Lean4AgenticRL: Advancing Agentic RL with Verifiable Multi-level Process Rewards

Equipping Large Language Models (LLMs) to execute reliable multi-step workflows has become a central challenge in artificial intelligence. Despite recent advances in LLMs' agentic capabilities, most agent systems still lack formal methods for specifying, verifying, and debugging their workflow and execution trajectories. This challenge mirrors a long-standing problem in mathematics, where the ambiguity of natural languages (NLs) motivates the development of formal languages (FLs). Inspired by this paradigm, we propose Lean4Agent, to the best of our knowledge, the first framework that uses Lean4, a dependent-type FL to model and verify agent behavior. Lean4Agent launches FormalAgentLib, an extensible Lean4 library for formally modeling and verifying agent workflows' semantic consistency under explicit assumptions, and enabling localization of execution-time failures revealed by trajectories. Building on FormalAgentLib, we further develop LeanEvolve, which applies results in FormalAgentLib to revise workflows to enhance its capability. Extensive experiments on a hard problem subset of SWE-Bench-Verified and a subset of ELAIP-Bench across 5 leading LLMs indicate that the verification-passing workflows outperform the failing ones by an average of 11.94%, and LeanEvolve further improves SWE performance by 7.47% on average. Furthermore, Lean4Agent establishes a foundation for a new field of using expressive dependent-type FL to formally model and verify agent behavior.

Reinforcement learning from verifiable rewards (RLVR) has improved the reasoning capabilities of large language models (LLMs), yet existing approaches predominantly rely on sparse outcome-level feedback, posing a substantial credit-assignment challenge in long-horizon agentic tasks. In this work, we study structured agentic reasoning problems that admit symbolic or algorithmic task-solving oracles. We propose Verifiable Process Rewards (VPR), a training framework that repurposes such task oracles as action-level process verifiers, providing dense rewards for intermediate actions and enabling fine-grained credit assignment. We instantiate VPR in three distinct settings: a search-based oracle for Sokoban, a constraint-based oracle for Sudoku, and a posterior-based oracle for Minesweeper. To optimize policies with these rewards, we introduce oracle-guided state-group rollout and locally normalized optimization. Empirically, VPR-trained Qwen3-4B outperforms outcome-reward GRPO and VinePPO across all three training environments. When jointly trained on math data and all three game environments, VPR achieves the highest average general-reasoning performance and strongest agentic results among the compared training configurations. To further assess its applicability to more general agentic tool-use settings, we apply VPR-style action-level supervision to $τ^2$-bench using an expert LLM as a reference policy and observe improved performance over outcome-reward GRPO on held-out tasks. Together, these results position VPR as a promising approach for leveraging reliable task oracles to improve agentic reasoning, while highlighting its dependence on the availability and reliability of task oracles and the challenge of extending intermediate verification to less structured, open-ended environments.

Reinforcement Learning (RL) has traditionally focused on training specialized agents to optimize predefined reward functions within narrowly defined environments. However, the advent of powerful Large Language Models (LLMs) and increasingly complex, open-ended tasks has catalyzed a paradigm shift towards agentic paradigms within RL. This emerging framework extends beyond traditional RL by emphasizing the development of autonomous agents capable of goal-setting, long-term planning, dynamic strategy adaptation, and interactive reasoning in uncertain, real-world environments. Unlike conventional approaches that rely heavily on static objectives and episodic interactions, LLM-based Agentic RL incorporates cognitive-like capabilities such as meta-reasoning, self-reflection, and multi-step decision-making directly into the learning loop. In this paper, we provide a deep insight for looking the conceptual foundations, methodological innovations, and effective designs underlying this trend. Furthermore, we identify critical challenges and outline promising future directions for building LLM-based Agentic RL.