让大模型通过自我激励迭代优化搜索能力，提升复杂问题求解准确率。

Large language models (LLMs) have been widely integrated into information retrieval to advance traditional techniques. However, effectively enabling LLMs to seek accurate knowledge in complex tasks remains a challenge due to the complexity of multi-hop queries as well as the irrelevant retrieved content. To address these limitations, we propose EXSEARCH, an agentic search framework, where the LLM learns to retrieve useful information as the reasoning unfolds through a self-incentivized process. At each step, the LLM decides what to retrieve (thinking), triggers an external retriever (search), and extracts fine-grained evidence (recording) to support next-step reasoning. To enable LLM with this capability, EXSEARCH adopts a Generalized Expectation-Maximization algorithm. In the E-step, the LLM generates multiple search trajectories and assigns an importance weight to each; the M-step trains the LLM on them with a re-weighted loss function. This creates a self-incentivized loop, where the LLM iteratively learns from its own generated data, progressively improving itself for search. We further theoretically analyze this training process, establishing convergence guarantees. Extensive experiments on four knowledge-intensive benchmarks show that EXSEARCH substantially outperforms baselines, e.g., +7.8% improvement on exact match score. Motivated by these promising results, we introduce EXSEARCH-Zoo, an extension that extends our method to broader scenarios, to facilitate future work.