[POC] Experimental support for l1 error. (#7812)

Support adaptive tree, a feature supported by both sklearn and lightgbm.  The tree leaf is recomputed based on residue of labels and predictions after construction.

For l1 error, the optimal value is the median (50 percentile).

This is marked as experimental support for the following reasons:
- The value is not well defined for distributed training, where we might have empty leaves for local workers. Right now I just use the original leaf value for computing the average with other workers, which might cause significant errors.
- Some follow-ups are required, for exact, pruner, and optimization for quantile function. Also, we need to calculate the initial estimation.

plugin/example/custom_obj.cc

@@ -1,5 +1,5 @@
 /*!
- * Copyright 2015-2019 by Contributors
+ * Copyright 2015-2022 by Contributors
  * \file custom_metric.cc
  * \brief This is an example to define plugin of xgboost.
  *  This plugin defines the additional metric function.
@@ -31,13 +31,9 @@ DMLC_REGISTER_PARAMETER(MyLogisticParam);
 // Implement the interface.
 class MyLogistic : public ObjFunction {
  public:
-  void Configure(const std::vector<std::pair<std::string, std::string> >& args) override {
-    param_.UpdateAllowUnknown(args);
-  }
+  void Configure(const Args& args) override { param_.UpdateAllowUnknown(args); }
 
-  struct ObjInfo Task() const override {
-    return {ObjInfo::kRegression, false};
-  }
+  ObjInfo Task() const override { return ObjInfo::kRegression; }
 
   void GetGradient(const HostDeviceVector<bst_float> &preds,
                    const MetaInfo &info,