Best Arm Identification for Prompt Learning under a Limited Budget

The remarkable instruction-following capability of large language models (LLMs) has sparked a growing interest in automatically learning suitable prompts. However, while many effective methods have been proposed, the cost incurred during the learning process (e.g., accessing LLM and evaluating the responses) has not been considered. To overcome this limitation, this work explicitly incorporates a finite budget constraint into prompt learning. Towards developing principled solutions, a novel connection is established between prompt learning and fixed-budget best arm identification (BAI-FB) in multi-armed bandits (MAB). Based on this connection, a general framework TRIPLE (besT aRm Identification for Prompt LEarning) is proposed to harness the power of BAI-FB in prompt learning systematically. Unique characteristics of prompt learning further lead to two embedding-based enhancements of TRIPLE by exploiting the ideas of clustering and function approximation. Extensive experiments on multiple well-adopted tasks using both GPT 3.5 and Llama2 demonstrate the significant performance improvement of TRIPLE over the previous baselines while satisfying the limited budget constraints.