Search agents achieve strong question-answering performance through multi-turn interactions with search engines, with Group Relative Policy Optimization (GRPO) being a widely used training algorithm. However, GRPO-style algorithms still face several challenges in multi-hop search settings. First, correct intermediate steps are often penalized when the final answer is wrong. Second, training is highly unstable, often causing degradation of natural language ability or even catastrophic training collapse. Our analysis attributes these issues to coarse-grained advantage assignment and an imbalance between positive and negative advantages. To address these problems, we propose CalibAdv, an advantage calibration method specifically designed for search agents that enables more accurate and more stable modeling of penalties and rewards. Specifically, CalibAdv leverages the correctness of intermediate steps to downscale excessive negative advantages at a fine-grained level. It then further rebalances positive and negative advantages to improve training stability. Importantly, CalibAdv adopts a lightweight design that calibrates advantages from standard rollout signals, making it simple and easy to deploy. Extensive experiments across three models and seven benchmarks demonstrate that CalibAdv improves both model performance and training stability. Our code is available at https://github.com/wujwyi/CalibAdv.

Dense retrieval (DR) has become a mainstream approach to information seeking, where a system is required to return relevant information to a user query. In real-life applications, typoed queries resulting from the users’ mistyping words or phonetic typing errors exist widely in search behaviors. Current dense retrievers experience a significant drop in retrieval effectiveness when they encounter typoed queries. Therefore, the search system requires the extra introduction of spell-checkers to deal with typos and then applies the DR model to perform robust matching. Herein, we argue that directly conducting the typos correction training would be beneficial to make an end-to-end retriever against misspellings. To this end, we propose a novel approach that can facilitate the incorporation of the spelling correction objective into the DR model using the encoder-decoder architecture. During typos correction training, we also develop a prompt-based augmentation technique to enhance the DR space alignment of the typoed query and its original query. Extensive experiments demonstrate that the effectiveness of our proposed end-to-end retriever significantly outperforms existing typos-aware training approaches and sophisticated training advanced retrievers. Our code is available at https://github.com/striver314/ToCoTR.