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

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 ℓ 0 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.