| """Problem instances, paper §6 (spec: specs/exp00_core.md, ambiguity #1).""" |
|
|
| import numpy as np |
|
|
|
|
| def make_instance(n, weight_decay, seed=0): |
| |
| |
| rng = np.random.default_rng(seed) |
| alpha = rng.uniform(1.0, 5.0, n) |
| beta = rng.uniform(1.0, 5.0, n) |
| mu = 0.1 + 0.9 * alpha / (alpha + beta) |
|
|
| if weight_decay == "exp": |
| w = 0.9 ** np.arange(n) |
| w = w / w.sum() |
| elif weight_decay == "linear": |
| i = np.arange(1.0, n + 1.0) |
| w = 1.0 + (i - 1.0) / (n - 1.0) |
| w = w / w.sum() |
| else: |
| raise ValueError(f"unknown weight_decay {weight_decay!r}") |
|
|
| return dict(mu=mu, alpha=alpha, beta=beta, w=w, weight_decay=weight_decay) |
|
|
|
|
| def gini_w(w, weight_decay): |
| """Orient w for the Gini oracle: w_1>=...>=w_n paired with ascending-sorted u. |
| |
| Exponential decay is already non-increasing (use as-is). Linear decay is |
| increasing in i, so for Gini the reversed vector is used (largest weight |
| on the smallest-utility rank) -- see spec ambiguity note on App. E weights. |
| """ |
| w = np.asarray(w, dtype=float) |
| if weight_decay == "exp": |
| return w |
| if weight_decay == "linear": |
| return w[::-1] |
| raise ValueError(f"unknown weight_decay {weight_decay!r}") |
|
|
