To address the limitations of current digital halftoning algorithms， such as slow processing speed and suboptimal halftoning effects， a data-driven halftoning framework is proposed. By introducing the Gumbel-Softmax reparameterization strategy， the non-differentiability issue caused by discrete halftone selection is resolved， enabling unbiased gradient estimation during network backpropagation. To further enhance the halftoning effects， a novel blue noise loss function is designed to optimize the distribution of halftone dots. Additionally， a Patch-wise Confidence Aggregation module is introduced to incorporate spatial correlations between pixels， allowing the network to focus more on pixel interactions during training. Based on these strategies， a label-free， self-supervised， differentiable halftoning framework is constructed by optimizing the expected value of the halftone quality metric. Experimental results demonstrate that the proposed method， without requiring image labels， can generate high-quality halftone images and maintain high processing speed and low parameter complexity， effectively preserving local structural information and texture details. Moreover， this framework can be flexibly extended to multi-level halftoning to accommodate the requirements of multi-level printheads.