Direct Alignment Algorithms (DAAs) such as DPO simplify RLHF by optimizing policies directly from preference pairs.However, the Bradley-Terry probability-gap objective can induce likelihood displacement and, under weak KL constraints, may even reduce the probability of preferred responses, while implicit rewards can be limited in generalization.We propose Reward Alignment Optimization (RAO), a point-wise direct alignment method that uses an explicit reward model to specify exact target generation probabilities and align the policy offline towards them.Our key insight is a theoretical principle we call "prefix consistency", which links the normalization terms of prompts that share a prefix.Leveraging this property, RAO decouples target reward differentials from bias terms, prevents decreasing preferred-response probabilities, and better exploits reward information both within and across prompts.Extensive experiments on multiple base LLMs show that RAO consistently outperforms existing DAAs while enabling controllable target probability distributions.

Reasoning large language models (LLMs) excel in complex tasks, which has drawn significant attention to reinforcement learning (RL) for LLMs. However, existing approaches allocate an equal number of rollouts to all questions during the RL process, which is inefficient. This inefficiency stems from the fact that training on simple questions yields limited gains, whereas more rollouts are needed for challenging questions to sample correct answers. Furthermore, while RL improves response precision, it limits the model’s exploration ability, potentially resulting in a performance cap below that of the base model prior to RL. To address these issues, we propose a mechanism for dynamically allocating rollout budgets based on the difficulty of the problems, enabling more efficient RL training. Additionally, we introduce an adaptive dynamic temperature adjustment strategy to maintain the entropy at a stable level, thereby encouraging sufficient exploration. This enables LLMs to improve response precision while preserving their exploratory ability to uncover potential correct pathways. The code and data is available on: https://anonymous.4open.science/r/E3-RL4LLMs-DB28