Add horizon-aware AUC for anytime evaluation

[Chonghe-Jiang]

Problem

The current metrics.auc() normalizes over the interval between the first and last recorded submissions. It therefore ignores both:

• time from the evaluation start to the first valid submission; and
• time from the last submission to the declared evaluation deadline.

This can make methods with materially different optimization speed receive the same anytime score.

For example, under a declared horizon of [0, 100], these curves currently both return 0.8:

first score 0.8 at t=10, then hold to t=100 -> current AUC 0.8
first score 0.8 at t=90, then hold to t=100 -> current AUC 0.8

With baseline 0 over the full horizon, their scores should instead be 0.72 and 0.08.

Proposed API

Keep the existing auc() behavior for compatibility and add a separate pure metric, for example:

auc_over_horizon(
    curve,
    start=0.0,
    end=budget_seconds,
    baseline=0.0,
    time="t",
    value="best_so_far",
)

Semantics to define

• use baseline from start until the first valid point;
• hold the last best-so-far value until end;
• define no-submission and single-submission behavior;
• reject invalid horizons such as end <= start;
• define how points outside the horizon are handled;
• do not infer whether an early stop was normal or an infrastructure failure—the caller should supply the intended comparison horizon.

Acceptance criteria

• Tests distinguish early and late first improvements over the same horizon.
• Tests cover empty, single-point, duplicate-time, boundary, and invalid-horizon inputs.
• The result is normalized by the declared horizon length.
• The function remains a pure pandas metric and documents its required columns.
• Existing auc() callers and behavior remain unchanged.