Large language models with search capabilities frequently exhibit miscalibrated confidence, producing incorrect answers with high certainty. We present Deliberative Searcher, a reasoning-primary framework that integrates search operations into chain-of-thought generation while maintaining explicit confidence calibration. Our method employs constrained reinforcement learning with adaptive Lagrangian multipliers to jointly optimize correctness and reliability. Experiments across five benchmarks demonstrate substantial improvements: our 7B model reduces average false-certain rates from 54% in baselines to 2%, while our 72B variant achieves competitive accuracy with closed-source models and reduces false-certain rates to 9%. The well-calibrated confidence scores also enable more efficient test-time compute: instead of standard majority voting, we use confidence-weighted aggregation and match the performance of 16-sample majority voting with only 4 samples, a 4× reduction in inference compute. These results establish calibrated confidence as a foundation for both trustworthy outputs and adaptive test-time compute, demonstrating the value of the proposed constrained RL framework in search-augmented language models.

Recent advances in Graphical User Interface (GUI) and embodied navigation have driven progress, yet these domains have largely evolved in isolation, with disparate datasets and training paradigms. In this paper, we observe that both tasks can be formulated as Markov Decision Processes (MDP), suggesting a foundational principle for their unification. Hence, we present NaviMaster, the first unified agent capable of unifying GUI navigation and embodied navigation within a single framework. Specifically, NaviMaster (i) proposes a visual-target trajectory collection pipeline that generates trajectories for both GUI and embodied tasks using a single formulation. (ii) employs a unified reinforcement learning framework on the mix data to improve generalization. (iii) designs a novel distance-aware reward to ensure efficient learning from the trajectories. Through extensive experiments on out-of-domain benchmarks, NaviMaster is shown to outperform state-of-the-art agents in GUI navigation, spatial affordance prediction, and embodied navigation. Ablation studies further demonstrate the efficacy of our unified training strategy, data mixing strategy, and reward design. Resources will be released to the community.

Recent advancements in large language models (LLMs) have shifted the post-training paradigm from traditional instruction tuning and human preference alignment toward reinforcement learning (RL) focused on reasoning capabilities. However, most current methods rely on rule-based evaluations of answer correctness, overlooking the importance of confidence-aware reasoning, especially for small to medium-sized models. These models often receive rewards for speculative answers without generating coherent reasoning chains. To address this limitation, we propose a novel confidence-based reward model tailored for enhancing STEM reasoning capabilities. Unlike conventional approaches, our model penalizes not only incorrect answers but also low-confidence correct responses, thereby promoting more robust and logically consistent reasoning. We validate the effectiveness of our approach through static evaluations, Best-of-N inference tests, and PPO-based RL training. Our method outperforms several state-of-the-art open-source reward models across diverse STEM benchmarks. We release our codes and model in https://github.com/qianxiHe147/C2RM.