  Black-box prompt tuning employs derivative-free optimization algorithms to
learn prompts within low-dimensional subspaces rather than back-propagating
through the network of Large Language Models (LLMs). Recent studies reveal that
black-box prompt tuning lacks versatility across tasks and LLMs, which we
believe is related to the suboptimal choice of subspaces. In this paper, we
introduce Black-box prompt tuning with Subspace Learning (BSL) to enhance the
versatility of black-box prompt tuning. Based on the assumption that nearly
optimal prompts for similar tasks reside in a common subspace, we propose
identifying such subspaces through meta-learning on a collection of similar
source tasks. Consequently, for a target task that shares similarities with the
source tasks, we expect that optimizing within the identified subspace can
yield a prompt that performs well on the target task. Experimental results
confirm that our BSL framework consistently achieves competitive performance
across various downstream tasks and LLMs.
