We observe that entropy in reinforcement learning functions analogously to the learning rate in LLMs. Maintaining stable entropy, as demonstrated in DAPO, helps stabilize RL training, while rapid entropy annealing (i.e., so-called entropy collapse) accelerates local performance improvement and enables faster convergence. We argue that these two processes are not antithetical, but can be effectively controlled and scheduled within a single training run, similar to learning rate scheduling. We propose Entropy Schduling (ES), which optimizes different pre-set goals (e.g. k in optimizing Pass@k) by controlling and scheduling entropy at each step of the RL process. We find that maintaining stable entropy early in training followed by entropy annealing achieves superior performance. Moreover, since stable-state entropy and annealed entropy exhibit distinctly different learning dynamics, curriculum learning can be seamlessly integrated to maximize model performance based on different entropy phases. We show that entropy scheduling is straightforward to implement and intuitive in design. Extensive experiments suggest that it delivers consistent and stable performance improvements across diverse models and algorithms.

With the rapid development of large language models (LLMs), it is highly demanded that LLMs can be adopted to make decisions to enable the artificial general intelligence. Most approaches leverage manually crafted examples to prompt the LLMs to imitate the decision process of human. However, designing optimal prompts is difficult and the patterned prompts can hardly be generalized to more complex environments. In this paper, we propose a novel model named Large Decision Model with Memory (LDM²), which leverages a dynamic memory mechanism to construct dynamic prompts, guiding the LLMs in making proper decisions according to the faced state. LDM² consists of two stages: memory formation and memory refinement. In the former stage, human behaviors are decomposed into state-action tuples utilizing the powerful summarizing ability of LLMs. Then, these tuples are stored in the memory, whose indices are generated by the LLMs, to facilitate the retrieval of the most relevant subset of memorized tuples based on the current state. In the latter stage, our LDM² employs tree exploration to discover more suitable decision processes and enrich the memory by adding valuable state-action tuples. The dynamic circle of exploration and memory enhancement provides LDM² a better understanding of the global environment. Extensive experiments conducted in two interactive environments have shown that our LDM² outperforms the baselines in terms of both score and success rate, which demonstrates its effectiveness.