diff --git a/src/Microsoft.ML.AutoML/Tuner/PipelineProposer.cs b/src/Microsoft.ML.AutoML/Tuner/PipelineProposer.cs
index 2d63b680ea..c3e2aab751 100644
--- a/src/Microsoft.ML.AutoML/Tuner/PipelineProposer.cs
+++ b/src/Microsoft.ML.AutoML/Tuner/PipelineProposer.cs
@@ -101,6 +101,13 @@ public string ProposeSearchSpace()
             {
                 var probabilities = _pipelineSchemas.Select(id => _eci[id]).ToArray();
                 probabilities = ArrayMath.Inverse(probabilities);
+                // _eci (estimator improve cost) might be infinity, which means the estimator cost for finding an improvement is positive infinity
+                // in that case, we used to set the probability to be a very small number, in some cases it can be zero ( 1 / double.infinity), so that it will be very unlikely to be picked.
+                // however, there's a special situation where all the estimators have infinity eci
+                // which could happen when all the estimators have been tried, all retrieves perfect loss and no improvement can be made.
+                // in which case, all probablities will be zero and in that case, we will never be able to pick any of them.
+                // Therefore, we need to make sure non of the probabilities is zero, and we can do that by adding a very small number (double.epsilon) to each of them after inverse.
+                probabilities = probabilities.Select(p => p + double.Epsilon).ToArray();
                 probabilities = ArrayMath.Normalize(probabilities);
 
                 // sample
diff --git a/test/Microsoft.ML.AutoML.Tests/TunerTests.cs b/test/Microsoft.ML.AutoML.Tests/TunerTests.cs
index be10b6856e..24ad39ab83 100644
--- a/test/Microsoft.ML.AutoML.Tests/TunerTests.cs
+++ b/test/Microsoft.ML.AutoML.Tests/TunerTests.cs
@@ -140,7 +140,8 @@ public void EciCfo_should_handle_trial_result_with_nan_value()
                 SearchSpace = searchSpace,
                 Seed = 1,
             });
-            var invalidLosses = new[] { double.NaN, double.NegativeInfinity, double.PositiveInfinity };
+            var invalidLosses = Enumerable.Repeat(new[] { double.NaN, double.NegativeInfinity, double.PositiveInfinity }, 100)
+                                .SelectMany(loss => loss);
             var id = 0;
             foreach (var loss in invalidLosses)
             {
@@ -155,7 +156,42 @@ public void EciCfo_should_handle_trial_result_with_nan_value()
                 {
                     TrialSettings = trialSetting,
                     DurationInMilliseconds = 10000,
-                    Loss = double.NaN,
+                    Loss = loss,
+                };
+                tuner.Update(trialResult);
+            }
+        }
+
+        [Fact]
+        public void EciCfo_should_handle_trial_result_with_no_improvements_over_losses()
+        {
+            // this test verify if tuner can find max value for LSE.
+            var context = new MLContext(1);
+            var pipeline = this.CreateDummySweepablePipeline(context);
+            var searchSpace = new SearchSpace.SearchSpace();
+            searchSpace["_pipeline_"] = pipeline.SearchSpace;
+            var tuner = new EciCostFrugalTuner(pipeline, new AutoMLExperiment.AutoMLExperimentSettings
+            {
+                SearchSpace = searchSpace,
+                Seed = 1,
+            });
+            var zeroLosses = Enumerable.Repeat(0.0, 100);
+            var randomLosses = Enumerable.Range(0, 100).Select(i => i * 0.1);
+            var id = 0;
+            foreach (var loss in zeroLosses.Concat(randomLosses))
+            {
+                var trialSetting = new TrialSettings
+                {
+                    TrialId = id++,
+                    Parameter = Parameter.CreateNestedParameter(),
+                };
+                var parameter = tuner.Propose(trialSetting);
+                trialSetting.Parameter = parameter;
+                var trialResult = new TrialResult
+                {
+                    TrialSettings = trialSetting,
+                    DurationInMilliseconds = 10000,
+                    Loss = loss,
                 };
                 tuner.Update(trialResult);
             }