PPO's Gaussian noise cannot compose phase-locked oscillations - deliver them as feed-forward and let the policy learn the residual
feedforward-for-phase-locked-skills.If a skill needs a temporally coherent (phase-locked) action component, do not expect step-wise exploration to find it: inject a verified feed-forward and train the policy as a residual stabilizer, keeping the feed-forward inside the deployment contract.
Symptom
Four different reward arrangements (no reference / wrong-sign reference / correct-sign reference / cage released) all failed to elicit sidewalk, while open-loop probes proved the behavior existed and was safe on the same platform with the same policy as base.
Context
Producing lateral velocity requires a phase-locked hip_roll oscillation synchronized to the gait clock. PPO's exploration is per-step, zero-mean, uncorrelated Gaussian noise - it can never compose a sustained phase-locked component, so the behavior is unreachable by exploration regardless of how it is rewarded. The fix changed the delivery channel: target = default + scale*action + lat_ff(cmd_vy, phi). The policy's action becomes a residual on top of the feed-forward, retaining full balance authority (it can even cancel the feed-forward); the feed-forward supplies exactly the component exploration cannot. This mirrors why the sagittal joint_pos_ref worked (it also delivered phase structure), just via a different channel.
Change
Contract-level change, done cleanly: new profile omni_ff (= omni + lat_ff_gain -0.5), existing omni profile bit-identical; feed-forward applied after the action delay stage; missing cmd/phase raises instead of silently dropping; deployment must use the same phi as build_obs (recomputing gives a one-tick phase misalignment).
Outcome
From C2-700, +100 iterations sufficed: product omni_c4_ff800 scored vy +120%/+125% (from +4%/-1%), 260/260 cells at 20/20 survival, zero old-skill regression, left/right gap 5 pp - the entire C4 saga resolved by changing the delivery mechanism, not the reward.
Mechanism
Exploration noise spans only the subspace its correlation structure can express; skills requiring coherent oscillation lie outside the span of i.i.d. per-step noise. Feed-forward moves the required structure into the action pipeline where it needs zero probability mass to appear, reducing the learning problem to stabilizing around a demonstrated behavior - which PPO does well.
Applies when
- a periodic/oscillatory skill trains flat under every reward variant
- open-loop injection of the behavior already works
- considering GRU/curriculum/exploration tricks for a rhythmic skill
“病因不在奖励，在探索形式：产生侧向速度需要相位锁定的 hip_roll 振荡，PPO 的逐步高斯噪声零均值无相关，合不出相位锁定分量。… target = default + scale·a + lat_ff(cmd_vy, φ)。策略动作因此是前馈之上的残差，保留全部平衡权限”