diff --git a/pyRDDLGym_jax/core/tuning.py b/pyRDDLGym_jax/core/tuning.py
index 5f3fab3..5ceb77a 100644
--- a/pyRDDLGym_jax/core/tuning.py
+++ b/pyRDDLGym_jax/core/tuning.py
@@ -8,6 +8,7 @@
 import warnings
 warnings.filterwarnings("ignore")
 
+from sklearn.gaussian_process.kernels import Matern, ConstantKernel
 from bayes_opt import BayesianOptimization
 from bayes_opt.acquisition import AcquisitionFunction, UpperConfidenceBound
 import jax
@@ -71,8 +72,7 @@ def __init__(self, env: RDDLEnv,
                  gp_iters: int=25,
                  acquisition: Optional[AcquisitionFunction]=None,
                  gp_init_kwargs: Optional[Kwargs]=None,
-                 gp_params: Optional[Kwargs]=None,
-                 gp_kernel_params: Optional[Kwargs]=None) -> None:
+                 gp_params: Optional[Kwargs]=None) -> None:
         '''Creates a new instance for tuning hyper-parameters for Jax planners
         on the given RDDL domain and instance.
         
@@ -98,8 +98,6 @@ def __init__(self, env: RDDLEnv,
         during initialization  
         :param gp_params: additional parameters to feed to Bayesian optimizer 
         after initialization optimization
-        :param gp_kernel_params: additional parameters to feed to the kernel of
-        the Bayesian optimizer
         '''        
         # objective parameters
         self.env = env
@@ -122,16 +120,24 @@ def __init__(self, env: RDDLEnv,
             gp_init_kwargs = {}
         self.gp_init_kwargs = gp_init_kwargs
         if gp_params is None:
-            gp_params = {'n_restarts_optimizer': 20}
+            gp_params = {'n_restarts_optimizer': 25, 
+                         'kernel': self.make_default_kernel()}
         self.gp_params = gp_params
-        if gp_kernel_params is None:
-            gp_kernel_params = {'length_scale_bounds': (0.2, 20.)}
-        self.gp_kernel_params = gp_kernel_params
         if acquisition is None:
             num_samples = self.gp_iters * self.num_workers
             acquisition = JaxParameterTuning.annealing_acquisition(num_samples)
         self.acquisition = acquisition
     
+    @staticmethod
+    def make_default_kernel():
+        weight1 = ConstantKernel(1.0, (0.01, 100.0))
+        weight2 = ConstantKernel(1.0, (0.01, 100.0))
+        weight3 = ConstantKernel(1.0, (0.01, 100.0))
+        kernel1 = Matern(length_scale=0.5, length_scale_bounds=(0.1, 0.5), nu=2.5)
+        kernel2 = Matern(length_scale=1.0, length_scale_bounds=(0.5, 1.0), nu=2.5)
+        kernel3 = Matern(length_scale=5.0, length_scale_bounds=(1.0, 5.0), nu=2.5)
+        return weight1 * kernel1 + weight2 * kernel2 + weight3 * kernel3
+        
     def summarize_hyperparameters(self) -> None:
         hyper_params_table = []
         for (_, param) in self.hyperparams_dict.items():
@@ -141,7 +147,6 @@ def summarize_hyperparameters(self) -> None:
               f'    tuned_hyper_parameters    =\n{hyper_params_table}\n'
               f'    initialization_args       ={self.gp_init_kwargs}\n'
               f'    gp_params                 ={self.gp_params}\n'
-              f'    gp_kernel_params          ={self.gp_kernel_params}\n'
               f'    tuning_iterations         ={self.gp_iters}\n'
               f'    tuning_timeout            ={self.timeout_tuning}\n'
               f'    tuning_batch_size         ={self.num_workers}\n'
@@ -335,8 +340,7 @@ def objective_function(params: ParameterValues,
     
     def tune_optimizer(self, optimizer: BayesianOptimization) -> None:
         '''Tunes the Bayesian optimization algorithm hyper-parameters.'''
-        print('\n' + f'The kernel length_scale was set to '
-              f'{optimizer._gp.kernel_.length_scale}.')
+        print('\n' + f'The current kernel is {repr(optimizer._gp.kernel_)}.')
         
     def tune(self, key: int, log_file: str, show_dashboard: bool=False) -> ParameterValues:
         '''Tunes the hyper-parameters for Jax planner, returns the best found.'''
@@ -409,11 +413,6 @@ def tune(self, key: int, log_file: str, show_dashboard: bool=False) -> Parameter
             
             for it in range(self.gp_iters): 
                 
-                # set the kernel parameters to user requested
-                optimizer._gp.kernel.set_params(**self.gp_kernel_params)
-                if hasattr(optimizer._gp, 'kernel_'):
-                    optimizer._gp.kernel_.set_params(**self.gp_kernel_params)
-            
                 # check if there is enough time left for another iteration
                 elapsed = time.time() - start_time
                 if elapsed >= self.timeout_tuning: