input/v1/SPEC.md

# Experiment Spec: ICML 2026 Chebyshev Policies reproduction

## Identity

- Experiment id: `icml2026_chebyshev_v1`
- Spec version: `1.0.0`
- OpenReview id: `aNWIVNjocB`
- arXiv input: `2605.22305v4` (2026-07-08)
- Challenge input: five anchored claims supplied on 2026-07-16
- Paper code commit: `fad6ebb46f976db29eb5ba509622dc3c24b7ac5f`
- Companion commit: `ed945331ce989592d75af9e8410823ee007e13a8`

## Research questions and claims

1. Does the argument of Theorem 2.4 imply a loss-minimizing action field
   `alpha(t) = C * x_dot(t)`, independent of position?
2. On 100 evenly spaced deterministic Mountain Car starts in `[-0.6, -0.4]`,
   does the two-phase analytical policy achieve the reported return range and
   outperform the bundled ARS, PPO, and SAC policies by the reported margins?
3. Under the released 20-seed, 80,000-step protocol, does degree-3 CH-ARS
   attain the current v4 Table 1 performance? Are the paper's parameter count
   and reduction factor arithmetically and implementation-wise correct?
4. Under the released protocols, do CH-3-PPO and CH-3-REINFORCE attain the
   current v4 Table 1 performance and regret improvements?
5. Does the released Pendulum protocol reproduce CH-6-ARS `-150.8` versus
   neural ARS `-218.3` on the 50 x 50 deterministic grid? The Aero 2 physical
   result is audited separately because the required hardware is unavailable.

## Version-drift contract

The generated challenge Claim 3 quotes an older manuscript (`regret 0.65`,
`4.18x`), while arXiv v4 reports `0.44` and `6.18x`. A generic judge claim also
quotes `268x`, while the anchored claim and v4 say `277x`. No value is silently
substituted: raw and derived outputs carry `claim_source`, `paper_version`, and
the reported comparator value. The logbook presents both the stale challenge
wording and the current paper result.

## Experimental units

- Claims 1-2: one deterministic episode per policy and start position.
- Claims 3-4: one independently initialized training run per algorithm and
  seed, followed by one deterministic episode per trained policy and start.
- REINFORCE selection: one training run per seed, 50 seeded random-start
  evaluation episodes per trained policy, select exactly the highest mean,
  then evaluate that selected policy on the fixed 100-start grid.
- Claim 5: one training run per CH-6-ARS seed and one episode per policy and
  point on the fixed 2,500-state Pendulum grid; select the highest grid mean.

## Systems and conditions

- Analytical two-phase Mountain Car policy with `C1=4.3346`, `C2=4.8358`.
- Released RL Baselines3 Zoo checkpoints: ARS, PPO, SAC.
- CH-3-ARS: degree 3, learning rate `0.018`, `delta_std=0.1`, `n_delta=4`,
  `n_top=1`, 80,000 steps, seeds `0, 123, ..., 2337`.
- CH-3-PPO: degree 3, learning rate `0.001`, `n_steps=2048`, batch size
  `1048`, 2 epochs, clip ranges `0.4`, 70,000 steps, the same 20 seeds.
- CH-3-REINFORCE: AdamW, degree 3, 100 episodes, discount `0.9`, learning
  rates `0.0003` for mean and `0.00003` for sigma, 20 explicit seeds, then 50
  evaluation episodes per policy.
- Pendulum CH-6-ARS: degree 6, learning rate `0.018`, `delta_std=0.3`,
  `n_delta=8`, all deltas retained, 2,000,000 steps, 30 released-protocol
  seeds, evaluated on 50 angles x 50 angular velocities.

## Primary metrics

- Episode return, with mean, standard deviation, minimum, and maximum.
- Regret: analytical-policy mean return minus evaluated-policy mean return.
- Regret improvement: neural baseline regret divided by Chebyshev regret.
- Trainable scalar count derived from executable model state and from the
  architecture stated in the paper; both sources remain separate.

## Secondary metrics

- Episode length, terminal velocity, wall time, peak resident memory.
- Per-start return and per-seed outcome distributions.
- Training checkpoints/evaluation curves when emitted by the algorithm.
- Policy action values on a fixed position-velocity grid for visualization.

## Panels and selection rules

- `mountaincar_primary_v1`: exactly 100 evenly spaced starts in
  `[-0.6, -0.4]`; all successful rows included.
- `training_all_seeds_v1`: every planned seed, including failures.
- `best_by_fixed_grid_mean_v1`: select the trained policy with the largest
  mean on the predeclared fixed evaluation grid. Never select by a single
  episode or by the paper target.
- `pendulum_primary_v1`: Cartesian product of 50 angles in `[-pi, pi]` and
  50 angular velocities in `[-1, 1]`.

## Success, failure, and exclusions

- A full empirical reproduction requires complete planned row coverage and a
  Hugging Face GPU Job. Any missing seed/start is a failed panel, not silently
  dropped.
- A run is successful only if the process exits zero, all metrics are finite,
  and the expected output/checkpoint count is exact.
- No retries are automatic. A retry receives a new `batch_id` and
  `attempt_id`; the original failure remains raw evidence.
- Local smoke profiles are explicitly `toy` and cannot support a full claim.
- Performance is considered numerically reproduced when the deterministic
  mean is within `0.05` return of the current paper value and the reported
  ordering holds. This tolerance was fixed before reportable collection.
- The historical priority phrase "first" and the physical Aero 2 result are
  not inferred from simulation. The former is a literature claim; the latter
  remains unverified without the hardware.

## Raw evidence

Each unique `runs/raw/<batch-id>/` contains `records.jsonl`, `manifest.json`,
environment metadata, stdout/stderr captured by Trackio/HF Jobs, and newly
trained coefficients. Raw directories are never overwritten.

## Canonical tables

- `runs/tables/episodes.csv`: one row per evaluated episode/start.
- `runs/tables/training_runs.csv`: one row per training seed/attempt.
- `runs/tables/summary.csv`: one row per method and declared panel.
- `runs/tables/parameter_audit.csv`: one row per parameter-count source.
- `runs/tables/MANIFEST.json`: hashes, row counts, source batches, command.

## Planned analysis outputs

- Interactive position-velocity policy microscope with trajectories.
- Per-start return curves for analytical, neural, and Chebyshev policies.
- All-seed strip/violin distributions with the selected seed identified.
- Parameter-count versus regret Pareto chart with count-source annotations.
- Pendulum initial-state return heatmaps and paired method differences.
- Claim-evidence map linking every conclusion to tables, scripts, and raw rows.

## Hardware and budget

Local execution is only a smoke test. Full empirical runs use Hugging Face
`t4-medium` Jobs (8 vCPU, 30 GB system RAM, one 16 GB T4) to stay below the
32 GB requirement. The released implementations are CPU-bound; GPU presence
is recorded honestly and no CUDA speedup is claimed. Each Job has a fixed
timeout no greater than 24 hours.

## Known limitations

- The two author repositories have no declared license, so they are fetched
  at pinned commits rather than republished.
- The released notebooks rely on an uncommitted PickleShare database. This
  reproduction executes source APIs from clean configs and does not treat
  notebook outputs as measurements.
- The physical Quanser Aero 2 experiment cannot be recreated without access
  to that system. Simulation is not substituted for the real-hardware claim.
- Theorem 2.4 is addressed with a proof audit and numerical consequences; a
  numerical experiment alone cannot establish historical priority.

## Revision log

- `1.0.0` (2026-07-16): Initial pre-collection specification. No reportable
  reproduction results had been collected in this repository.