diff --git a/src/caffe/test/test_gradient_based_solver.cpp b/src/caffe/test/test_gradient_based_solver.cpp
index cae6ce1d27a..3fd6c479b09 100644
--- a/src/caffe/test/test_gradient_based_solver.cpp
+++ b/src/caffe/test/test_gradient_based_solver.cpp
@@ -555,10 +555,12 @@ class GradientBasedSolverTest : public MultiDeviceTest<TypeParam> {
     const vector<Blob<Dtype>*>& params = solver_->net()->learnable_params();
     for (int i = 0; i < params.size(); ++i) {
       for (int j = 0; j < params[i]->count(); ++j) {
-        EXPECT_EQ(param_copies[i]->cpu_data()[j], params[i]->cpu_data()[j])
-            << "param " << i << " data differed at dim " << j;
-        EXPECT_EQ(param_copies[i]->cpu_diff()[j], params[i]->cpu_diff()[j])
-            << "param " << i << " diff differed at dim " << j;
+        Dtype rel_error = Dtype(std::max(1., fabs(params[i]->cpu_data()[j])) *
+            1.e-5);
+        EXPECT_NEAR(param_copies[i]->cpu_data()[j], params[i]->cpu_data()[j],
+            rel_error) << "param " << i << " data differed at dim " << j;
+        EXPECT_NEAR(param_copies[i]->cpu_diff()[j], params[i]->cpu_diff()[j],
+            rel_error) << "param " << i << " diff differed at dim " << j;
       }
     }
 
@@ -566,10 +568,12 @@ class GradientBasedSolverTest : public MultiDeviceTest<TypeParam> {
     const vector<shared_ptr<Blob<Dtype> > >& history = solver_->history();
     for (int i = 0; i < history.size(); ++i) {
       for (int j = 0; j < history[i]->count(); ++j) {
-        EXPECT_EQ(history_copies[i]->cpu_data()[j], history[i]->cpu_data()[j])
-            << "history blob " << i << " data differed at dim " << j;
-        EXPECT_EQ(history_copies[i]->cpu_diff()[j], history[i]->cpu_diff()[j])
-            << "history blob " << i << " diff differed at dim " << j;
+        Dtype rel_error = Dtype(std::max(1., fabs(history[i]->cpu_data()[j])) *
+            1.e-5);
+        EXPECT_NEAR(history_copies[i]->cpu_data()[j], history[i]->cpu_data()[j],
+            rel_error) << "history blob " << i << " data differed at dim " << j;
+        EXPECT_NEAR(history_copies[i]->cpu_diff()[j], history[i]->cpu_diff()[j],
+            rel_error) << "history blob " << i << " diff differed at dim " << j;
       }
     }
   }