[D] Regression with examples of wrong answers • r/MachineLearning

Consider a regression problem of approximating f(x): Rn Rm when we have two datasets: a set of correct answers corresponding to a typical regression dataset, and an additional set of wrong answers. For a wrong answer ( xi, yi), we only know that the output of f( xi) shouldn't be yi . How can we incorporate this knowledge into the regression? We can add to the loss function a term -( yi - yhati)2 rewarding the model for yielding results far away from the negative examples. But then we'd need to somehow clamp/saturate this reward and add regularization to avoid sending the model output to infinity. This adds hyperparameters and doesn't have any clear theoretical justification.