JG1310/repro-change-points-bundle

Reproduction bundle — The Cost of Learning Under Multiple Change Points

Independent CPU-only reproduction of Gafni, Iyengar & Zeevi, ICML 2026 (OpenReview xQLcklRDfM, arXiv 2602.11406).

Logbook: https://huggingface.co/spaces/JG1310/repro-the-cost-of-learning-under-multiple-change-points

Contents

Path	What it is
atc_core.py	ATC (Algorithm 1), exact + geometric scan; sliding-window and discounted-mean baselines; environment generators; population SNR quantities (Eqs. 9–13)
claim1.py	Claim 1 — horizon-freeness, threshold re-derivation, Lemmas A.2/A.4/A.5, Theorem 4.1/4.2 scaling, log(S) gap
claim2.py	Claim 2 — Proposition 3.1 sweep, confounding isolation, passive baselines, constant thresholds, NAB
claim3.py	Claim 3 — selective detection sweep, adversarial + dense regimes, complexity
make_figures.py	All logbook figures
data/	NAB ec2_cpu_utilization_ac20cd.csv (from the public Numenta Anomaly Benchmark repo; md5 14a0e0d6b9d46a2dbdcfac9464336c02, byte-identical to the copy vendored in the authors' release)
outputs/*.json	Every measured number, including per-configuration raw rows
figures/*.png	Rendered figures
logs/*.log	Verbatim stdout of every run
pages/*.md	Logbook page sources

Reproducing

pip install numpy scipy matplotlib joblib numba
cd repro

# Claim 1 — fast re-derivation checks, then the paper-scale sweeps
python3 claim1.py hf thr gap lb          # horizon-freeness, Eq. (7) calibration, log(S) gap, LB optimisation
python3 claim1.py l2 l4 l5               # Lemmas A.2 / A.4 / A.5 at 20,000 replications
python3 claim1.py t41 t41s               # Theorem 4.1: Fig. 3(c) at 5000 MC, Fig. 9 linear-in-S

# Claim 2
python3 claim2.py conf p31 passive const nab

# Claim 3
python3 claim3.py sel adv dense comp

python3 make_figures.py

All re-derivation checks are self-asserting: a violated lemma or structural check raises and exits non-zero. t41, t41s, passive, const, adv and dense are measurement sweeps and print fits rather than asserting.

Runtime on 16 CPU cores: roughly 12 min for the Claim 1 sweep at the paper's 5000 Monte-Carlo replications, and about 1.5 h for the whole bundle.

Implementation notes

atc_core.py was written from the paper's equations, then diffed line-by-line against the authors' released code (icml/ATC.py at https://github.com/gafnito/cost-of-learning-multiple-change-points, the URL given in the paper's footnote 3). The module docstring records the full comparison: which conventions differ (restart index, regret summation range, sigma placement — all resolved in favour of the paper) and which were confirmed identical (alpha_r schedule, threshold, scan range, alarm rule, and the midpoint candidate in the geometric scan).

We also found that Algorithm 1 line 7 is a typo: it typesets sigma inside the radical, contradicting the dimensionally correct Eq. (4). We follow Eq. (4), as does the authors' release.

The exact-scan inner loop is algebraically rewritten to be division- and sqrt-free (see the comment in run_atc); it was verified bit-exact against a direct transcription of Eq. (4) on multiple seeds before use.

A correction worth recording

check_sel in claim3.py previously compared App. A.1.6's ceiling R(t) <= min{a Delta^2, sigma^2 (gamma_t^r)^2} against total post-change regret minus a Delta=0 control run, and appeared to falsify it. That comparison is invalid: the Delta=0 control never restarts, so it does not contain the fresh Theta(sigma^2 log L) estimation-variance cost that a large-Delta run pays after its restart, and subtracting it leaves a positive variance residue. The check now forms the paper's own Lemma A.1 bias/variance decomposition across the Monte-Carlo ensemble and compares only the bias branch, which is the quantity the ceiling actually bounds. Under the corrected comparison the ceiling holds at every Delta (worst ratio 0.97).