# High-State Example

Read this page as the concrete GLADIUS setup: high-dimensional state features,
low-dimensional reward projection, and an anchor action. The anchor is what
turns the learned Q objects into reward evidence.

The primary evaluation cell for GLADIUS uses 21 discrete states encoded into
64-dimensional feature vectors, a 4-parameter linear reward, and an anchor
action with known rewards. This setup follows the motivating design from
{ref}`Kang, Yoganarasimhan, and Jain (2025) <kang-2025>`: high-dimensional
state representation, low-dimensional reward structure, and an observable
anchor to pin the reward level.

```python
from econirl.estimation import GLADIUSConfig, GLADIUSEstimator

config = GLADIUSConfig(
    anchor_action=2,
    anchor_rewards=anchor_rewards,   # shape (n_states,): known reward for action 2
    anchor_bellman_loss=True,
    anchor_bellman_mode="anchor_moment",
    q_hidden_dim=128,
    q_num_layers=3,
    v_hidden_dim=128,
    v_num_layers=3,
    max_epochs=500,
    batch_size=512,
    bellman_penalty_weight=1.0,
    patience=50,
    alternating_updates=True,
    verbose=True,
)

estimator = GLADIUSEstimator(config=config)
summary = estimator.estimate(panel, utility, problem, transitions)

print(summary.parameters)        # projected structural vector (4 parameters)
print(summary.policy[:5, :])     # imitation policy for first 5 states
```

## What the Networks Learn

The Q-network maps `(state_features, action_onehot)` - a vector of length
`state_dim + n_actions` - to a scalar action-value. The zeta network maps the
same input to a scalar approximation of $\mathbb{E}[V(s') \mid s, a]$.
During training, the zeta network is updated on even mini-batches against the
soft value of next states from the Q-network held fixed during that step; the Q-network is updated on
odd mini-batches against the NLL of observed choices and the anchor Bellman
residual.

After training, implied rewards are extracted as
$\hat{r}(s,a) = Q(s,a) - \beta\,\zeta(s,a)$ and projected onto the action-
difference feature matrix to recover the 4-parameter structural vector.

## Interpretation

The primary cell result (parameter cosine 0.9752, projected reward NRMSE 0.198,
policy TV 0.037) shows that GLADIUS recovers the directional structure of the
reward well and imitates the policy closely. The raw Bellman reward NRMSE (0.571)
and value NRMSE (0.420) reveal that the absolute scale of the implied reward
does not match the data-generating truth, even with the anchor pinning Q at one
action. This gap is the reason structural counterfactual analysis requires
caution with current GLADIUS results.

## Replication Boundary

This page illustrates the evaluation setup, not a full historical replication.
The estimator's recovery properties on this cell are established in the
[Simulation Study](validation.md) page. The results file
[`gladius.json`](https://github.com/rawatpranjal/EconIRL/blob/main/validation/results/gladius.json)
contains all numeric results.