{
  "schemaVersion": 1,
  "lessonId": "rl-04",
  "contentHash": "60ee26b667e26e302f7f6417e510aff429e2068da88b725c7268c907aa9f2a03",
  "executedAt": "2026-10-20T10:49:26.500487+00:00",
  "environment": {
    "backend": "cpu",
    "deviceCount": 1,
    "python": "3.14.3",
    "jax": "0.9.2",
    "numpy": "2.4.4",
    "matplotlib": "3.10.8"
  },
  "stdout": "training seeds: [0, 7, 23, 41, 59]\nheld-out mean per agent: [0.9759717  0.97472161 0.97537106 0.96944821 0.97455072]\nexact mean per agent: [0.97578394 0.9749347  0.97562152 0.97113729 0.97404611]\nuniform baseline mean: 0.46628910303115845\nacross-agent mean / sample sd: 0.9740126609802247 0.0026129212275767476\ntraining seeds: [0, 7, 23, 41, 59]\nheld-out mean per agent: [0.9759717  0.97472161 0.97537106 0.96944821 0.97455072]\nexact mean per agent: [0.97578394 0.9749347  0.97562152 0.97113729 0.97404611]\nuniform baseline mean: 0.46628910303115845\nacross-agent mean / sample sd: 0.9740126609802247 0.0026129212275767476\nleft / random / right: -0.07999999821186066 0.46628910303115845 0.9850389361381531\npaired improvements: [0.5096826  0.50843251 0.50908196 0.50315911 0.50826162]\nmean improvement across trained agents: 0.5077235579490662\nsample sd / independence-assuming SE: 0.09999999999999998 0.05773502691896257\nPASS: rl-04\n",
  "notebookCells": [
    {
      "sourceHash": "af95e59a5d7f21b8f48aacaed167169baf923af14c9cc2792a48ff275369a743",
      "outputs": []
    },
    {
      "sourceHash": "4701931233a88aa473c4058149871c02297f4638585b48f21ad9dae8e71ad711",
      "outputs": []
    },
    {
      "sourceHash": "f7369b37b546f8530b8333b0b828620b25465d72fbfc60fd1f20261b16a6ab3b",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "training seeds: [0, 7, 23, 41, 59]\n",
            "held-out mean per agent: [0.9759717  0.97472161 0.97537106 0.96944821 0.97455072]\n",
            "exact mean per agent: [0.97578394 0.9749347  0.97562152 0.97113729 0.97404611]\n",
            "uniform baseline mean: 0.46628910303115845\n",
            "across-agent mean / sample sd: 0.9740126609802247 0.0026129212275767476\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "910b7ef30bf9de68d459b47cd2cf69334b1133402d037f656f7298e82cae1b65",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "training seeds: [0, 7, 23, 41, 59]\n",
            "held-out mean per agent: [0.9759717  0.97472161 0.97537106 0.96944821 0.97455072]\n",
            "exact mean per agent: [0.97578394 0.9749347  0.97562152 0.97113729 0.97404611]\n",
            "uniform baseline mean: 0.46628910303115845\n",
            "across-agent mean / sample sd: 0.9740126609802247 0.0026129212275767476\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "18506b6161ee5ac04e5dc26adfdbfbc23afadbf9781a10f8f874eb646fa50e41",
      "outputs": []
    },
    {
      "sourceHash": "25df6d662f9d3f0c4e984c6a201f79fa0cfd7a2633dc4b0773dfba6c2dd4ee6c",
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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            "text/plain": [
              "Executed Matplotlib figure"
            ]
          }
        }
      ]
    },
    {
      "sourceHash": "72f302eff008830c3ba175f21047d8767a0e20c65ce385f70ae7f5a381366541",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "left / random / right: -0.07999999821186066 0.46628910303115845 0.9850389361381531\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "127bd83c6457b93e70fe4e57a87e438e0f92c8e967216cb230459ba311448609",
      "outputs": []
    },
    {
      "sourceHash": "b740b67b8c77c6ef25a9e95ced5c469e49308d9507bb7aa4cb28680b0f530834",
      "outputs": []
    },
    {
      "sourceHash": "f6619796ae268b2ac74ee075fe8c0b37bb5ff3a8e1257f05a28e7264dc73a48e",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "paired improvements: [0.5096826  0.50843251 0.50908196 0.50315911 0.50826162]\n",
            "mean improvement across trained agents: 0.5077235579490662\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "0499d2230e66af77b0bf49d5505f03b4479399331700c53a4d62013bf1c9af55",
      "outputs": []
    },
    {
      "sourceHash": "3d9038b72b5f69997ea676c573cadcc065140d8d291b41895e8d3f7c34227c29",
      "outputs": []
    },
    {
      "sourceHash": "a0b5412631ffb915ca95e89bf6d1f665db345fb6582a819c6b1492c7722f32fc",
      "outputs": []
    },
    {
      "sourceHash": "db61a8a42866aab523d411a1edac5c55674aa955301b0174eeca4a683a5421d0",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "sample sd / independence-assuming SE: 0.09999999999999998 0.05773502691896257\n"
          ]
        }
      ]
    }
  ],
  "scope": "Recorded instructor reference run; all script assertions and notebook code cells passed. No accelerator performance claim."
}