diff --git a/bayes_opt/acquisition.py b/bayes_opt/acquisition.py
index 546ca7be..4c8c7191 100644
--- a/bayes_opt/acquisition.py
+++ b/bayes_opt/acquisition.py
@@ -452,6 +452,14 @@ def __init__(
         if kappa < 0:
             error_msg = "kappa must be greater than or equal to 0."
             raise ValueError(error_msg)
+        if exploration_decay is not None and not (0 < exploration_decay <= 1):
+            error_msg = "exploration_decay must be greater than 0 and less than or equal to 1."
+            raise ValueError(error_msg)
+        if exploration_decay_delay is not None and (
+            not isinstance(exploration_decay_delay, int) or exploration_decay_delay < 0
+        ):
+            error_msg = "exploration_decay_delay must be an integer greater than or equal to 0."
+            raise ValueError(error_msg)
 
         super().__init__(random_state=random_state)
         self.kappa = kappa
@@ -604,6 +612,18 @@ def __init__(
         exploration_decay_delay: int | None = None,
         random_state: int | RandomState | None = None,
     ) -> None:
+        if xi < 0:
+            error_msg = "xi must be greater than or equal to 0."
+            raise ValueError(error_msg)
+        if exploration_decay is not None and not (0 < exploration_decay <= 1):
+            error_msg = "exploration_decay must be greater than 0 and less than or equal to 1."
+            raise ValueError(error_msg)
+        if exploration_decay_delay is not None and (
+            not isinstance(exploration_decay_delay, int) or exploration_decay_delay < 0
+        ):
+            error_msg = "exploration_decay_delay must be an integer greater than or equal to 0."
+            raise ValueError(error_msg)
+
         super().__init__(random_state=random_state)
         self.xi = xi
         self.exploration_decay = exploration_decay
@@ -766,6 +786,7 @@ class ExpectedImprovement(AcquisitionFunction):
         Decay rate for xi. If None, no decay is applied.
 
     exploration_decay_delay : int, default None
+        Delay for decay. If None, decay is applied from the start.
 
     random_state : int, RandomState, default None
         Set the random state for reproducibility.
@@ -778,6 +799,18 @@ def __init__(
         exploration_decay_delay: int | None = None,
         random_state: int | RandomState | None = None,
     ) -> None:
+        if xi < 0:
+            error_msg = "xi must be greater than or equal to 0."
+            raise ValueError(error_msg)
+        if exploration_decay is not None and not (0 < exploration_decay <= 1):
+            error_msg = "exploration_decay must be greater than 0 and less than or equal to 1."
+            raise ValueError(error_msg)
+        if exploration_decay_delay is not None and (
+            not isinstance(exploration_decay_delay, int) or exploration_decay_delay < 0
+        ):
+            error_msg = "exploration_decay_delay must be an integer greater than or equal to 0."
+            raise ValueError(error_msg)
+
         super().__init__(random_state=random_state)
         self.xi = xi
         self.exploration_decay = exploration_decay
diff --git a/bayes_opt/bayesian_optimization.py b/bayes_opt/bayesian_optimization.py
index 443cdc06..0df53b6d 100644
--- a/bayes_opt/bayesian_optimization.py
+++ b/bayes_opt/bayesian_optimization.py
@@ -55,6 +55,11 @@ class BayesianOptimization:
         Dictionary with parameters names as keys and a tuple with minimum
         and maximum values.
 
+    acquisition_function: AcquisitionFunction, optional(default=None)
+            The acquisition function to use for suggesting new points to evaluate.
+            If None, defaults to UpperConfidenceBound for unconstrained problems
+            and ExpectedImprovement for constrained problems.
+
     constraint: NonlinearConstraint.
         Note that the names of arguments of the constraint function and of
         f need to be the same.
diff --git a/tests/test_acquisition.py b/tests/test_acquisition.py
index 30150bcf..efb7bb5f 100644
--- a/tests/test_acquisition.py
+++ b/tests/test_acquisition.py
@@ -377,6 +377,66 @@ def test_upper_confidence_bound_invalid_kappa_error(kappa: float):
         acquisition.UpperConfidenceBound(kappa=kappa)
 
 
+@pytest.mark.parametrize("exploration_decay", [-0.1, 0.0, 1.1, 2.0, np.inf])
+def test_upper_confidence_bound_invalid_exploration_decay_error(exploration_decay: float):
+    with pytest.raises(
+        ValueError, match="exploration_decay must be greater than 0 and less than or equal to 1."
+    ):
+        acquisition.UpperConfidenceBound(kappa=1.0, exploration_decay=exploration_decay)
+
+
+@pytest.mark.parametrize("exploration_decay_delay", [-1, -10, "not_an_int", 1.5])
+def test_upper_confidence_bound_invalid_exploration_decay_delay_error(exploration_decay_delay):
+    with pytest.raises(
+        ValueError, match="exploration_decay_delay must be an integer greater than or equal to 0."
+    ):
+        acquisition.UpperConfidenceBound(kappa=1.0, exploration_decay_delay=exploration_decay_delay)
+
+
+@pytest.mark.parametrize("xi", [-0.1, -1.0, -np.inf])
+def test_probability_of_improvement_invalid_xi_error(xi: float):
+    with pytest.raises(ValueError, match="xi must be greater than or equal to 0."):
+        acquisition.ProbabilityOfImprovement(xi=xi)
+
+
+@pytest.mark.parametrize("exploration_decay", [-0.1, 0.0, 1.1, 2.0, np.inf])
+def test_probability_of_improvement_invalid_exploration_decay_error(exploration_decay: float):
+    with pytest.raises(
+        ValueError, match="exploration_decay must be greater than 0 and less than or equal to 1."
+    ):
+        acquisition.ProbabilityOfImprovement(xi=0.01, exploration_decay=exploration_decay)
+
+
+@pytest.mark.parametrize("exploration_decay_delay", [-1, -10, "not_an_int", 1.5])
+def test_probability_of_improvement_invalid_exploration_decay_delay_error(exploration_decay_delay):
+    with pytest.raises(
+        ValueError, match="exploration_decay_delay must be an integer greater than or equal to 0."
+    ):
+        acquisition.ProbabilityOfImprovement(xi=0.01, exploration_decay_delay=exploration_decay_delay)
+
+
+@pytest.mark.parametrize("xi", [-0.1, -1.0, -np.inf])
+def test_expected_improvement_invalid_xi_error(xi: float):
+    with pytest.raises(ValueError, match="xi must be greater than or equal to 0."):
+        acquisition.ExpectedImprovement(xi=xi)
+
+
+@pytest.mark.parametrize("exploration_decay", [-0.1, 0.0, 1.1, 2.0, np.inf])
+def test_expected_improvement_invalid_exploration_decay_error(exploration_decay: float):
+    with pytest.raises(
+        ValueError, match="exploration_decay must be greater than 0 and less than or equal to 1."
+    ):
+        acquisition.ExpectedImprovement(xi=0.01, exploration_decay=exploration_decay)
+
+
+@pytest.mark.parametrize("exploration_decay_delay", [-1, -10, "not_an_int", 1.5])
+def test_expected_improvement_invalid_exploration_decay_delay_error(exploration_decay_delay):
+    with pytest.raises(
+        ValueError, match="exploration_decay_delay must be an integer greater than or equal to 0."
+    ):
+        acquisition.ExpectedImprovement(xi=0.01, exploration_decay_delay=exploration_decay_delay)
+
+
 def verify_optimizers_match(optimizer1, optimizer2):
     """Helper function to verify two optimizers match."""
     assert len(optimizer1.space) == len(optimizer2.space)