Low-rank representation learning has emerged as a powerful tool for recovering missing values in power load data due to its ability to exploit the inherent low-dimensional structures of spatiotemporal measurements. Among various techniques, low-rank factorization models are favoured for their efficiency and interpretability. However, their performance is highly sensitive to the choice of regularization parameters, which are typically fixed or manually tuned, resulting in limited generalization capability or slow convergence in practical scenarios. In this paper, we propose a Regularization-optimized Low-Rank Factorization, which introduces a Proportional-Integral-Derivative controller to adaptively adjust the regularization coefficient. Furthermore, we provide a detailed algorithmic complexity analysis, showing that our method preserves the computational efficiency of stochastic gradient descent while improving adaptivity. Experimental results on real-world power load datasets validate the superiority of our method in both imputation accuracy and training efficiency compared to existing baselines.