  Due to privacy or commercial constraints, large pre-trained language models
(PLMs) are often offered as black-box APIs. Fine-tuning such models to
downstream tasks is challenging because one can neither access the model's
internal representations nor propagate gradients through it. This paper
addresses these challenges by developing techniques for adapting PLMs with only
API access. Building on recent work on soft prompt tuning, we develop methods
to tune the soft prompts without requiring gradient computation. Further, we
develop extensions that in addition to not requiring gradients also do not need
to access any internal representation of the PLM beyond the input embeddings.
Moreover, instead of learning a single prompt, our methods learn a distribution
over prompts allowing us to quantify predictive uncertainty. Ours is the first
work to consider uncertainty in prompts when only having API access to the PLM.
Finally, through extensive experiments, we carefully vet the proposed methods
and find them competitive with (and sometimes even improving on) gradient-based
approaches with full access to the PLM.
