Counterfactuals

Read this page as diagnostic counterfactual evidence. The regret numbers are useful, but structural validity requires the upstream reward, value, Q, and projection checks to pass.

GLADIUS projects implied rewards onto structural features via action-difference regression. The projected parameters are only partially identified. The action-difference projection removes a state-dependent additive constant. It does not guarantee that the recovered reward matches the data-generating reward in an absolute sense.

Full structural counterfactual validity requires both projected-reward recovery and raw Bellman reward and value recovery. The current evaluation cells fail the raw Bellman reward and value checks, so GLADIUS has not reached structural counterfactual validity. Counterfactual analysis using projected GLADIUS parameters should be treated as diagnostic, not as structural.

Counterfactual Families Checked

The evaluation cells track welfare regret for three intervention types, compared against oracle objects derived from the data-generating process:

Family	Intervention	Checked against
Type A	Reward shift (a payoff component changes).	Oracle policy, value, and welfare regret.
Type B	Transition change (the dynamics change).	Oracle policy, value, and welfare regret.
Type C	Action removal (one action is penalized away).	Oracle policy, value, and welfare regret.

Reported Results

Counterfactual regret on the two synthetic cells:

Cell	Type A regret	Type B regret	Type C regret
gladius_paper_high_state	0.00854	0.0529	0.00852
gladius_paper_high_state_scaled	0.00274	0.00742	0.000493

Regret is the welfare loss incurred by following the GLADIUS-projected policy instead of the true optimal policy in the counterfactual world. The scaled cell shows markedly lower regret, consistent with its better projected-reward recovery.

These numbers are useful diagnostics but are not sufficient for structural validity. Reaching structural counterfactual validity requires the full check bundle - projected reward, raw Bellman reward, value, Q, and counterfactual regret - to pass together. The raw Bellman reward and value checks currently fail on both cells. See the Simulation Study for the full check table and the results files for exact metric values: gladius.json and gladius_scaled.json.