diff --git a/src/torchjd/_linalg/_dual_cone.py b/src/torchjd/_linalg/_dual_cone.py
index 7dd324829..ff4bc692c 100644
--- a/src/torchjd/_linalg/_dual_cone.py
+++ b/src/torchjd/_linalg/_dual_cone.py
@@ -78,8 +78,8 @@ def __init__(
         reg_eps: float = 0.0001,
     ) -> None:
         super().__init__()
-        self._norm_eps = norm_eps
-        self._reg_eps = reg_eps
+        self.norm_eps = norm_eps
+        self.reg_eps = reg_eps
 
     @property
     def norm_eps(self) -> float:
diff --git a/tests/unit/linalg/test_dual_cone.py b/tests/unit/linalg/test_dual_cone.py
index 045b1a643..aed115bb8 100644
--- a/tests/unit/linalg/test_dual_cone.py
+++ b/tests/unit/linalg/test_dual_cone.py
@@ -136,6 +136,16 @@ def test_reg_eps_setter_rejects_negative() -> None:
         projector.reg_eps = -1e-9
 
 
+def test_init_rejects_negative_norm_eps() -> None:
+    with raises(ValueError, match="norm_eps"):
+        QuadprogProjector(norm_eps=-1e-9)
+
+
+def test_init_rejects_negative_reg_eps() -> None:
+    with raises(ValueError, match="reg_eps"):
+        QuadprogProjector(reg_eps=-1e-9)
+
+
 def test_qp_solver_based_failure() -> None:
     """
     Tests that `QPSolverBased._project_weight_vector` raises an error when the input G has too large