Fides optimizer: clarify use of Hessian and FIM (#1706)

* try to clarify `hessian_update`

* typo

* review; clarify docstring

Author: dilpath

pypesto/optimize/optimizer.py

@@ -1700,9 +1700,15 @@ def __init__(
             Optimizer options. See :meth:`fides.minimize.Optimizer.minimize`
             and :class:`fides.constants.Options` for details.
         hessian_update:
-            Hessian update strategy. If this is ``None``, a hybrid approximation
-            that switches from the ``problem.objective`` provided Hessian (
-            approximation) to a BFGS approximation will be used.
+            Hessian update strategy. Defaults to a BFGS approximation if
+            ``problem.objective`` does not provide a Hessian. Otherwise, it is
+            assumed that the ``problem.objective`` Hessian is actually the
+            Fisher information matrix (FIM), and hence a Hessian approximation
+            strategy is the default, which uses the FIM initially but switches
+            to BFGS during later iterations.
+            If your ``problem.objective`` Hessian is actually the Hessian,
+            then use ``None`` to have Fides use the ``problem.objective``
+            Hessian for all iterations.
         """
         super().__init__()
 
@@ -1762,15 +1768,23 @@ def minimize(
 
         if self.hessian_update == "default":
             if not problem.objective.has_hess:
-                warnings.warn(
+                logger.debug(
                     "Fides is using BFGS as hessian approximation, "
                     "as the problem does not provide a Hessian. "
-                    "Specify a Hessian to use a more efficient "
-                    "hybrid approximation scheme.",
+                    "Specify a Hessian (or Fisher information matrix, to use "
+                    "a more efficient hybrid approximation scheme. See the "
+                    "docstring for `hessian_update` in the class constructor "
+                    "for more details.",
                     stacklevel=1,
                 )
                 _hessian_update = fides.BFGS()
             else:
+                logger.debug(
+                    "A hybrid Hessian approximation strategy will be "
+                    "employed. See the docstring for `hessian_update` in "
+                    "the class constructor for more details.",
+                    stacklevel=1,
+                )
                 _hessian_update = fides.HybridFixed()
         else:
             _hessian_update = self.hessian_update