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

In recent years, advances in neural variational inference have achieved many successes in text processing. Examples include neural topic models which are typically built upon variational autoencoder (VAE) with an objective of minimising the error of reconstructing original documents based on the learned latent topic vectors. However, minimising reconstruction errors does not necessarily lead to high quality topics. In this paper, we borrow the idea of reinforcement learning and incorporate topic coherence measures as reward signals to guide the learning of a VAE-based topic model. Furthermore, our proposed model is able to automatically separating background words dynamically from topic words, thus eliminating the pre-processing step of filtering infrequent and/or top frequent words, typically required for learning traditional topic models. Experimental results on the 20 Newsgroups and the NIPS datasets show superior performance both on perplexity and topic coherence measure compared to state-of-the-art neural topic models.