High-precision robot learning depends on expensive task-specific demonstrations, while abundant imperfect data is usually discarded. ε4P upcycles that data with source-dependent flow-time admission: low-precision target-task data contributes at high noise, and high-precision task-mismatched data contributes at low noise. The method changes only flow-time sampling — not the policy architecture or objective.
High-quality demonstrations for a specific task are costly to collect. Lower-precision data from the same task and precise data from other tasks are more accessible, but naive co-training also transfers their mismatches across the full flow trajectory.
ε4P keeps the high-precision target-task source active throughout the flow trajectory, while routing each imperfect source only to the region where its useful information remains.
The policy relies more strongly on the noised action input at low flow times and increasingly on task context at high flow times. This transition explains why the two imperfect sources are useful in different regions.
ε4P retains the original source-sampling distribution and changes only the flow-time support assigned to each source.
At low flow time, the policy relies more strongly on the noised action input. Precise demonstrations from a mismatched task can transfer low-level execution skill with limited influence from the mismatched context.
Best source: high-precision, task-mismatched Dtm.
At high flow time, target-task context remains valuable even when demonstrated actions are less precise. A classifier identifies when noised actions from Dpm and Dpt can no longer be reliably separated.
Best source: target-task, precision-mismatched Dpm.
ε4P is a drop-in training change. Everything stays standard — only source-dependent flow-time sampling changes.
Find tpm with a flow-time-conditioned source classifier and find ttm with action/context intervention probes on the final post-trained policy.
High precision. ε4P is evaluated on ATX 24-pin connector insertion (about 0.2 mm nominal clearance) and two-stage cable plugging (about 0.3 mm lateral clearance).
Generality. Bolt–nut sorting tests whether the method also helps on a coarse-grained manipulation task. All policies use the same architecture, checkpoint, optimizer, source probabilities, and training budget.
RB-Y1 platform · 60 trials per target task
Native co-training with both imperfect sources achieves 38.3%. ε4P routes the same sources to complementary windows and improves success to 80.0%.
Compared with 78.3% using target-task data alone and 33.3% under native co-training with both imperfect sources.
The result shows that source-dependent admission is not limited to sub-millimeter insertion tasks.
Figure 5 compares flow-time admission with global loss reweighting and checks whether the identified boundaries align with strong downstream performance.
Reducing the loss weight of Dpm limits the harm from native co-training, but no tested nonzero weight exceeds the Dpt-only baseline (48.3%). ε4P keeps wpm = 1 and changes only its flow-time support, reaching 73.3% success.
The identified boundaries, ttm = 0.30 and tpm = 0.70, lie in the high-performing regions of the dense sweeps. This supports the complementary admission windows for task-mismatched and precision-mismatched data.
The identified ttm = 0.40 reaches 81.7% full-task success, compared with 70.0% at 0.20 and 66.7% at 0.60. It is the best of the tested settings, providing local validation on a second task.
Admission boundaries are estimated from offline diagnostics. The downstream sweeps and perturbations validate those choices; they are not used to select the boundaries.
@misc{anonymous2027varepsilon4p,
title = {Imperfection for Precision: Upcycling Imperfect Data
for High-Precision Robotic Manipulation},
author = {Anonymous Authors},
year = {2027},
url = {https://varepsilon4p.github.io/}
}