Pre-Estimation Checks

Read this page before fitting GLADIUS. The anchor and action-difference projection are what turn learned Q objects into reward evidence.

GLADIUS uses neural networks and an action-difference projection, so it carries the usual high-dimensional estimation risks plus a few specific to the anchor Bellman strategy.

Check	Why it matters for GLADIUS
Feature rank	A rank-deficient action-difference feature matrix leaves a direction of theta undetermined in the projection.
Feature condition number	Ill-conditioning inflates the variance of the action-difference OLS.
State coverage	The projection is scored at all states; very thin coverage leaves the reward surface underidentified in those regions.
Action support per state	A state where one action is never taken makes the action-difference construction degenerate at that state.
Anchor validity	The anchor action must appear in every state for the anchor Bellman loss to pin Q everywhere.
Transition row sums	Transition tensors must be row-stochastic in the (n_actions, n_states, n_states) orientation; row errors above 1e-6 indicate a construction bug.
Network scaling	With a high discount factor (\(\beta\) near 1), Q-values are large; the default value_scale = 1/(1-beta) rescales the MLP output to a numerically stable range.

Canonical Simulation Checks

Values from the primary synthetic cell (see Simulation Study):

Check	Value	Status
Feature rank	4 / 4	pass
Feature condition number	4.376	pass
Observed states	21 / 21	pass
State-action coverage	1.000	pass
Single-action states	0	pass
Anchor valid	true	pass
Max transition row error	2.4e-08	pass

Common Risk Patterns

The anchor Bellman loss is the main lever for structural reward recovery. When anchor rewards are not supplied, Q is identified only up to a state-dependent constant and the action-difference projection can still recover reward slopes, but level parameters require the anchor to pin the scale. Check anchor_bellman_loss=True and verify that anchor_rewards is a vector of length n_states containing the correct known rewards for the anchor action.

Policy TV can be good even when raw Bellman reward or value recovery fails. Inspect the projected_reward_normalized_rmse and raw_bellman_reward_normalized_rmse fields in the results file alongside policy TV before drawing any structural conclusions. A good imitation policy is a necessary but not sufficient condition for structural counterfactual validity.