# 论文基线对照报告

- 高噪声主评估点: `0.30`
- `rho_raw = 0.9692`
- `rho_proj = 0.9000`
- `projection_cost = 948.1848`
- apples-to-apples 核心对照: 6 个 matched TD3 变体。
- broader safe RL comparators: PPO-Penalty / PPO-Lagrangian / SAC-Lagrangian / Shielded SAC。
- `Shielded SAC` 指执行时经过 Koopman-CBF / projection postprocess 的 plain SAC actor。

| 方法 | Return | RMSE | Applied Var | Diff MSE | Dense violation | Bellman-Lyapunov max |
|---|---:|---:|---:|---:|---:|---:|
| Direct TD3 | -59.590 +/- 7.037 | 0.537 +/- 0.050 | 0.1138 +/- 0.0059 | 0.2731 +/- 0.0158 | 0.939 +/- 0.122 | 92.3911 +/- 30.8738 |
| TD3 + action-diff penalty | -63.337 +/- 8.737 | 0.565 +/- 0.061 | 0.1118 +/- 0.0053 | 0.2657 +/- 0.0154 | 0.939 +/- 0.122 | 109.0962 +/- 39.6698 |
| TD3 + low-pass only | -45.037 +/- 10.245 | 0.530 +/- 0.082 | 0.0544 +/- 0.0029 | 0.0962 +/- 0.0120 | 0.933 +/- 0.120 | 54.1755 +/- 14.2398 |
| TD3 + projection only | -55.285 +/- 12.383 | 0.505 +/- 0.097 | 0.1033 +/- 0.0126 | 0.2761 +/- 0.0328 | 0.122 +/- 0.057 | 82.3203 +/- 46.7980 |
| TD3 + variance regularizer only | -74.433 +/- 12.637 | 0.661 +/- 0.076 | 0.0984 +/- 0.0021 | 0.2212 +/- 0.0073 | 0.917 +/- 0.102 | 208.1761 +/- 70.8725 |
| Full method | -9.322 +/- 0.197 | 0.282 +/- 0.004 | 0.0064 +/- 0.0008 | 0.0072 +/- 0.0030 | 0.000 +/- 0.000 | 6.7080 +/- 1.3189 |
| PPO-Penalty | -190.951 +/- 146.747 | 1.133 +/- 0.614 | 0.0937 +/- 0.0055 | 0.2066 +/- 0.0225 | 0.833 +/- 0.156 | 3083.9876 +/- 3827.8611 |
| PPO-Lagrangian | -126.863 +/- 37.426 | 0.885 +/- 0.127 | 0.0912 +/- 0.0023 | 0.1916 +/- 0.0108 | 0.933 +/- 0.084 | 2163.1639 +/- 1695.6028 |
| SAC-Lagrangian | -55.368 +/- 4.221 | 0.464 +/- 0.039 | 0.1340 +/- 0.0017 | 0.3378 +/- 0.0152 | 0.756 +/- 0.090 | 45.6897 +/- 7.5815 |
| Shielded SAC | -40.977 +/- 1.238 | 0.382 +/- 0.016 | 0.1056 +/- 0.0089 | 0.2972 +/- 0.0339 | 0.167 +/- 0.050 | 42.3887 +/- 9.7968 |

## Checks

- Full method satisfies `rho_proj < 1`: `True`
- Full method reduces applied variance vs Direct TD3: `True`
- Full method reduces applied variance vs TD3 + action-diff penalty: `True`
- Full method reduces applied variance vs TD3 + projection only: `True`
- Full method reduces dense safety violations vs TD3 + variance regularizer only: `True`
- Full method reduces Bellman-Lyapunov residual vs TD3 + variance regularizer only: `True`
- TD3 + low-pass only improves action-diff MSE vs Direct TD3: `True`
- TD3 + projection only reduces dense safety violations vs Direct TD3: `True`
- PPO-Penalty produced finite aggregated results: `True`
- PPO-Penalty wrote complete per-seed artifacts: `True`
- PPO-Lagrangian produced finite aggregated results: `True`
- PPO-Lagrangian wrote complete per-seed artifacts: `True`
- SAC-Lagrangian produced finite aggregated results: `True`
- SAC-Lagrangian wrote complete per-seed artifacts: `True`
- Shielded SAC produced finite aggregated results: `True`
- Shielded SAC wrote complete per-seed artifacts: `True`
