Research on Memory Algorithm Based on Time Series Model and Reinforcement Learning

ABSTRACT Spaced repetition is a highly effective method of memorization that helps learners to remember large amounts of content efficiently. This paper presents a spaced repetition framework integrating time‐series modelling with reinforcement learning. We propose the GLD‐HLR model, which utilizes Discrete Cosine Transform (DCT) to decouple multi‐scale temporal features in the frequency domain and a Legendre Projection Unit (LPU) to represent continuous memory trajectories via orthogonal basis functions. This architecture significantly reduces computational complexity while enhancing responsiveness to non‐linear memory changes. Furthermore, a PPO‐MMC algorithm is developed to optimize review intervals within a continuous state space. By achieving joint learning of memory prediction and policy scheduling, the framework effectively minimizes review costs while maximizing long‐term retention. This paper validated through ablation and comparative experiments that the mean absolute error (MAE) of the GLD‐HLR model's recall probability predictions remained below 0.03, achieving at least a 4% reduction compared to the LSTM‐HLR model. The mean absolute percentage error (MAPE) for half‐life predictions was below 0.2, which is smaller than the prediction errors of all other models. The PPO‐MMC algorithm achieved a cumulative number of words learned (WTL) exceeding 8000 within 1000 days, with the number of words memorized at the target half‐life (THR) surpassing 7000. This indicates that the algorithm can efficiently help learners master a large number of vocabulary words within a limited time frame and achieve long‐term retention.