# Partition-control grid summary

protocol sha256 `db3627c504311700b059edecc04bf7fbd5e3f30757e3e25aa9358ddc2a3efb29`; runs found 80/80

## Final return at 100k (mean [bootstrap 95% CI] (n))

| task | rad | se | rand | value |
|---|---|---|---|---|
| cartpole_swingup | 629.1 [514.0, 745.8] (n=5) | 187.5 [96.5, 289.7] (n=5) | 232.2 [121.8, 342.7] (n=5) | 352.3 [286.3, 418.3] (n=5) |
| ball_in_cup_catch | 617.7 [450.0, 765.8] (n=10) | 814.5 [720.6, 892.2] (n=10) | 869.0 [820.7, 910.2] (n=10) | 727.7 [578.6, 857.3] (n=10) |
| cheetah_run | 334.7 [273.2, 384.5] (n=5) | 328.1 [273.8, 397.1] (n=5) | 331.9 [300.1, 364.4] (n=5) | 355.6 [327.6, 383.8] (n=5) |

## Paired contrasts (final return)

| contrast | cartpole_swingup | ball_in_cup_catch | cheetah_run | aggregate (normalised) |
|---|---|---|---|---|
| se-rand | -44.7 [-175.8, 129.8] (n=5) 2/5 | -54.5 [-146.3, 33.3] (n=10) 4/10 | -3.8 [-83.0, 89.8] (n=5) 2/5 | -0.058 [-0.174, +0.069] |
| value-rad | -276.9 [-419.4, -142.7] (n=5) 0/5 | 110.0 [-58.8, 278.5] (n=10) 7/10 | 20.9 [-31.9, 82.6] (n=5) 2/5 | -0.077 [-0.208, +0.049] |
| se-rad | -441.6 [-558.7, -318.5] (n=5) 0/5 | 196.8 [86.7, 330.9] (n=10) 10/10 | -6.6 [-97.8, 67.5] (n=5) 3/5 | -0.144 [-0.260, -0.026] |
| rand-rad | -396.9 [-610.5, -182.3] (n=5) 0/5 | 251.3 [101.1, 437.0] (n=10) 9/10 | -2.8 [-68.3, 81.8] (n=5) 2/5 | -0.087 [-0.249, +0.078] |
| value-se | 164.7 [34.0, 295.5] (n=5) 4/5 | -86.8 [-192.0, 1.4] (n=10) 3/10 | 27.5 [-56.4, 104.9] (n=5) 4/5 | +0.067 [-0.043, +0.177] |
| value-rand | 120.1 [-7.1, 210.1] (n=5) 4/5 | -141.3 [-275.0, -10.6] (n=10) 2/10 | 23.7 [-6.9, 49.1] (n=5) 4/5 | +0.009 [-0.093, +0.102] |

## Decision

```
{
 "se_membership_matters": false,
 "se_minus_rand_aggregate": {
  "normalised_mean_diff": -0.057863534720889294,
  "ci95": [
   -0.1739594181735754,
   0.06883700963792594
  ],
  "normalised_mean_diff_x_return_units_note": "fraction of the v1 RAD per-task mean final return, averaged over tasks"
 },
 "tasks_with_se_gt_rand": 0,
 "value_membership_helps": false,
 "value_minus_rad_aggregate": {
  "normalised_mean_diff": -0.07749113835392407,
  "ci95": [
   -0.20828165829425663,
   0.04921688369196393
  ],
  "normalised_mean_diff_x_return_units_note": "fraction of the v1 RAD per-task mean final return, averaged over tasks"
 },
 "grid_complete": true
}
```

## Gate

```
{
 "per_task": {
  "cartpole_swingup": {
   "windows": 60,
   "on": 23,
   "on_fraction": 0.38333333333333336
  },
  "ball_in_cup_catch": {
   "windows": 240,
   "on": 240,
   "on_fraction": 1.0
  },
  "cheetah_run": {
   "windows": 120,
   "on": 115,
   "on_fraction": 0.9583333333333334
  }
 },
 "identical_used_decisions": {
  "task_seed_triples_identical": 20,
  "triples_differing": 0
 },
 "own_vs_used_agreement": {
  "se": {
   "agree": 420,
   "windows": 420,
   "fraction": 1.0
  },
  "rand": {
   "agree": 379,
   "windows": 420,
   "fraction": 0.9023809523809524
  },
  "value": {
   "agree": 387,
   "windows": 420,
   "fraction": 0.9214285714285714
  }
 },
 "overall": {
  "windows": 420,
  "on": 378,
  "on_fraction": 0.9
 },
 "fallbacks": {
  "se": 0,
  "rand": 0,
  "value": 0
 },
 "null_diagnostics": {
  "ipf_max_rel_err": 0.37015289690340875,
  "n_nonpos_weights": 0,
  "margin_bits": {
   "n": 420,
   "min": -1.0473734827137307,
   "median": 1.2537583070951797,
   "max": 2.6201885874283084
  }
 }
}
```

## Invariants

```
{
 "se": {
  "abs_steps_logged": 4175,
  "size_multiset_equal_to_same_batch_SE": 4175,
  "size_multiset_mismatch": 0,
  "n_clusters_median": 20.0,
  "n_clusters_min": 2,
  "n_clusters_max": 195,
  "h1_mean": 7.867515873010772,
  "h2_se_mean": 5.213522380520599,
  "h2_used_mean": 5.213522380520599,
  "h2_used_minus_h2_se_mean": 0.0,
  "h2_used_minus_h2_se_min": 0.0,
  "ari_mean": 1.0,
  "ari_max": 1.0,
  "nmi_mean": 1.0,
  "nmi_max": 1.0000000000000002,
  "v_std_mean": 30.426785413045806,
  "within_value_var_fraction_used_mean": 0.14161453975233682,
  "within_value_var_fraction_se_mean": 0.14161453975233682,
  "degenerate_steps": 0,
  "exceptions": 0,
  "applied_steps": 3775,
  "gated_off_steps": 400
 },
 "rand": {
  "abs_steps_logged": 4175,
  "size_multiset_equal_to_same_batch_SE": 4175,
  "size_multiset_mismatch": 0,
  "n_clusters_median": 19.0,
  "n_clusters_min": 2,
  "n_clusters_max": 197,
  "h1_mean": 7.8704657246501215,
  "h2_se_mean": 5.233306602275124,
  "h2_used_mean": 7.579075605386685,
  "h2_used_minus_h2_se_mean": 2.3457690031115614,
  "h2_used_minus_h2_se_min": 0.25492700407480395,
  "ari_mean": -0.00024205067930178139,
  "ari_max": 0.08347644462945253,
  "nmi_mean": 0.2766637959700257,
  "nmi_max": 0.938860103626943,
  "v_std_mean": 26.270029152373354,
  "within_value_var_fraction_used_mean": 0.846291246527999,
  "within_value_var_fraction_se_mean": 0.15018188770370397,
  "degenerate_steps": 0,
  "exceptions": 0,
  "applied_steps": 3775,
  "gated_off_steps": 400
 },
 "value": {
  "abs_steps_logged": 4175,
  "size_multiset_equal_to_same_batch_SE": 4175,
  "size_multiset_mismatch": 0,
  "n_clusters_median": 20.0,
  "n_clusters_min": 2,
  "n_clusters_max": 198,
  "h1_mean": 7.86676321495457,
  "h2_se_mean": 5.191291077509499,
  "h2_used_mean": 7.049939756933141,
  "h2_used_minus_h2_se_mean": 1.858648679423643,
  "h2_used_minus_h2_se_min": 0.11534666720934705,
  "ari_mean": 0.10293935949027858,
  "ari_max": 0.7735218013104067,
  "nmi_mean": 0.4295327309388831,
  "nmi_max": 0.9420289855072462,
  "v_std_mean": 25.4571163108418,
  "within_value_var_fraction_used_mean": 0.13926005060753585,
  "within_value_var_fraction_se_mean": 0.15773036023407241,
  "degenerate_steps": 0,
  "exceptions": 0,
  "applied_steps": 3775,
  "gated_off_steps": 400
 },
 "per_task": {
  "cartpole_swingup": {
   "se": {
    "abs_steps": 575,
    "K_median": 154.0,
    "K_iqr": [
     108.0,
     162.0
    ],
    "singleton_share_median": 0.28515625,
    "applied_fraction": 0.391304347826087,
    "h2_used_minus_h2_se_mean": 0.0,
    "h1_minus_h2_se_mean": 2.875630734953619,
    "ari_mean": 1.0,
    "nmi_mean": 1.0,
    "wf_used_mean": 0.1368885883811454,
    "wf_se_mean": 0.1368885883811454,
    "v_std_mean": 6.34084590433394,
    "n_edges_median": 277.0
   },
   "rand": {
    "abs_steps": 575,
    "K_median": 151.0,
    "K_iqr": [
     96.0,
     162.0
    ],
    "singleton_share_median": 0.26953125,
    "applied_fraction": 0.391304347826087,
    "h2_used_minus_h2_se_mean": 2.8425229202716897,
    "h1_minus_h2_se_mean": 2.924737429552376,
    "ari_mean": -0.0006149963385947654,
    "nmi_mean": 0.7308575640838652,
    "wf_used_mean": 0.5189288628799265,
    "wf_se_mean": 0.1341911671450881,
    "v_std_mean": 8.28550355738218,
    "n_edges_median": 278.0
   },
   "value": {
    "abs_steps": 575,
    "K_median": 151.0,
    "K_iqr": [
     96.5,
     162.0
    ],
    "singleton_share_median": 0.26953125,
    "applied_fraction": 0.391304347826087,
    "h2_used_minus_h2_se_mean": 2.456101587104205,
    "h1_minus_h2_se_mean": 2.94664025470624,
    "ari_mean": 0.07034010375813508,
    "nmi_mean": 0.7704917461649478,
    "wf_used_mean": 0.013966153672945915,
    "wf_se_mean": 0.1285670387843209,
    "v_std_mean": 7.592644747958339,
    "n_edges_median": 277.0
   }
  },
  "ball_in_cup_catch": {
   "se": {
    "abs_steps": 2400,
    "K_median": 13.0,
    "K_iqr": [
     8.0,
     21.0
    ],
    "singleton_share_median": 0.01171875,
    "applied_fraction": 1.0,
    "h2_used_minus_h2_se_mean": 0.0,
    "h1_minus_h2_se_mean": 2.3953609976122134,
    "ari_mean": 1.0,
    "nmi_mean": 1.0,
    "wf_used_mean": 0.14695294337348694,
    "wf_se_mean": 0.14695294337348694,
    "v_std_mean": 48.688021694563275,
    "n_edges_median": 1176.5
   },
   "rand": {
    "abs_steps": 2400,
    "K_median": 12.0,
    "K_iqr": [
     8.0,
     20.0
    ],
    "singleton_share_median": 0.0078125,
    "applied_fraction": 1.0,
    "h2_used_minus_h2_se_mean": 1.957121125250212,
    "h1_minus_h2_se_mean": 2.3267395403756246,
    "ari_mean": -0.0003251482114078067,
    "nmi_mean": 0.11487493689726766,
    "wf_used_mean": 0.9449022846231522,
    "wf_se_mean": 0.1670450904907154,
    "v_std_mean": 41.05536489393983,
    "n_edges_median": 1242.0
   },
   "value": {
    "abs_steps": 2400,
    "K_median": 12.0,
    "K_iqr": [
     8.0,
     20.0
    ],
    "singleton_share_median": 0.01171875,
    "applied_fraction": 1.0,
    "h2_used_minus_h2_se_mean": 1.5020657148455558,
    "h1_minus_h2_se_mean": 2.3914311001883486,
    "ari_mean": 0.11813160888570666,
    "nmi_mean": 0.3131788308431747,
    "wf_used_mean": 0.20029202238964283,
    "wf_se_mean": 0.17738048588139765,
    "v_std_mean": 39.6808803923345,
    "n_edges_median": 1136.5
   }
  },
  "cheetah_run": {
   "se": {
    "abs_steps": 1200,
    "K_median": 36.0,
    "K_iqr": [
     21.0,
     64.0
    ],
    "singleton_share_median": 0.0625,
    "applied_fraction": 0.9583333333333334,
    "h2_used_minus_h2_se_mean": 0.0,
    "h1_minus_h2_se_mean": 3.0650573035656876,
    "ari_mean": 1.0,
    "nmi_mean": 1.0,
    "wf_used_mean": 0.13320225087539905,
    "wf_se_mean": 0.13320225087539905,
    "v_std_mean": 5.445492197935301,
    "n_edges_median": 433.0
   },
   "rand": {
    "abs_steps": 1200,
    "K_median": 39.0,
    "K_iqr": [
     21.0,
     70.0
    ],
    "singleton_share_median": 0.06640625,
    "applied_fraction": 0.9583333333333334,
    "h2_used_minus_h2_se_mean": 2.885036840195032,
    "h1_minus_h2_se_mean": 3.120200347517916,
    "ari_mean": 0.00010284751332149044,
    "nmi_mean": 0.3826070002276603,
    "wf_used_mean": 0.8059303125023943,
    "wf_se_mean": 0.12411770239735118,
    "v_std_mean": 5.316942850173658,
    "n_edges_median": 419.0
   },
   "value": {
    "abs_steps": 1200,
    "K_median": 40.0,
    "K_iqr": [
     22.0,
     68.25
    ],
    "singleton_share_median": 0.06640625,
    "applied_fraction": 0.9583333333333334,
    "h2_used_minus_h2_se_mean": 2.2855350903162144,
    "h1_minus_h2_se_mean": 3.113619489104204,
    "ari_mean": 0.08817533740440778,
    "nmi_mean": 0.4988643363344773,
    "wf_used_mean": 0.07723276599114627,
    "wf_se_mean": 0.13240420046742787,
    "v_std_mean": 5.56964743840473,
    "n_edges_median": 415.5
   }
  }
 },
 "cross_arm_same_update": {
  "compared": 4175,
  "equal": 0,
  "first_divergence_u": [
   [
    "cartpole_swingup",
    1,
    0
   ],
   [
    "cartpole_swingup",
    2,
    0
   ],
   [
    "cartpole_swingup",
    3,
    0
   ],
   [
    "cartpole_swingup",
    4,
    0
   ],
   [
    "cartpole_swingup",
    5,
    0
   ],
   [
    "ball_in_cup_catch",
    1,
    0
   ],
   [
    "ball_in_cup_catch",
    2,
    0
   ],
   [
    "ball_in_cup_catch",
    3,
    0
   ],
   [
    "ball_in_cup_catch",
    4,
    0
   ],
   [
    "ball_in_cup_catch",
    5,
    0
   ],
   [
    "ball_in_cup_catch",
    6,
    0
   ],
   [
    "ball_in_cup_catch",
    7,
    0
   ],
   [
    "ball_in_cup_catch",
    8,
    0
   ],
   [
    "ball_in_cup_catch",
    9,
    0
   ],
   [
    "ball_in_cup_catch",
    10,
    0
   ],
   [
    "cheetah_run",
    1,
    0
   ],
   [
    "cheetah_run",
    2,
    0
   ],
   [
    "cheetah_run",
    3,
    0
   ],
   [
    "cheetah_run",
    4,
    0
   ],
   [
    "cheetah_run",
    5,
    0
   ]
  ]
 },
 "counters_from_result_json": {
  "rad": {
   "abs_fire": 0,
   "abs_applied": 0,
   "abs_gated_off": 0,
   "abs_degenerate": 0,
   "abs_skip": 0,
   "runs": 20
  },
  "se": {
   "abs_fire": 4175,
   "abs_applied": 3775,
   "abs_gated_off": 400,
   "abs_degenerate": 0,
   "abs_skip": 0,
   "runs": 20
  },
  "rand": {
   "abs_fire": 4175,
   "abs_applied": 3775,
   "abs_gated_off": 400,
   "abs_degenerate": 0,
   "abs_skip": 0,
   "runs": 20
  },
  "value": {
   "abs_fire": 4175,
   "abs_applied": 3775,
   "abs_gated_off": 400,
   "abs_degenerate": 0,
   "abs_skip": 0,
   "runs": 20
  }
 }
}
```

## Determinism vs v1 RAD

```
{
 "final_identical": 0,
 "step0_identical": 15,
 "curve_identical": 0,
 "n": 15,
 "abs_diff_median": 104.70089869508064,
 "abs_diff_max": 498.1
}
```