The development of the Internet of Things (IoT) has brought great convenience to people. However, some information security problems such as privacy leakage are caused by communicating with risky users. It is a challenge to choose reliable users with which to interact in the IoT. Therefore, trust plays a crucial role in the IoT because trust may avoid some risks. Agents usually choose reliable users with high trust to maximize their own interests based on reinforcement learning. However, trust propagation is time-consuming, and trust changes with the interaction process in social networks. To track the dynamic changes in trust values, a dynamic trust inference algorithm named Dynamic Double DQN Trust (Dy-DDQNTrust) is proposed to predict the indirect trust values of two users without direct contact with each other. The proposed algorithm simulates the interactions among users by double DQN. Firstly, CurrentNet and TargetNet networks are used to select users for interaction. The users with high trust are chosen to interact in future iterations. Secondly, the trust value is updated dynamically until a reliable trust path is found according to the result of the interaction. Finally, the trust value between indirect users is inferred by aggregating the opinions from multiple users through a Modified Collaborative Filtering Average-based Similarity (SMCFAvg) aggregation strategy. Experiments are carried out on the FilmTrust and the Epinions datasets. Compared with TidalTrust, MoleTrust, DDQNTrust, DyTrust and Dynamic Weighted Heuristic trust path Search algorithm (DWHS), our dynamic trust inference algorithm has higher prediction accuracy and better scalability.