[Breaking] Don't drop trees during DART prediction by default (#5115)

* Simplify DropTrees calling logic

* Add `training` parameter for prediction method.

* [Breaking]: Add `training` to C API.

* Change for R and Python custom objective.

* Correct comment.

Co-authored-by: Philip Hyunsu Cho <chohyu01@cs.washington.edu>
Co-authored-by: Jiaming Yuan <jm.yuan@outlook.com>

include/xgboost/c_api.h

@@ -416,6 +416,7 @@ XGB_DLL int XGBoosterEvalOneIter(BoosterHandle handle,
  *          4:output feature contributions to individual predictions
  * \param ntree_limit limit number of trees used for prediction, this is only valid for boosted trees
  *    when the parameter is set to 0, we will use all the trees
+ * \param training Whether the prediction value is used for training.
  * \param out_len used to store length of returning result
  * \param out_result used to set a pointer to array
  * \return 0 when success, -1 when failure happens
@@ -424,6 +425,7 @@ XGB_DLL int XGBoosterPredict(BoosterHandle handle,
                              DMatrixHandle dmat,
                              int option_mask,
                              unsigned ntree_limit,
+                             int training,
                              bst_ulong *out_len,
                              const float **out_result);
 /*

include/xgboost/gbm.h

@@ -84,6 +84,7 @@ class GradientBooster : public Model, public Configurable {
    */
   virtual void PredictBatch(DMatrix* dmat,
                             HostDeviceVector<bst_float>* out_preds,
+                            bool training,
                             unsigned ntree_limit = 0) = 0;
   /*!
    * \brief online prediction function, predict score for one instance at a time

include/xgboost/learner.h

@@ -96,6 +96,7 @@ class Learner : public Model, public Configurable, public rabit::Serializable {
                        bool output_margin,
                        HostDeviceVector<bst_float> *out_preds,
                        unsigned ntree_limit = 0,
+                       bool training = false,
                        bool pred_leaf = false,
                        bool pred_contribs = false,
                        bool approx_contribs = false,