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Providing natural language instructions in prompts is a useful new paradigm for improving task performance of large language models in a zero-shot setting. Recent work has aimed to improve such prompts via manual rewriting or gradient-based tuning. However, manual rewriting is time-consuming and requires subjective interpretation, while gradient-based tuning can be extremely computationally demanding for large models and may not be feasible for API-based models. In this work, we introduce Gradient-free Instructional Prompt Search (GrIPS), a gradient-free, edit-based search approach for improving task instructions for large language models. GrIPS takes in instructions designed for humans and automatically returns an improved, edited prompt, while allowing for API-based tuning. With InstructGPT models, GrIPS improves the average task performance by up to 4.30 percentage points on eight classification tasks from the Natural Instructions dataset (with similar improvements for OPT, BLOOM, and FLAN-T5). We see improvements for both instruction-only prompts and instruction + k-shot examples prompts. Notably, GrIPS outperforms manual rewriting and purely example-based prompts while controlling for the available compute and data budget. Further, performance of GrIPS is comparable to select gradient-based tuning approaches. Qualitatively, we show our edits can simplify instructions and at times make them incoherent but nonetheless improve accuracy. Our code is available at: https://github.com/archiki/GrIPS