This chapter addresses the challenge of expensive evaluations in hyper-parameter optimization by introducing a multi-fidelity optimization approach. Hyper-parameter optimization often involves time-consuming evaluations, especially with large datasets or complex models. The chapter proposes a method that combines low-fidelity evaluations (using subsets of data) with high-fidelity evaluations (using full datasets) to accelerate the optimization process. A key innovation is the Transfer Series Expansion (TSE) algorithm, which predicts the residual between low and high-fidelity evaluations, allowing for efficient optimization with fewer costly evaluations. The chapter presents the TseSRacos algorithm, which integrates TSE with the SRacos optimization framework. Empirical studies on LightGBM hyper-parameter optimization tasks demonstrate that the proposed method significantly reduces evaluation time while maintaining high optimization performance. The results highlight the effectiveness of multi-fidelity optimization in improving efficiency, particularly for large-scale datasets. The chapter concludes that TSE-based multi-fidelity optimization is a powerful tool for accelerating hyper-parameter tuning in machine learning.