  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 (LDM$^2$), which leverages a
dynamic memory mechanism to construct dynamic prompts, guiding the LLMs in
making proper decisions according to the faced state. LDM$^2$ 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 LDM$^2$ 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 LDM$^2$ a better
understanding of the global environment. Extensive experiments conducted in two
interactive environments have shown that our LDM$^2$ outperforms the baselines
in terms of both score and success rate, which demonstrates its effectiveness.
