Teaching large language models (LLMs) to be faithful in the provided context is crucial for building reliable information-seeking systems. Therefore, we propose a systematic framework, CANOE, to reduce faithfulness hallucinations of LLMs across different downstream tasks without human annotations. Specifically, we first synthesize short-form question-answering (QA) data with four diverse tasks to construct high-quality and easily verifiable training data without human annotation. Also, we propose Dual-GRPO, a rule-based reinforcement learning method that includes three tailored rule-based rewards derived from synthesized short-form QA data, while simultaneously optimizing both short-form and long-form response generation. Notably, Dual-GRPO eliminates the need to manually label preference data to train reward models and avoids over-optimizing short-form generation when relying only on the synthesized short-form QA data. Experimental results show that CANOE greatly improves the faithfulness of LLMs across 11 different tasks, even outperforming the most advanced LLMs, e.g., GPT-4o and OpenAI o1.