Personalized Learning Path Identification and Multi-Objective Optimization Based on Knowledge-Tracing State Estimation and Constrained Reinforcement Learning

To address the difficulty of simultaneously considering knowledge state, forgetting risk, and pedagogical constraints in personalized learning-path recommendation, this study proposes KTS-CMORL, a knowledge-tracing state-estimation and constrained multi-objective reinforcement-learning framework. KTS-CMORL-KT denotes only the knowledge-tracing state-estimation submodule, whereas KTS-CMORL denotes the complete learning-path optimization framework. The model integrates resource semantics, response performance, behavioral features, time intervals, and knowledge-graph relations to estimate knowledge mastery, forgetting risk, and state uncertainty. Feasible paths are identified through knowledge-gap detection, prerequisite backtracking, review-node insertion, and action masking, while knowledge gain, long-term retention, learning efficiency, and engagement are optimized under constraints on time budget, cognitive load, difficulty fluctuation, and resource repetition. State-estimation performance is evaluated on real learner-interaction records from RACE-H and Zhixue, whereas path recommendation and constrained optimization are evaluated through offline learning-path simulations driven by a frozen GRU learner simulator trained on real logs. Compared with AKT, AUC increases by 2.2 percentage points; compared with RFKT, AUC and ACC increase by 1.3 and 1.0 percentage points, respectively. Relative to ELPR-DARL, NDCG@10, HR@10, and knowledge coverage increase by 2.7, 3.6, and 6.8 percentage points, respectively. Relative to MORL, HV improves by 9.2%, while the overall constraint violation rate decreases from 12.8% to 1.8%. These results demonstrate the effectiveness of the proposed framework in real-data state estimation and simulation-based path optimization.