the user, serving as a guide for the generative LLM in content generation. Despite existing methods for prompt selection that are based on human labor, we consider facilitating this selection through simulation optimization, aiming to maximize a pre-defined score for the selected prompt. Specifically, we propose a two-stage framework. In the first stage, we determine a feasible set of prompts in sufficient numbers, where each prompt is represented by a moderate-dimensional vector. In the subsequent stage for evaluation and selection, we construct a surrogate model of the score regarding the moderate-dimensional vectors that represent the prompts. We propose sequentially selecting the prompt for evaluation based on this constructed surrogate model. We prove the consistency of the sequential evaluation procedure in our framework. We also conduct numerical experiments to demonstrate the efficacy of our proposed framework, providing practical instructions for implementation.

• The paper proposes a two-stage framework that transforms textual prompts into soft vectors and sequentially evaluates them to maximize a predefined score.
• It employs PCA for dimensionality reduction and a Bayesian surrogate model with a Modified UCB to balance exploration and exploitation in prompt selection.
• Experiments demonstrate that Bayesian Neural Networks outperform alternative methods, ensuring robust prompt optimization as evaluation budgets increase.

A Two-Stage Framework for Efficient LLM Prompt Selection via Simulation Optimization

Overview of the Framework

The paper introduces a two-stage framework aimed at efficient prompt selection for generative LLMs through simulation optimization. At its core, the framework acknowledges the challenge of prompt selection, given the vast potential prompt space and seeks to maximize a pre-defined score for the selected prompt. The first stage focuses on constructing a feasible set of prompts by numerical representation, while the second involves evaluating and selecting the optimal prompt through a surrogate model and a sequential evaluation strategy.

Constructing the Feasible Set

The initial step involves transforming textual prompts into moderate-dimensional vectors, referred to as "soft prompts." This process utilizes a text autoencoder for numerical representation followed by perturbation and dimensionality reduction techniques, such as Principal Component Analysis (PCA), to establish a diverse yet manageable set of potential prompts in vector form.

Evaluation and Selection Strategy

Sequential evaluation is pivotal in the proposed framework, wherein an acquisition function is optimized to balance exploration and exploitation across the soft prompt space. Specifically, a Bayesian parametric model, constructed based on observed scores from the generative LLM, serves as a surrogate to approximate the mean score associated with each soft prompt. The framework employs the Modified Upper Confidence Bound (M-UCB) acquisition function, which accounts for both the expected performance and the uncertainty of unexplored prompts.

Demonstrated Efficacy Through Experiments

Numerical experiments underline the framework's effectiveness, where Bayesian Neural Networks (BNNs) emerged as superior surrogate models for approximating the mean score function, particularly with large sets of prompts. The analysis revealed that while direct search in high-dimensional latent spaces using Projection Stochastic Kriging (PSK) models was feasible, it underperformed compared to the structured approach of the two-stage framework, especially when refined with additional evaluations post-selection.

Theoretical Underpinnings and Practical Implications

The consistency of the sequential evaluation procedure is established under reasonable assumptions, affirming that the proposed framework reliably identifies prompts that maximize the mean score as evaluation budget increases. This consistency, coupled with the framework’s ability to refine the selection post-initial evaluation, offers a robust method for leveraging generative LLMs, especially beneficial for small businesses and nonprofits seeking cost-effective AI solutions.

Future Trajectories in AI and Operational Management

The methodology extends beyond prompt selection, promising applications in diverse fields requiring optimization in the face of vast, complex decision spaces. Its adaptability to different surrogate models and optimization strategies opens avenues for further research, particularly in refining budget allocation between evaluation stages and enhancing the surrogate models' accuracy and computational efficiency.

Conclusion

The framework posits a systematic and efficient approach to the prompt selection problem for generative LLMs, addressing scalability and performance concerns. By combining advances in simulation optimization with machine learning, it offers a pragmatic solution with broad implications for both theoretical research and practical applications in AI-driven operational management.