This paper explores the potential of large language models (LLMs) to generate hypotheses, particularly based on labeled examples. The authors propose HypoGeniC, an algorithm that iteratively updates hypotheses to improve their quality. Inspired by multi-armed bandits, the algorithm uses a reward function to balance exploration and exploitation. HypoGeniC outperforms few-shot prompting in classification tasks, improving accuracy by 31.7% on a synthetic dataset and 13.9%, 3.3%, and 24.9% on three real-world datasets. The generated hypotheses not only corroborate existing theories but also uncover new insights, demonstrating the algorithm's ability to discover novel knowledge. The paper also discusses the generalizability of the generated hypotheses across different LLMs and out-of-distribution datasets, showing consistent performance. The authors conclude that HypoGeniC is a robust method for generating high-quality hypotheses, which can be applied to complex social science tasks and potentially to natural sciences.This paper explores the potential of large language models (LLMs) to generate hypotheses, particularly based on labeled examples. The authors propose HypoGeniC, an algorithm that iteratively updates hypotheses to improve their quality. Inspired by multi-armed bandits, the algorithm uses a reward function to balance exploration and exploitation. HypoGeniC outperforms few-shot prompting in classification tasks, improving accuracy by 31.7% on a synthetic dataset and 13.9%, 3.3%, and 24.9% on three real-world datasets. The generated hypotheses not only corroborate existing theories but also uncover new insights, demonstrating the algorithm's ability to discover novel knowledge. The paper also discusses the generalizability of the generated hypotheses across different LLMs and out-of-distribution datasets, showing consistent performance. The authors conclude that HypoGeniC is a robust method for generating high-quality hypotheses, which can be applied to complex social science tasks and potentially to natural sciences.