TD-MPC-Glass, Part 35: What an Abstraction Is Actually Good For — Interpretable, Reusable, Stable (Not the Success Ceiling)
Across Parts 23-34 the verdict on the success-rate scoreboard is clear and modest: the value-aware abstraction-in-loop ties PPO where the prior fits, hits a physical ceiling on PickCube, and trails PPO on harder variation. This capstone asks the better question — what is the abstraction actually good for? — along the three axes a user flagged: interpretable, reusable, stable.
Why success rate is the wrong scoreboard
| task / regime | abstraction | PPO | note |
|---|---|---|---|
| PandaPickCube (prior fits) | ~0.79 | ~0.82 | tie; abstraction more sample-efficient (Part 27) |
| PickCube ceiling | ~0.83 | ~0.83 | physical (far-reach upright IK 99.9% infeasible, Part 30) |
| PickCubeOrientation, fixed prior | 0.33 | 0.82 | abstraction loses (wrong prior, Part 31) |
| PickCubeOrientation, parametrized | ~0.67 | 0.82 | recovers ~70% (Part 33) |
| PickCubeOrientation, fuller param | ~0.68 | 0.82 | class ceiling (Part 34) |
On asymptotic success the abstraction never beats PPO. If that were the whole story, the answer would be “don’t bother.” But three other axes tell a different, more defensible story.
1. Reusability — real, but conditional on a parametrized prior
The abstraction transfers across tasks only when its prior is parametrized to the task’s degrees of freedom:
- Fixed top-down/fixed-yaw prior on a random-yaw target → 0.33 (worse than learning-from-scratch, Part 31).
- Parametrize the prior by the target yaw → 0.67, recovering ~70% of the gap (Part 33), with no further gain from richer parametrization (Part 34).
So reusability is not free and not automatic: a fixed abstraction is a liability off its design regime; a parametrized abstraction is a genuine, transferable asset (and far more sample-efficient early — it carries a head-start the from-scratch learner lacks). The design lesson: parametrize priors to the task’s variation, do not hard-code them.
2. Stability — a matched prior makes the correction small and stable
Stability tracks how well the prior fits:
- Fixed PickCube residual: fragile optimum — peaks ~0.79 then collapses under continued training (Part 28). A large correction on a so-so prior is brittle.
- Orientation-aware residual: peak ≈ final (0.68, ~0.03 drop, Part 33/34) — a small correction on a matched prior is stable.
- Over-complicated prior (v2 combo): larger peak→final drop (0.63→0.55, Part 34) — stacking levers re-introduces instability.
- For external calibration: PPO is stable at its ceiling; and the InFOM reproduction shows the other face of instability — 1 of 3 seeds collapsed to 0.16 while two hit ~0.97 (seed-variance), a reminder that “stable” must be measured across seeds, not asserted.
The pattern: the right (matched, parametrized) prior buys stability — the learned part stays a small, robust correction instead of a large, fragile one.
3. Interpretability — structural, and the campaign relied on it
This axis is structural rather than a single metric, but it did real work throughout:
- The controller is a human-readable phase machine (reach → descend → grasp → lift → place), not a black-box MLP. You can read what the policy is trying to do.
- Failures are phase-attributable: the ~17% PickCube tail was localized to the grasp phase orientation (Parts 28-29), then proven a physical far-reach-upright limit (Part 30) — a diagnosis you can only make when the policy’s structure is legible.
- The residual-magnitude diagnostic told us where the learned part was doing work: “the residual was already compensating for the controller’s orientation limit” (Part 29) — which is why hard-coding the tilt was redundant. That is an interpretability win with direct experimental consequences.
- PPO offers none of this: a 0.82 success rate and an opaque network.
The honest takeaway
An abstraction does not beat strong model-free RL on asymptotic success — on PandaPickCube it ties and hits a physical ceiling; on harder variation it trails even when parametrized. Its value is elsewhere, and it is real: sample-efficiency (Part 27), stability when the prior is matched, reusability when the prior is parametrized to the task’s DOF, and interpretability (legible structure, phase-attributable failures, a residual diagnostic). That is a narrower but far more defensible claim than “abstraction wins” — and it is what the data actually supports. The route forward for capability is learning the skill (end-to-end RL); the route forward for trustworthy, transferable, debuggable control is a parametrized abstraction with a small learned residual on top.
Caveats
A synthesis of Parts 23-34 (all numbers cited there, read from JSON). The interpretability axis is structural,
not a new quantitative metric — claims are tied to specific diagnoses the structure enabled (Parts 28-30),
not to a fresh number. Reusability/stability are quantified from the orientation-task arc (Parts 31/33/34) and
the PickCube fragile-optimum (Part 28); the InFOM seed-variance (0.16 vs ~0.97) is from the OGBench cube
reproduction. Data across exp/tdmpc_glass/{generalization_PandaPickCubeOrientation*, hl_*} and the InFOM
repro_results/. Prior: Parts 27 (tie + sample-efficiency), 28 (fragile optimum), 30 (physical ceiling), 31/33/34
(reusability arc).