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The target of my current neural network is to predict a label. The dataset contains some features, there is a label $y_i$ in transaction $i$, indicating its classification. There is one feature $f^{i}_j$ can be used while training and is not available in deployment (this is very common in real-world applications). I consider this feature as a constraint value because the real label $y_i$ must be subject to some constraint function, for example, $y_i <= \mathbf{C}(f_j)$ where $\mathbf{C}(\cdot)$ is a constraint function.

My question is if I consider it as a constrained optimization problem? How can I get started? Could you please provide some helpful papers? Or if I consider the feature as an auxiliary feature, how can I leverage it?

Another perspective is to consider the $f^{i}_j$ as a prior, and the target is to maximize the posterior of the label prediction $\hat{y}_i$.

Thank you very much.

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