Construction of embankments over soft soils is associated with consolidation settlement and instability. The combined use of geocells and floating piles is an effective solution; however, the lack of explicit design relationships has limited its widespread application. In this study, the behavior of a geocell-reinforced embankment supported by floating piles was investigated using three-dimensional finite element modeling with a unit cell approach under static effective stress analysis considering soil-water interaction. For the soft subgrade, the Mohr-Coulomb model with effective parameters (c' and φ') was employed. Using Latin hypercube sampling, a database comprising 749 samples and 15 effective input parameters was generated, and six key system responses were considered. Five machine learning algorithms were evaluated. The results showed that second-order ridge regression, with a coefficient of determination of 0.987 for subgrade vertical stress and 0.982 for vertical settlements, provides the most accurate and stable prediction and enables the extraction of approximate algebraic relationships for preliminary design. Parameter importance analysis indicated that geometric properties and component stiffness play a dominant role; embankment height, pile length, and geocell position had the greatest influence on subgrade vertical stress, stress concentration ratio, and geocell horizontal stress, respectively. The parametric study revealed optimal thresholds for geocell thickness, geocell modulus, and pile modulus. Within the range of the studied parameters, the proposed relationships can serve as an efficient tool for preliminary analyses and sensitivity assessment; however, their application outside this range requires validation and model retraining.