A single run's drift direction may be a limit cycle, not a policy bias - check the sign distribution across seeds
multiseed-sign-test-for-drift.Distinguish "bias" from "broken symmetry limit cycle" by the sign distribution over many seeds; report drift as (mean, sign split), and never compare single-run drift magnitudes across versions.
Symptom
Net yaw over 15 s appeared to worsen from -41 deg (v2) to -84 deg (v4), inviting the conclusion that the new version drifted more.
Context
The Isaac-side view across 32 environments told a different story: per-env yaw was mixed-sign (20 negative / 12 positive) with mean ~0 - the drift is a limit cycle whose direction depends on initial conditions, not a systematic policy bias. The single MuJoCo run had sampled one draw from that distribution, so its magnitude could not be compared across versions as if it were a property.
Change
Evaluation rule: before classifying drift as systematic, run multiple seeds and examine the sign distribution; single-trajectory drift magnitudes are samples, not properties.
Outcome
The v2-vs-v4 drift "regression" was reclassified as not-established; later drift work (hip_roll l+r bias) used cross-policy, cross-seed evidence instead.
Mechanism
Symmetric dynamical systems can settle into either of two mirrored limit cycles; the selected cycle is decided by noise and initial state. A statistic whose sign is initial-condition-dependent has no meaning as a single sample - only its distribution does.
Applies when
- comparing heading drift or lateral drift across policy versions
- a symmetric-looking behavior shows a consistent direction in one run
- deciding whether to fix "drift" in reward or calibration
“偏航反而变差(−41° → −84°):注意 Isaac 侧 32 env 的逐 env 偏航是正负混合(20/12)、均值 ≈0,说明这是极限环性质(方向随初值)而非策略偏置 —— MuJoCo 单次跑测到的是分布里的一个样本,不能当作系统性偏差。要判断需多种子统计。”