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The increasing scale of general-purpose Pre-trained Language Models (PLMs) necessitates the study of more efficient adaptation across different downstream tasks. In this paper, we establish a Black-box Discrete Prompt Learning (BDPL) to resonate with pragmatic interactions between the cloud infrastructure and edge devices. Particularly, instead of fine-tuning the model in the cloud, we adapt PLMs by prompt learning, which efficiently optimizes only a few parameters of the discrete prompts. Moreover, we consider the scenario that we do not have access to the parameters and gradients of the pre-trained models, except for its outputs given inputs. This black-box setting secures the cloud infrastructure from potential attack and misuse to cause a single-point failure, which is preferable to the white-box counterpart by current infrastructures. Under this black-box constraint, we apply a variance-reduced policy gradient algorithm to estimate the gradients of parameters in the categorical distribution of each discrete prompt. In light of our method, the user devices can efficiently tune their tasks by querying the PLMs bounded by a range of API calls. Our experiments on RoBERTa and GPT-3 demonstrate that the proposed algorithm achieves significant improvement on eight benchmarks in a cloud-device collaboration manner. Finally, we conduct in-depth case studies to comprehensively analyze our method in terms of various data sizes, prompt lengths, training budgets, optimization objectives, prompt transferability, and explanations of the learned prompts. Our code will be available at https://github.com/shizhediao/Black-Box-Prompt-Learning.