Convergence issue under pseudo-huber loss for simple experiment data
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Hi, I am recently conducting some numerical experiments for a new tree boosting trick. I designed a simple example for robust regression, in which there are three data points involved: (1.2, 1.5, 2.3, 100), (1.2, 1.5, 2.3, 300), and (1.2, 1.5, 2.3, 1000). The heading 3 value are features, and the last value is the regression target. I applied XGBoost with pseudo-huber error to fit this data, with huber-delta set as 1. Since pseudo-huber error is a smoothing variant of absolute-error, so the fitted value is expected to be around 300. However, no matter how hard I tried(e.g. by tuning the regularization weight lambda as well as the learning rate), the fitted value was consistently stuck in a large number, even when there were just a few boosting iterations and large regularization weights were applied. Since the gradient of pseudo-huber error is bounded in absolute value by the huber-delta, this phenomenon was quite unexpected. Does anyone know how to resolve this issue?
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