ENH: Export value function evaluated at states for debugging

[MImmesberger]

Is your feature request related to a problem?

Currently, lcm does not throw errors in cases where it should do so. When inspecting the results of a successful run (or even one with errors), it would be extremely helpful to have more information about the value function than just the result given optimal choices. In particular, it would be helpful to be able to look at the value function evaluated at all state-choice combinations.

Describe the solution you'd like

Already discussed this shortly with @timmens. He proposed, as a "easy" to implement interim solution, to let lcm export a .pkl file that the user could read in to explore unexpected behavior.

Maybe one could combine this with the already existing debug_mode argument of get_lcm_function. The user could specify a path, where the debug file is dropped.

API breaking implications

None, except potentially changes to the debug_mode argument.

Describe alternatives you've considered

Alternatives regarding the export itself may be considered. For example, the lcm function may also return the whole array (or only parts of it, specified by the user, e.g. all alternative-specific value functions for some specific choice) as a function output, instead of saving a .pkl file to the drive. Then, users do not have to read it in themselves. Given that this is an interim feature, I'm indifferent regarding the two options.