Large language models (LLMs) have recently advanced in reasoning when optimized with reinforcement learning (RL) under verifiable rewards. Existing methods primarily rely on outcome-based supervision to strengthen internal LLM reasoning, often leading to inefficient exploration and sparse rewards. To mitigate this issue, we propose Expert-Assisted Policy Optimization (EAPO), a novel RL framework that enhances exploration by incorporating multi-turn interactions with external experts during training. Unlike prior methods, where policies reason in isolation, EAPO incentivizes the policy to adaptively determine when and how to consult experts, yielding richer reward signals and more reliable reasoning trajectories. External assistance ultimately internalizes expert knowledge into the policy model, amplifying the model's inherent reasoning capabilities. During evaluation, the policy model has been well-optimized to solve questions independently, producing improved reasoning paths and more accurate solutions. Experiments on mathematical reasoning benchmarks, including AIME 2024, AIME 2025, and AIMO 2025, show that EAPO consistently outperforms expert-assisted workflow, expert-distilled models, and RL baselines, with an average gain of 5 points over self-exploratory models.

Entropy Regularisation is a widely adopted technique that enhances policy optimisation performance and stability. A notable form of entropy regularisation is augmenting the objective with an entropy term, thereby simultaneously optimising the expected return and the entropy. This framework, known as maximum entropy reinforcement learning (MaxEnt RL), has shown theoretical and empirical successes. However, its practical application in straightforward on-policy actor-critic settings remains surprisingly underexplored. We hypothesise that this is due to the difficulty of managing the entropy reward in practice. This paper proposes a simple method of separating the entropy objective from the MaxEnt RL objective, which facilitates the implementation of MaxEnt RL in on-policy settings. Our empirical evaluations demonstrate that extending Proximal Policy Optimisation (PPO) and Trust Region Policy Optimisation (TRPO) within the MaxEnt framework improves policy optimisation performance in both MuJoCo and Procgen tasks. Additionally, our results highlight MaxEnt RL's capacity to enhance generalisation.