Sea ice, crucial to the Arctic and Earth's climate, requires consistent monitoring and high-resolution mapping. Manual sea ice mapping, however, is time-consuming and subjective, prompting the need for automated deep learning-based classification approaches. However, training these algorithms is challenging because expert-generated ice charts, commonly used as training data, do not map single ice types but instead map polygons with multiple ice types. Moreover, the distribution of various ice types in these charts is frequently imbalanced, resulting in a performance bias towards the dominant class. In this paper, we present a novel GeoAI approach to training sea ice classification by formalizing it as a partial label learning task with explicit confidence scores to address multiple labels and class imbalance. We treat the polygon-level labels as candidate partial labels, assign the corresponding ice concentrations as confidence scores to each candidate label, and integrate them with focal loss to train a Convolutional Neural Network (CNN). Our proposed approach leads to enhanced performance for sea ice classification in Sentinel-1 dual-polarized SAR images, improving classification accuracy (from 87% to 92%) and weighted average F-1 score (from 90% to 93%) compared to the conventional training approach of using one-hot encoded labels and Categorical CrossEntropy loss. It also improves the F-1 score in 4 out of the 6 sea ice classes.