diff --git a/.mypy.ini b/.mypy.ini
index 7bd8f7a..152ead6 100644
--- a/.mypy.ini
+++ b/.mypy.ini
@@ -4,3 +4,4 @@ disallow_untyped_defs = True
 disallow_untyped_calls = True
 disallow_incomplete_defs = True
 pretty = True
+no_implicit_optional = True
\ No newline at end of file
diff --git a/miplearn/classifiers/adaptive.py b/miplearn/classifiers/adaptive.py
index eef4507..1135034 100644
--- a/miplearn/classifiers/adaptive.py
+++ b/miplearn/classifiers/adaptive.py
@@ -58,7 +58,7 @@ class AdaptiveClassifier(Classifier):
 
     def __init__(
         self,
-        candidates: Dict[str, CandidateClassifierSpecs] = None,
+        candidates: Optional[Dict[str, CandidateClassifierSpecs]] = None,
     ) -> None:
         super().__init__()
         if candidates is None:
diff --git a/miplearn/solvers/gurobi.py b/miplearn/solvers/gurobi.py
index 06266b4..ffd744d 100644
--- a/miplearn/solvers/gurobi.py
+++ b/miplearn/solvers/gurobi.py
@@ -149,9 +149,9 @@ class GurobiSolver(InternalSolver):
     def solve(
         self,
         tee: bool = False,
-        iteration_cb: IterationCallback = None,
-        lazy_cb: LazyCallback = None,
-        user_cut_cb: UserCutCallback = None,
+        iteration_cb: Optional[IterationCallback] = None,
+        lazy_cb: Optional[LazyCallback] = None,
+        user_cut_cb: Optional[UserCutCallback] = None,
     ) -> MIPSolveStats:
         self._raise_if_callback()
         assert self.model is not None
diff --git a/miplearn/solvers/internal.py b/miplearn/solvers/internal.py
index 0faac1a..7640f1b 100644
--- a/miplearn/solvers/internal.py
+++ b/miplearn/solvers/internal.py
@@ -52,9 +52,9 @@ class InternalSolver(ABC, EnforceOverrides):
     def solve(
         self,
         tee: bool = False,
-        iteration_cb: IterationCallback = None,
-        lazy_cb: LazyCallback = None,
-        user_cut_cb: UserCutCallback = None,
+        iteration_cb: Optional[IterationCallback] = None,
+        lazy_cb: Optional[LazyCallback] = None,
+        user_cut_cb: Optional[UserCutCallback] = None,
     ) -> MIPSolveStats:
         """
         Solves the currently loaded instance. After this method finishes,
diff --git a/miplearn/solvers/learning.py b/miplearn/solvers/learning.py
index 6ea6c31..ddbbe20 100644
--- a/miplearn/solvers/learning.py
+++ b/miplearn/solvers/learning.py
@@ -93,9 +93,9 @@ class LearningSolver:
 
     def __init__(
         self,
-        components: List[Component] = None,
+        components: Optional[List[Component]] = None,
         mode: str = "exact",
-        solver: InternalSolver = None,
+        solver: Optional[InternalSolver] = None,
         use_lazy_cb: bool = False,
         solve_lp: bool = True,
         simulate_perfect: bool = False,
diff --git a/miplearn/solvers/pyomo/base.py b/miplearn/solvers/pyomo/base.py
index 311dfa5..8fb1e48 100644
--- a/miplearn/solvers/pyomo/base.py
+++ b/miplearn/solvers/pyomo/base.py
@@ -88,9 +88,9 @@ class BasePyomoSolver(InternalSolver):
     def solve(
         self,
         tee: bool = False,
-        iteration_cb: IterationCallback = None,
-        lazy_cb: LazyCallback = None,
-        user_cut_cb: UserCutCallback = None,
+        iteration_cb: Optional[IterationCallback] = None,
+        lazy_cb: Optional[LazyCallback] = None,
+        user_cut_cb: Optional[UserCutCallback] = None,
     ) -> MIPSolveStats:
         if lazy_cb is not None:
             raise Exception("lazy callback not currently supported")
diff --git a/miplearn/solvers/pyomo/gurobi.py b/miplearn/solvers/pyomo/gurobi.py
index 5448e29..6a242a6 100644
--- a/miplearn/solvers/pyomo/gurobi.py
+++ b/miplearn/solvers/pyomo/gurobi.py
@@ -28,7 +28,7 @@ class GurobiPyomoSolver(BasePyomoSolver):
 
     def __init__(
         self,
-        params: SolverParams = None,
+        params: Optional[SolverParams] = None,
     ) -> None:
         if params is None:
             params = {}
diff --git a/miplearn/solvers/pyomo/xpress.py b/miplearn/solvers/pyomo/xpress.py
index e30368d..d49db8c 100644
--- a/miplearn/solvers/pyomo/xpress.py
+++ b/miplearn/solvers/pyomo/xpress.py
@@ -3,6 +3,7 @@
 #  Released under the modified BSD license. See COPYING.md for more details.
 
 import logging
+from typing import Optional
 
 from overrides import overrides
 from pyomo import environ as pe
@@ -25,7 +26,10 @@ class XpressPyomoSolver(BasePyomoSolver):
         {"Threads": 4} to set the number of threads.
     """
 
-    def __init__(self, params: SolverParams = None) -> None:
+    def __init__(
+        self,
+        params: Optional[SolverParams] = None,
+    ) -> None:
         if params is None:
             params = {}
         params["randomseed"] = randint(low=0, high=1000).rvs()
diff --git a/tests/solvers/test_learning_solver.py b/tests/solvers/test_learning_solver.py
index 7a39a1b..9596e82 100644
--- a/tests/solvers/test_learning_solver.py
+++ b/tests/solvers/test_learning_solver.py
@@ -38,6 +38,10 @@ def test_learning_solver() -> None:
             assert sample.lower_bound == 1183.0
             assert sample.upper_bound == 1183.0
             assert sample.lp_solution is not None
+            assert sample.lp_solution["x[0]"] is not None
+            assert sample.lp_solution["x[1]"] is not None
+            assert sample.lp_solution["x[2]"] is not None
+            assert sample.lp_solution["x[3]"] is not None
             assert round(sample.lp_solution["x[0]"], 3) == 1.000
             assert round(sample.lp_solution["x[1]"], 3) == 0.923
             assert round(sample.lp_solution["x[2]"], 3) == 1.000