  Most downstream adaptation methods tune all or part of the parameters of
pre-trained models (PTMs) through gradient descent, where the tuning cost
increases linearly with the growth of the model size. By contrast,
gradient-free methods only require the forward computation of the PTM to tune
the prompt, retaining the benefits of efficient tuning and deployment. Though,
past work on gradient-free tuning often introduces gradient descent to seek a
good initialization of prompt and lacks versatility across tasks and PTMs. In
this paper, we present BBTv2, an improved version of Black-Box Tuning, to drive
PTMs for few-shot learning. We prepend continuous prompts to every layer of the
PTM and propose a divide-and-conquer gradient-free algorithm to optimize the
prompts at different layers alternately. Extensive experiments across various
tasks and PTMs show that BBTv2 can achieve comparable performance to full model
tuning and state-of-the-art parameter-efficient methods (e.g., Adapter, LoRA,
BitFit, etc.) under few-shot settings while maintaining much fewer tunable
parameters.
