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4780f16 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | """Problem instances, paper §6 (spec: specs/exp00_core.md, ambiguity #1)."""
import numpy as np
def make_instance(n, weight_decay, seed=0):
# alpha/beta are drawn once with default_rng(0) and held constant across
# all seeds/configurations (ambiguity #1) -- callers should not vary seed.
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}")
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