Search arXivSearch

arXiv · 2510.16552

LANPO: Bootstrapping Language and Numerical Feedback for Reinforcement Learning in LLMs

Abstract

Reinforcement learning in large language models (LLMs) often relies on scalar rewards, a practice that discards valuable textual rationale buried in the rollouts, forcing the model to explore \textit{de novo} with each attempt and hindering sample efficiency. While LLMs can uniquely learn from language feedback provided in-context, naively integrating on-line experiences into RL training presents a paradox: feedback from the same problem risks information leakage and memorization, while feedback from different problems often leads to behavior collapse due to irrelevant context. To resolve this tension, we propose \textbf{Language-And-Numerical Policy Optimization (LANPO)}, a framework that cleanly separates the roles of feedback: language guides exploration, while numerical rewards drive optimization. LANPO builds a dynamic experience pool from past trials and introduces two principles to ensure feedback is effective: \emph{Reward-Agnostic Reflection} for safe intra-sample self-correction and \emph{Relevant Abstraction} to distill generalizable lessons from inter-sample experiences. Across mathematical reasoning benchmarks, LANPO enables 7B and 14B models to significantly outperform strong baselines trained with GRPO in test accuracy. Our work provides a robust method for integrating historical experiences into the LLM RL loop, creating more effective and data-efficient learning agents.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ang Li, Yifei Wang, Zhihang Yuan, Stefanie Jegelka, Yisen Wang. 2025-10-18. LANPO: Bootstrapping Language and Numerical Feedback for Reinforcement Learning in LLMs. https://arxiv.org/abs/2510.16552

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Online Regularized Statistical Learning in Reproducing Kernel Hilbert Space With Non-Stationary Data

We study recursive regularized learning algorithms in the reproducing kernel Hilbert space (RKHS) with non-stationary online data streams. We introduce the concept of a random Tikhonov regularization path and decompose the tracking error of the algorithm's output for the regularization path into random difference equations in RKHS. We show that the tracking error vanishes in mean square and almost surely if the regularization path is slowly time-varying. Then, leveraging the monotonicity of inverse operators and the spectral decomposition of compact operators, and introducing the RKHS persistence of excitation condition, we develop a dominated convergence method to prove the mean square and almost sure consistency between the regularization path and the unknown function to be learned. Especially, for independent and non-identically distributed data streams, the mean square and almost sure consistency between the algorithm's output and the unknown function is achieved if the input data's marginal probability measures are slowly time-varying and the average measure over each fixed-length time period is uniformly above a strictly positive finite Borel measure.

cs.LG

Reflective Policy Optimization

On-policy reinforcement learning methods, like Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO), often demand extensive data per update, leading to sample inefficiency. This paper introduces Reflective Policy Optimization (RPO), a novel on-policy extension that amalgamates past and future state-action information for policy optimization. This approach empowers the agent for introspection, allowing modifications to its actions within the current state. Theoretical analysis confirms that policy performance is monotonically improved and contracts the solution space, consequently expediting the convergence procedure. Empirical results demonstrate RPO's feasibility and efficacy in two reinforcement learning benchmarks, culminating in superior sample efficiency. The source code of this work is available at https://github.com/Edgargan/RPO.

cs.LG

Transductive Off-policy Proximal Policy Optimization

Proximal Policy Optimization (PPO) is a popular model-free reinforcement learning algorithm, esteemed for its simplicity and efficacy. However, due to its inherent on-policy nature, its proficiency in harnessing data from disparate policies is constrained. This paper introduces a novel off-policy extension to the original PPO method, christened Transductive Off-policy PPO (ToPPO). Herein, we provide theoretical justification for incorporating off-policy data in PPO training and prudent guidelines for its safe application. Our contribution includes a novel formulation of the policy improvement lower bound for prospective policies derived from off-policy data, accompanied by a computationally efficient mechanism to optimize this bound, underpinned by assurances of monotonic improvement. Comprehensive experimental results across six representative tasks underscore ToPPO's promising performance.

cs.LG