Title: PromptSum: Planning with Mixed Prompts for Parameter-Efficient Controllable Abstractive Summarization. Abstract: Prompt tuning (PT), a technique that only tunes the additional prompt embeddings while keeping the backbone pretrained language model frozen, has shown promising results in language understanding tasks, especially in low-resource scenarios. However, there lacks better prompt design methods for generation tasks such as summarization. At the same time, summarization guided through instructions (discrete prompts) can achieve a desirable double objective of higher quality and controllability in summary generation. Towards a triple goal of data-efficiency, parameter-efficiency and controllability, we introduce PromptSum, a method combining PT with a multi-task objective and discrete entity prompts for abstractive summarization. Our model achieves state-of-the-art results on several popular few-shot benchmarks as well as a strong level of controllability through entities, all while only tuning several orders of magnitude less parameters.