Free Energy-Driven Reinforcement Learning with Adaptive Advantage Shaping for Unsupervised Reasoning in LLMs

ACL ARR 2026 January Submission221 Authors

Keywords: Unsupervised Reinforcement Learning, Free Energy Principle, Large Language Models

Abstract: Unsupervised reinforcement learning (RL) has emerged as a promising paradigm for enabling self-improvement in large language models (LLMs). However, existing unsupervised RL-based methods often lack the capacity to adapt to the model's evolving reasoning capabilities during training. Therefore, these methods can misdirect policy optimization in the absence of ground-truth supervision. To address this issue, we introduce FREIA, a novel RL-based algorithm built on two key innovations: (1) Free Energy-Driven Reward (FER) adapts rewards to balance consensus and exploration based on the Free Energy Principle. (2) Adaptive Advantage Shaping (AAS) adaptively adjusts learning signals based on the statistical characteristics of sampled rewards. Empirical evaluations on nine datasets across three reasoning tasks showcase that FREIA outperforms other unsupervised RL-based baselines. Notably, in mathematical reasoning tasks, FREIA surpasses other methods by an average of 0.5 to 3.5 points in Pass@1 using the DeepSeek-R1-Distill-Qwen-1.5B model.

Paper Type: Long

Research Area: Mathematical, Symbolic, Neurosymbolic, and Logical Reasoning

Research Area Keywords: Mathematical reasoning

Contribution Types: NLP engineering experiment, Publicly available software and/or pre-trained models

Languages Studied: English

Submission Number: 221