Rework the NDCG objective.

R-package/src/Makevars.in

@@ -33,6 +33,7 @@ OBJECTS= \
     $(PKGROOT)/src/objective/regression_obj.o \
     $(PKGROOT)/src/objective/multiclass_obj.o \
     $(PKGROOT)/src/objective/rank_obj.o \
+    $(PKGROOT)/src/objective/lambdarank_obj.o \
     $(PKGROOT)/src/objective/hinge.o \
     $(PKGROOT)/src/objective/aft_obj.o \
     $(PKGROOT)/src/objective/adaptive.o \

R-package/src/Makevars.win

@@ -33,6 +33,7 @@ OBJECTS= \
     $(PKGROOT)/src/objective/regression_obj.o \
     $(PKGROOT)/src/objective/multiclass_obj.o \
     $(PKGROOT)/src/objective/rank_obj.o \
+    $(PKGROOT)/src/objective/lambdarank_obj.o \
     $(PKGROOT)/src/objective/hinge.o \
     $(PKGROOT)/src/objective/aft_obj.o \
     $(PKGROOT)/src/objective/adaptive.o \

src/common/math.h

@@ -1,22 +1,25 @@
-/*!
- * Copyright 2015 by Contributors
+/**
+ * Copyright 2015-2023 by XGBoost Contributors
  * \file math.h
  * \brief additional math utils
  * \author Tianqi Chen
  */
 #ifndef XGBOOST_COMMON_MATH_H_
 #define XGBOOST_COMMON_MATH_H_
 
-#include <xgboost/base.h>
+#include <xgboost/base.h>  // for XGBOOST_DEVICE
 
-#include <algorithm>
-#include <cmath>
-#include <limits>
-#include <utility>
-#include <vector>
+#include <algorithm>    // for max
+#include <cmath>        // for exp, abs, log, lgamma
+#include <limits>       // for numeric_limits
+#include <type_traits>  // for is_floating_point, conditional, is_signed, is_same, declval, enable_if
+#include <utility>      // for pair
 
 namespace xgboost {
 namespace common {
+
+template <typename T> XGBOOST_DEVICE T Sqr(T const &w) { return w * w; }
+
 /*!
  * \brief calculate the sigmoid of the input.
  * \param x input parameter
@@ -30,9 +33,11 @@ XGBOOST_DEVICE inline float Sigmoid(float x) {
   return y;
 }
 
-template <typename T>
-XGBOOST_DEVICE inline static T Sqr(T a) { return a * a; }
-
+XGBOOST_DEVICE inline double Sigmoid(double x) {
+  auto denom = std::exp(-x) + 1.0;
+  auto y = 1.0 / denom;
+  return y;
+}
 /*!
  * \brief Equality test for both integer and floating point.
  */
@@ -134,10 +139,6 @@ inline static bool CmpFirst(const std::pair<float, unsigned> &a,
                             const std::pair<float, unsigned> &b) {
   return a.first > b.first;
 }
-inline static bool CmpSecond(const std::pair<float, unsigned> &a,
-                             const std::pair<float, unsigned> &b) {
-  return a.second > b.second;
-}
 
 // Redefined here to workaround a VC bug that doesn't support overloading for integer
 // types.

src/common/ranking_utils.h

@@ -70,15 +70,15 @@ struct LambdaRankParam : public XGBoostParameter<LambdaRankParam> {
   // pairs
   // should be accessed by getter for auto configuration.
   // nolint so that we can keep the string name.
-  PairMethod lambdarank_pair_method{PairMethod::kMean};  // NOLINT
+  PairMethod lambdarank_pair_method{PairMethod::kTopK};  // NOLINT
   std::size_t lambdarank_num_pair_per_sample{NotSet()};  // NOLINT
 
  public:
   static constexpr position_t NotSet() { return std::numeric_limits<position_t>::max(); }
 
   // unbiased
   bool lambdarank_unbiased{false};
-  double lambdarank_bias_norm{2.0};
+  double lambdarank_bias_norm{1.0};
   // ndcg
   bool ndcg_exp_gain{true};
 
@@ -135,7 +135,7 @@ struct LambdaRankParam : public XGBoostParameter<LambdaRankParam> {
         .set_default(false)
         .describe("Unbiased lambda mart. Use extended IPW to debias click position");
     DMLC_DECLARE_FIELD(lambdarank_bias_norm)
-        .set_default(2.0)
+        .set_default(1.0)
         .set_lower_bound(0.0)
         .describe("Lp regularization for unbiased lambdarank.");
     DMLC_DECLARE_FIELD(ndcg_exp_gain)