I understand functional gradient descent algorithms implemented in mboost and coxboost. I am also under an impression (please correct me if this is wrong) that gbm and xgboost implement tree-based boosting, constrasting the ‘functional’ based boosting algorithms. The prediction output of both gbm and xgboost are the f(x) of the proportional hazard function h(t)= h_0 * exp(f(x)), in other words, the linear predictor of the cox model. This is different from other tree-based methods, say random forest, where the prediction output is the cumulative hazard distribution (non-parametric).

Thus I am looking for an exposition or references containing accessible explanations on how gbm/xgboost packages implement tree-based gradient descent algorithm in the context of survival data (specifically in relation to the cox models). I have a document (attached) from the gbm package with a description of the procedure, but I find it difficult to understand it as there were minimum explanations.

Any help/insights on this would be very much appreciated!