Subspace Selection based Prompt Tuning with Nonconvex Nonsmooth Black-Box Optimization

Haozhen Zhang, Hualin Zhang, Bin Gu, Yi Chang

Abstract: In this paper, we introduce a novel framework for black-box prompt tuning with a subspace learning and selection strategy, leveraging derivative-free optimization algorithms. This approach is crucial for scenarios where user interaction with language models is restricted to API usage, without direct access to their internal structures or gradients, a situation typical in Language-Model-as-a-Service (LMaaS). Our framework focuses on exploring the low-dimensional subspace of continuous prompts. Previous work on black-box prompt tuning necessitates a substantial number of API calls due to the random choice of the subspace. To tackle this problem, we propose to use a simple zeroth-order optimization algorithm to tackle nonconvex optimization challenges with nonsmooth nonconvex regularizers: the Zeroth-Order Mini-Batch Stochastic Proximal Gradient method (ZO-MB-SPG). A key innovation is the incorporation of nonsmooth nonconvex regularizers, including the indicator function of the l0 constraint, which enhances our ability to select optimal subspaces for prompt optimization. The experimental results show that our proposed black-box prompt tuning method on a few labeled samples can attain similar performance to the methods applicable to LMaaS with much fewer API calls.