[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.

tests/cpp/predictor/test_cpu_predictor.cc

@@ -1,5 +1,5 @@
 /*!
- * Copyright 2017-2020 XGBoost contributors
+ * Copyright 2017-2022 XGBoost contributors
  */
 #include <dmlc/filesystem.h>
 #include <gtest/gtest.h>
@@ -222,7 +222,7 @@ void TestUpdatePredictionCache(bool use_subsampling) {
   PredictionCacheEntry predtion_cache;
   predtion_cache.predictions.Resize(kRows*kClasses, 0);
   // after one training iteration predtion_cache is filled with cached in QuantileHistMaker::Builder prediction values
-  gbm->DoBoost(dmat.get(), &gpair, &predtion_cache);
+  gbm->DoBoost(dmat.get(), &gpair, &predtion_cache, nullptr);
 
   PredictionCacheEntry out_predictions;
   // perform fair prediction on the same input data, should be equal to cached result