Pre-Estimation Checks

Read this page before fitting RHIP. The checks tell you whether feature matching can support reward recovery for the planning horizon you intend to use.

Most RHIP failures are visible before optimization starts. Check feature variation, support, transition validity, and normalization before treating a fit as reward recovery.

Check	Why it matters
Feature rank	Rank below the number of reward features means some reward directions are unidentified.
Feature condition number	A high condition number signals unstable feature matching.
Action dependence	Multi-action reward recovery needs features that vary across actions.
Transition row sums	Occupancy measures require valid probability rows.
Transition orientation	The tensor must be (n_actions, n_states, n_states). Wrong orientation can have valid row sums and still produce the wrong occupancy measure.
State coverage	Unobserved states weaken the occupancy comparison.
Action support	Rare actions make action-specific rewards weakly pinned down.
Reward anchor	RHIP rewards need a normalization for level and scale.
Planning horizon	The horizon H sets the behavioral model the estimator matches. Choose it for the demonstrator-noise regime. It is a planner hyperparameter, not an identifying assumption.

Canonical Simulation Checks

Values from the primary high-dimensional route-choice synthetic run (see Simulation Study), 150-node random geometric road network, features [edge_cost, amenity, goal], true parameters [1.0, 0.5, 1.0]:

Check	Value	Status
Feature rank	3 / 3	pass
Feature condition number	2.46e+01	pass
Action-contrast rank	3 / 3	pass
Transition row error	< 1e-10	pass
Observed states	150 / 150	pass
Transition orientation	(4, 150, 150)	pass
Action support	4 actions, 400 agents	pass
Reward anchor	true	pass

Common Risk Patterns

A state-only feature matrix can produce a plausible reward vector while still failing to identify action-specific payoffs. Sparse demonstrations can match the dominant actions while leaving rare-action rewards weak. Transition tensors with the wrong orientation can have valid row sums and still produce the wrong occupancy measure. Choosing a horizon much higher than the demonstrator’s actual lookahead does not fail silently, but the extra soft backups add cost without improving recovery.