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

TL;DR

FREIA introduces a novel unsupervised reinforcement learning algorithm for large language models that adaptively shapes rewards and advantages to improve reasoning capabilities.

Contribution

The paper proposes FREIA, combining Free Energy-Driven Reward and Adaptive Advantage Shaping to enhance unsupervised RL in LLMs, addressing adaptation issues during training.

Findings

FREIA outperforms baseline methods on nine reasoning datasets.

In mathematical reasoning, FREIA exceeds others by 0.5 to 3.5 points in Pass@1.

Empirical results demonstrate improved reasoning accuracy with FREIA.

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.