Hybrid Reward Normalization for Process-supervised Non-verifiable Agentic Tasks

Large Language Models (LLMs) increasingly rely on external tools such as search engines to solve complex agentic tasks that require reasoning and external knowledge retrieval. Recently, reinforcement learning with verifiable rewards (RL VR) has demonstrated its effectiveness in advancing capabilities of LLMs by rewarding the final answers via outcome rewards. While straightforward to supervise, outcome rewards only provide sparse signals and delayed feedback, which limits their effectiveness on long trajectories. Process rewards address this by evaluating intermediate steps, providing fine-grained supervision and encouraging grounded problem solving. However, it is notoriously hard to annotate step-wise labels, especially in non-verifiable process without "golden" answers. Furthermore, stepwise judgment requires the balance between local quality with contribution to the final outcome, as optimizing towards higher process reward may not always align with better final outcomes. To address the above challenges, we introduce Principle Process Reward (PPR), an RL approach that unifies principled step-level assessment and outcome verification. We train a principle-based reward model to improve the transparency and reliability of process evaluation, and further introduce a Reward Normalization (ReNorm) strategy to calibrate outcome and process rewards. Experiment results show that PPR achieves state-of-the-art performance across a wide range of benchmarks, demonstrating its impressive robustness and generalization. Our code and model collection is available in this link.Figure 1: Performance of PPR on various benchmarks with other baselines Large Language Models (LLMs) have achieved remarkable progress across a wide range of tasks, from open-domain question answering to multi-step reasoning (Guo et al., 2025; OpenAI, 2025b; Comanici et al., 2025). A key factor for success is their abilities to leverage external tools such as search engines, calculators, code interpreters, and browsers (DeepMind, 2025; Guo et al., 2024; OpenAI, 2025a). In particular, the search engine is a linchpin tool that provides verifiable and up-to-date knowledge for LLMs, helping to ground their answers and reduce hallucinations. However, training LLM agents to leverage tools effectively still remains challenging, as the complex behavior involving task decomposition, query generation, information aggregation, and stopping decisions.