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+ """Turn raw job JSON into the numbers behind each claim.
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+
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+ Usage: python analyze.py <claim> <results.json> [more.json ...]
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+ """
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+
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+ from __future__ import annotations
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+
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+ import glob
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+ import json
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+ import sys
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+
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+ import numpy as np
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+
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+
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+ def load(paths):
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+ out = []
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+ for p in paths:
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+ for f in sorted(glob.glob(p)):
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+ with open(f) as fh:
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+ out.append(json.load(fh))
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+ return out
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+
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+
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+ # --------------------------------------------------------------------------
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+ # Claim 1 / Claim 5: from the ablation records
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+ # --------------------------------------------------------------------------
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+
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+
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+ def claim1(paths):
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+ """Proposition 1: the standard (EIG) utility choice is suboptimal w.r.t. the
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+ Lagrangian utility that accounts for the drifter's future trajectory.
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+
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+ The paper's formal proof (App. D) is a one-line argmax argument giving only
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+ the weak inequality LU(x^S) <= LU(x*). Here we measure whether the gap is
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+ real and how big it is, using the ground-truth field to define LU = B(.;true).
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+ """
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+ recs = [r for d in load(paths) for r in d["records"]]
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+ rows = []
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+ for r in recs:
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+ u_true = np.array(r["u_true"])
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+ u_eig = np.array(r["u_eig"])
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+ u_ball = np.array(r["u"]).mean(0)
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+ i_eig, i_ball, i_star = u_eig.argmax(), u_ball.argmax(), u_true.argmax()
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+ rows.append({
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+ "t": r["t"],
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+ "LU_star": u_true[i_star],
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+ "LU_eig": u_true[i_eig],
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+ "LU_ballast": u_true[i_ball],
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+ "LU_mean": u_true.mean(), # uniform policy
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+ "strict": bool(u_true[i_eig] < u_true[i_star] - 1e-9),
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+ "eig_is_argmax": bool(i_eig == i_star),
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+ })
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+ out = {}
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+ for t in sorted(set(r["t"] for r in rows)):
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+ sub = [r for r in rows if r["t"] == t]
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+ gap_eig = np.array([(r["LU_star"] - r["LU_eig"]) / abs(r["LU_star"]) * 100 for r in sub])
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+ gap_bal = np.array([(r["LU_star"] - r["LU_ballast"]) / abs(r["LU_star"]) * 100 for r in sub])
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+ gap_uni = np.array([(r["LU_star"] - r["LU_mean"]) / abs(r["LU_star"]) * 100 for r in sub])
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+ out[t] = {
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+ "n": len(sub),
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+ "pct_strictly_suboptimal": 100 * np.mean([r["strict"] for r in sub]),
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+ "gap_eig_pct": [gap_eig.mean(), 2 * gap_eig.std() / np.sqrt(len(sub))],
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+ "gap_ballast_pct": [gap_bal.mean(), 2 * gap_bal.std() / np.sqrt(len(sub))],
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+ "gap_unif_pct": [gap_uni.mean(), 2 * gap_uni.std() / np.sqrt(len(sub))],
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+ }
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+ return out
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+
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+
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+ def claim5(paths):
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+ """Sec. 5.1 / G.1: percentage utility gap vs J, and the J at which it drops
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+ below 1%.
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+
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+ Gap_MC(J) = B(s*; inf) - B(s*_J; inf), approximated with J=200
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+ Gap_Full(J) = B(s*_true; true) - B(s*_J; true)
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+ """
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+ recs = [r for d in load(paths) for r in d["records"]]
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+ ts = sorted(set(r["t"] for r in recs))
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+ out = {}
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+ for t in ts:
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+ sub = [r for r in recs if r["t"] == t]
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+ Jmax = np.array(sub[0]["u"]).shape[0]
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+ Js = np.arange(1, Jmax + 1)
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+ mc = np.zeros((len(sub), Jmax))
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+ full = np.zeros((len(sub), Jmax))
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+ eig_mc, eig_full, uni_mc, uni_full = [], [], [], []
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+ for i, r in enumerate(sub):
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+ u = np.array(r["u"]) # (Jmax, N)
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+ u_true = np.array(r["u_true"])
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+ u_eig = np.array(r["u_eig"])
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+ B_inf = u.mean(0) # B(.; inf) approximated by J=200
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+ s_star = B_inf.argmax()
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+ s_true = u_true.argmax()
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+ run = np.cumsum(u, axis=0) / Js[:, None] # B(.; J) for each J
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+ sJ = run.argmax(axis=1) # s*_J
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+ mc[i] = (B_inf[s_star] - B_inf[sJ]) / abs(B_inf[s_star]) * 100
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+ full[i] = (u_true[s_true] - u_true[sJ]) / abs(u_true[s_true]) * 100
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+ ie = u_eig.argmax()
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+ eig_mc.append((B_inf[s_star] - B_inf[ie]) / abs(B_inf[s_star]) * 100)
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+ eig_full.append((u_true[s_true] - u_true[ie]) / abs(u_true[s_true]) * 100)
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+ uni_mc.append((B_inf[s_star] - B_inf.mean()) / abs(B_inf[s_star]) * 100)
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+ uni_full.append((u_true[s_true] - u_true.mean()) / abs(u_true[s_true]) * 100)
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+
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+ def band(a):
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+ return a.mean(0), 2 * a.std(0) / np.sqrt(a.shape[0])
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+
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+ m_mc, s_mc = band(mc)
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+ m_fu, s_fu = band(full)
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+ below = np.where(m_mc < 1.0)[0]
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+ out[t] = {
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+ "n_reps": len(sub),
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+ "J": Js.tolist(),
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+ "gap_mc_mean": m_mc.tolist(), "gap_mc_se2": s_mc.tolist(),
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+ "gap_full_mean": m_fu.tolist(), "gap_full_se2": s_fu.tolist(),
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+ "J_at_1pct_mc": int(Js[below[0]]) if len(below) else None,
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+ "eig_gap_mc": float(np.mean(eig_mc)), "eig_gap_full": float(np.mean(eig_full)),
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+ "unif_gap_mc": float(np.mean(uni_mc)), "unif_gap_full": float(np.mean(uni_full)),
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+ "gap_at_J20_mc": float(m_mc[19]), "gap_at_J20_full": float(m_fu[19]),
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+ }
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+ return out
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+
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+
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+ # --------------------------------------------------------------------------
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+ # Claims 3 / 4: policy comparison
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+ # --------------------------------------------------------------------------
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+
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+ POLICY_ORDER = ["unif", "sobol", "dist_sep", "eig", "ballast_opt", "ballast_true"]
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+
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+
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+ def claim34(paths):
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+ from ballast.experiment import iso_performance
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+
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+ res = [r for d in load(paths) for r in d["results"]]
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+ seeds = sorted(set(r["seed"] for r in res))
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+ pols = [p for p in POLICY_ORDER if any(r["policy"] == p for r in res)]
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+ by = {(r["seed"], r["policy"]): np.array(r["errors"]) for r in res}
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+ n_dep = len(next(iter(by.values())))
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+
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+ # runs where every policy completed
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+ good = [s for s in seeds if all((s, p) in by for p in pols)]
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+ E = {p: np.stack([by[(s, p)] for s in good]) for p in pols} # (n_runs, n_dep)
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+
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+ # --- average policy rank per iteration (1 = best)
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+ stack = np.stack([E[p] for p in pols]) # (n_pol, n_runs, n_dep)
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+ order = stack.argsort(axis=0).argsort(axis=0) + 1
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+ rank_mean = order.mean(axis=1) # (n_pol, n_dep)
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+ rank_se2 = 2 * order.std(axis=1) / np.sqrt(len(good))
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+
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+ # --- iso-performance vs UNIF
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+ iso = {}
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+ for p in pols:
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+ v = np.stack([iso_performance(E[p][i], E["unif"][i]) for i in range(len(good))])
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+ iso[p] = {
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+ "mean": np.nanmean(v, axis=0).tolist(),
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+ "se2": (2 * np.nanstd(v, axis=0) / np.sqrt(len(good))).tolist(),
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+ "final": float(np.nanmean(v[:, -1])),
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+ "final_se2": float(2 * np.nanstd(v[:, -1]) / np.sqrt(len(good))),
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+ }
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+ n_policy_chosen = n_dep - 1 # the first drifter is placed uniformly at random
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+ return {
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+ "n_runs": len(good),
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+ "policies": pols,
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+ "n_deploy": n_dep,
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+ "rank_mean": rank_mean.tolist(),
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+ "rank_se2": rank_se2.tolist(),
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+ "err_mean": {p: E[p].mean(0).tolist() for p in pols},
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+ "err_se2": {p: (2 * E[p].std(0) / np.sqrt(len(good))).tolist() for p in pols},
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+ "iso": iso,
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+ "savings_pct": {
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+ p: 100 * iso[p]["final"] / n_policy_chosen for p in pols
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+ },
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+ "n_obs_mean": {
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+ p: float(np.mean([r["n_obs"] for r in res if r["policy"] == p])) for p in pols
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+ },
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+ }
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+
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+
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+ if __name__ == "__main__":
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+ which, paths = sys.argv[1], sys.argv[2:]
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+ fn = {"claim1": claim1, "claim5": claim5, "claim34": claim34}[which]
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+ print(json.dumps(fn(paths), indent=2, default=float))