[backport] Fix default metric configuration. (#9575) (#9590)

src/learner.cc

@@ -1317,7 +1317,9 @@ class LearnerImpl : public LearnerIO {
     if (metrics_.empty() && tparam_.disable_default_eval_metric <= 0) {
       metrics_.emplace_back(Metric::Create(obj_->DefaultEvalMetric(), &ctx_));
       auto config = obj_->DefaultMetricConfig();
-      metrics_.back()->LoadConfig(config);
+      if (!IsA<Null>(config)) {
+        metrics_.back()->LoadConfig(config);
+      }
       metrics_.back()->Configure({cfg_.begin(), cfg_.end()});
     }
 

src/objective/regression_obj.cu

@@ -268,6 +268,13 @@ class PseudoHuberRegression : public FitIntercept {
     }
     FromJson(in["pseudo_huber_param"], &param_);
   }
+  [[nodiscard]] Json DefaultMetricConfig() const override {
+    CHECK(param_.GetInitialised());
+    Json config{Object{}};
+    config["name"] = String{this->DefaultEvalMetric()};
+    config["pseudo_huber_param"] = ToJson(param_);
+    return config;
+  }
 };
 
 XGBOOST_REGISTER_OBJECTIVE(PseudoHuberRegression, "reg:pseudohubererror")