bandit-delayed-feedback

{"output": "total 3008\ndrwxr-xr-x 2 root root    4096 Mar  4 09:09 .\ndrwxr-xr-x 1 root root    4096 Mar  4 09:10 ..\n-rw-rw-r-- 1 root root    1128 Mar  4 09:05 arms_metadata.json\n-rw-rw-r-- 1 root root  135100 Mar  4 09:05 conversions.csv\n-rw-rw-r-- 1 root root 2818804 Mar  4 09:05 impressions.csv\n-rw-rw-r-- 1 root root  108862 Mar  4 09:05 test_contexts.csv", "exit_code": 0, "error": null}

I'll analyze this multi-armed bandit problem with delayed feedback. Let me start by exploring the data structure.

→ terminal({"command": "ls -la /app/data/"})

{"content": "     1|impression_id,arm_id,timestamp,hour_of_day,day_of_week,user_segment,device_type,context_feature_1,context_feature_2\n     2|IMP_000000,0,1709340758,9,5,young,mobile,0.7797,0.5969\n     3|IMP_000001,6,1710354874,3,3,young,desktop,0.7081,0.0206\n     4|IMP_000002,9,1710010543,3,6,young,desktop,0.6117,0.0071\n     5|IMP_000003,3,1710416879,20,3,senior,mobile,0.7852,0.1997\n     6|IMP_000004,8,1709492338,3,0,young,desktop,0.1705,0.0651\n     7|IMP_000005,4,1709917161,1,5,young,mobile,0.2309,0.241\n     8|IMP_000006,3,1710022391,7,6,senior,mobile,0.3911,0.1822\n     9|IMP_000007,5,1709490636,3,0,senior,desktop,0.4498,0.3952\n    10|IMP_000008,1,1709706679,15,2,middle,mobile,0.0452,0.3253\n    11|IMP_000009,0,1709752356,4,3,middle,tablet,0.607,0.276\n    12|IMP_000010,2,1709267784,13,4,senior,mobile,0.3949,0.2935\n    13|IMP_000011,6,1709232786,3,4,senior,desktop,0.074,0.3585\n    14|IMP_000012,3,1710297911,11,2,middle,mobile,0.3708,0.6688\n    15|IMP_000013,3,1709243338,6,4,senior,mobile,0.1196,0.7132\n    16|IMP_000014,1,1710116221,9,0,senior,mobile,0.7107,0.1109\n    17|IMP_000015,6,1710317391,17,2,senior,mobile,0.5633,0.6955\n    18|IMP_000016,5,1710192348,6,1,senior,desktop,0.2288,0.077\n    19|IMP_000017,1,1709634315,19,1,middle,desktop,0.2956,0.1055\n    20|IMP_000018,7,1709244739,7,4,middle,tablet,0.3243,0.1221\n    21|IMP_000019,1,1709904240,22,4,young,desktop,0.0005,0.3526\n    22|IMP_000020,7,1709447376,15,6,senior,mobile,0.2441,0.1683\n    23|IMP_000021,5,1709337251,8,5,young,mobile,0.2539,0.2469\n    24|IMP_000022,0,1709810260,20,3,young,tablet,0.2668,0.9766\n    25|IMP_000023,1,1709488336,2,0,young,mobile,0.1449,0.4895\n    26|IMP_000024,4,1710337843,22,2,senior,desktop,0.2376,0.7282\n    27|IMP_000025,1,1710202037,9,1,middle,desktop,0.0903,0.8353\n    28|IMP_000026,1,1710283084,7,2,senior,desktop,0.6776,0.0166\n    29|IMP_000027,0,1709877071,14,4,senior,mobile,0.6909,0.3867\n    30|IMP_000028,9,1710275531,5,2,young,mobile,0.9247,0.8773\n    31|", "total_lines": 50001, "file_size": 2818804, "truncated": true, "hint": "Use offset=31 to continue reading (showing 1-30 of 50001 lines)", "is_binary": false, "is_image": false}

{"content": "     1|impression_id,conversion_timestamp,delay_hours,conversion_value\n     2|IMP_000010,1709305348,10.43,3.58\n     3|IMP_000013,1709320719,21.49,1.07\n     4|IMP_000022,1709843815,9.32,3.47\n     5|IMP_000069,1710312110,4.57,2.48\n     6|IMP_000071,1710446648,25.86,1.37\n     7|IMP_000090,1709973192,28.94,1.46\n     8|IMP_000097,1710100917,68.48,1.67\n     9|IMP_000109,1709851031,16.83,1.67\n    10|IMP_000119,1709561787,17.17,3.28\n    11|IMP_000124,1709437238,6.31,1.1\n    12|IMP_000126,1709398071,12.93,2.35\n    13|IMP_000127,1709550349,3.65,3.02\n    14|IMP_000130,1709845772,67.73,1.5\n    15|IMP_000131,1709832027,11.88,0.96\n    16|IMP_000138,1709742702,27.46,2.38\n    17|IMP_000152,1710203669,9.83,1.31\n    18|IMP_000188,1710048427,4.77,1.79\n    19|IMP_000201,1709914355,4.67,2.85\n    20|IMP_000202,1710336058,72.0,1.63\n    21|IMP_000213,1710348149,29.0,3.11\n    22|IMP_000218,1709681051,25.35,1.82\n    23|IMP_000220,1710010244,12.4,1.14\n    24|IMP_000224,1710015389,41.47,1.45\n    25|IMP_000231,1710325201,8.36,1.11\n    26|IMP_000246,1709806072,12.57,2.36\n    27|IMP_000255,1710275599,11.5,2.59\n    28|IMP_000258,1709250382,3.75,1.87\n    29|IMP_000270,1709913684,72.0,1.63\n    30|IMP_000271,1710186715,11.24,2.48\n    31|", "total_lines": 4175, "file_size": 135100, "truncated": true, "hint": "Use offset=31 to continue reading (showing 1-30 of 4175 lines)", "is_binary": false, "is_image": false}

{"content": "     1|{\n     2|  \"arms\": [\n     3|    {\n     4|      \"arm_id\": 0,\n     5|      \"name\": \"Campaign A\",\n     6|      \"category\": \"electronics\",\n     7|      \"base_bid\": 0.3\n     8|    },\n     9|    {\n    10|      \"arm_id\": 1,\n    11|      \"name\": \"Campaign B\",\n    12|      \"category\": \"fashion\",\n    13|      \"base_bid\": 0.4\n    14|    },\n    15|    {\n    16|      \"arm_id\": 2,\n    17|      \"name\": \"Campaign C\",\n    18|      \"category\": \"home\",\n    19|      \"base_bid\": 0.5\n    20|    },\n    21|    {\n    22|      \"arm_id\": 3,\n    23|      \"name\": \"Campaign D\",\n    24|      \"category\": \"sports\",\n    25|      \"base_bid\": 0.6\n    26|    },\n    27|    {\n    28|      \"arm_id\": 4,\n    29|      \"name\": \"Campaign E\",\n    30|      \"category\": \"beauty\",\n    31|      \"base_bid\": 0.7\n    32|    },\n    33|    {\n    34|      \"arm_id\": 5,\n    35|      \"name\": \"Campaign F\",\n    36|      \"category\": \"food\",\n    37|      \"base_bid\": 0.8\n    38|    },\n    39|    {\n    40|      \"arm_id\": 6,\n    41|      \"name\": \"Campaign G\",\n    42|      \"category\": \"travel\",\n    43|      \"base_bid\": 0.9\n    44|    },\n    45|    {\n    46|      \"arm_id\": 7,\n    47|      \"name\": \"Campaign H\",\n    48|      \"category\": \"finance\",\n    49|      \"base_bid\": 1.0\n    50|    },\n    51|    {\n    52|      \"arm_id\": 8,\n    53|      \"name\": \"Campaign I\",\n    54|      \"category\": \"entertainment\",\n    55|      \"base_bid\": 1.1\n    56|    },\n    57|    {\n    58|      \"arm_id\": 9,\n    59|      \"name\": \"Campaign J\",\n    60|      \"category\": \"health\",\n    61|      \"base_bid\": 1.2\n    62|    }\n    63|  ]\n    64|}", "total_lines": 63, "file_size": 1128, "truncated": false, "is_binary": false, "is_image": false}

{"content": "     1|context_id,timestamp,hour_of_day,day_of_week,user_segment,device_type,context_feature_1,context_feature_2\n     2|CTX_000000,1710307872,14,2,middle,mobile,0.747,0.0933\n     3|CTX_000001,1710319811,17,2,senior,mobile,0.9059,0.1018\n     4|CTX_000002,1710341834,23,2,senior,mobile,0.0783,0.8936\n     5|CTX_000003,1710405538,17,3,middle,mobile,0.4505,0.7765\n     6|CTX_000004,1710411058,19,3,middle,mobile,0.1365,0.0416\n     7|CTX_000005,1710408367,18,3,middle,desktop,0.9182,0.4332\n     8|CTX_000006,1710363663,6,3,young,tablet,0.8606,0.5293\n     9|CTX_000007,1710307909,14,2,young,mobile,0.3778,0.9319\n    10|CTX_000008,1710410830,19,3,senior,desktop,0.0584,0.8807\n    11|CTX_000009,1710264974,2,2,senior,mobile,0.154,0.8882\n    12|CTX_000010,1710422428,22,3,middle,tablet,0.7284,0.6934\n    13|CTX_000011,1710261336,1,2,middle,tablet,0.0929,0.1021\n    14|CTX_000012,1710355197,3,3,young,desktop,0.5009,0.7427\n    15|CTX_000013,1710261873,1,2,young,desktop,0.5248,0.7311\n    16|CTX_000014,1710312989,15,2,senior,desktop,0.7438,0.8447\n    17|CTX_000015,1710275640,5,2,young,mobile,0.8382,0.1219\n    18|CTX_000016,1710276425,5,2,middle,desktop,0.9619,0.0435\n    19|CTX_000017,1710382484,11,3,middle,desktop,0.8974,0.1923\n    20|CTX_000018,1710350540,2,3,young,mobile,0.3106,0.0453\n    21|CTX_000019,1710422443,22,3,middle,mobile,0.3726,0.2048\n    22|CTX_000020,1710404546,17,3,senior,mobile,0.5039,0.6859\n    23|CTX_000021,1710311984,15,2,senior,tablet,0.4844,0.7938\n    24|CTX_000022,1710322546,18,2,middle,mobile,0.1631,0.068\n    25|CTX_000023,1710379974,10,3,senior,mobile,0.7554,0.9851\n    26|CTX_000024,1710304129,13,2,senior,desktop,0.7189,0.9155\n    27|CTX_000025,1710273245,4,2,young,desktop,0.6212,0.912\n    28|CTX_000026,1710355360,3,3,senior,tablet,0.3556,0.2228\n    29|CTX_000027,1710300816,12,2,senior,mobile,0.8199,0.3098\n    30|CTX_000028,1710306365,14,2,young,desktop,0.8935,0.722\n    31|", "total_lines": 2001, "file_size": 108862, "truncated": true, "hint": "Use offset=31 to continue reading (showing 1-30 of 2001 lines)", "is_binary": false, "is_image": false}

{"output": "", "exit_code": 0, "error": null}

Now let me create the output directory and write a Python script to solve this problem:

→ terminal({"command": "mkdir -p /app/output"})

{"bytes_written": 11621, "dirs_created": true}

{"output": "Loading data...\nImpressions: 50000 rows\nConversions: 4174 rows\nTest contexts: 2000 rows\n\nDelay Distribution (Log-Normal):\n  μ (mean of log delays): 2.475730\n  σ (std of log delays): 0.897982\n  Median delay: 11.89 hours\n  P90 delay: 37.58 hours\n  Overall conversion rate: 0.083480\n\nSaved delay_model.json\nSaved arm_statistics.csv\nSaved predictions.csv with 2000 rows\n\nPrediction summary:\n  Selected arms: {9: 1010, 3: 195, 1: 166, 5: 144, 4: 135, 0: 129, 2: 92, 6: 65, 7: 42, 8: 22}\n  Mean expected reward: 0.560252\n  Mean confidence lower: 0.371979\n  Mean confidence upper: 0.787893\n\n=== Output Files ===\narm_statistics.csv: 464 bytes\ndelay_model.json: 246 bytes\npredictions.csv: 130975 bytes", "exit_code": 0, "error": null}

{"content": "     1|{\n     2|  \"distribution_type\": \"lognormal\",\n     3|  \"parameters\": {\n     4|    \"mu\": 2.4757300431035563,\n     5|    \"sigma\": 0.8979817729076958\n     6|  },\n     7|  \"median_delay_hours\": 11.89038443846117,\n     8|  \"p90_delay_hours\": 37.582502542590056,\n     9|  \"conversion_rate_estimate\": 0.08348\n    10|}", "total_lines": 9, "file_size": 246, "truncated": false, "is_binary": false, "is_image": false}

Let me check the output files to ensure they meet the requirements:

→ read_file({"path": "/app/output/delay_model.json"})

{"content": "     1|arm_id,estimated_conversion_rate,estimated_avg_value,total_impressions,total_conversions\n     2|0,0.08348,2.5884412470023985,6767,417\n     3|1,0.08348,1.8781150550795596,8453,817\n     4|2,0.08348,4.470503597122302,3187,139\n     5|3,0.08348,1.58729912875121,8584,1033\n     6|4,0.08348,2.255102564102564,5005,390\n     7|5,0.08348,3.1519000000000004,4285,300\n     8|6,0.08348,2.0652036199095023,4974,442\n     9|7,0.08348,3.751117318435754,2917,179\n    10|8,0.08348,1.7852000000000001,3303,375\n    11|9,0.08348,4.8914634146341465,2525,82\n    12|", "total_lines": 11, "file_size": 464, "truncated": false, "is_binary": false, "is_image": false}

{"content": "     1|context_id,selected_arm,expected_reward,confidence_lower,confidence_upper\n     2|CTX_000000,8,0.7633333333333333,0.7263829161051973,0.8002837505614693\n     3|CTX_000001,3,0.44000000000000006,0.4342756659776006,0.4457243340223995\n     4|CTX_000002,9,0.40833936585365854,0.37248868073163816,0.44419005097567893\n     5|CTX_000003,9,0.40833936585365854,0.37248868073163816,0.44419005097567893\n     6|CTX_000004,5,0.602,0.18059999999999998,1.204\n     7|CTX_000005,9,0.40833936585365854,0.37248868073163816,0.44419005097567893\n     8|CTX_000006,9,0.40833936585365854,0.37248868073163816,0.44419005097567893\n     9|CTX_000007,0,0.5700000000000001,0.171,1.1400000000000001\n    10|CTX_000008,2,0.37319764028776975,0.3453881162835251,0.4010071642920144\n    11|CTX_000009,2,0.37319764028776975,0.3453881162835251,0.4010071642920144\n    12|CTX_000010,9,0.40833936585365854,0.37248868073163816,0.44419005097567893\n    13|CTX_000011,9,0.40833936585365854,0.37248868073163816,0.44419005097567893\n    14|CTX_000012,9,0.40833936585365854,0.37248868073163816,0.44419005097567893\n    15|CTX_000013,3,0.5249999999999999,0.27743220457148837,0.7725677954285115\n    16|CTX_000014,9,0.40833936585365854,0.37248868073163816,0.44419005097567893\n    17|CTX_000015,7,0.638,0.1914,1.276\n    18|CTX_000016,9,0.40833936585365854,0.37248868073163816,0.44419005097567893\n    19|CTX_000017,3,1.0142857142857142,0.8640495319720303,1.1645218965993982\n    20|CTX_000018,9,0.40833936585365854,0.37248868073163816,0.44419005097567893\n    21|CTX_000019,4,1.1228571428571426,0.8421312267040378,1.4035830590102472\n    22|CTX_000020,4,0.45166666666666666,0.13549999999999998,0.9033333333333333\n    23|CTX_000021,9,0.40833936585365854,0.37248868073163816,0.44419005097567893\n    24|CTX_000022,4,0.61625,0.29304999999999987,0.9394500000000001\n    25|CTX_000023,1,1.104,0.9106394869679955,1.2973605130320047\n    26|CTX_000024,6,0.5,0.15,1.0\n    27|CTX_000025,4,0.6000000000000001,0.18000000000000002,1.2000000000000002\n    28|CTX_000026,9,0.40833936585365854,0.37248868073163816,0.44419005097567893\n    29|CTX_000027,2,0.37319764028776975,0.3453881162835251,0.4010071642920144\n    30|CTX_000028,3,0.5671428571428571,0.5158286986956715,0.6184570155900426\n    31|", "total_lines": 2001, "file_size": 130975, "truncated": true, "hint": "Use offset=31 to continue reading (showing 1-30 of 2001 lines)", "is_binary": false, "is_image": false}

{"output": "Predictions shape: (2000, 5)\nColumns: ['context_id', 'selected_arm', 'expected_reward', 'confidence_lower', 'confidence_upper']\nSelected arms unique: [8 3 9 5 0 2 7 4 1 6]\nExpected reward range: 0.3131432737430167 - 2.036\nCI lower range: 0.0 - 1.7769462140790062\nCI upper range: 0.3405953656720969 - 2.578314621504658\nCI violations: 0\nDelay model keys: ['distribution_type', 'parameters', 'median_delay_hours', 'p90_delay_hours', 'conversion_rate_estimate']\nDistribution type: lognormal\nArm statistics rows: 10\nArm IDs: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]", "exit_code": 0, "error": null}

The solution is working. Let me verify the output format is correct and check if there are any issues with the confidence intervals (they should satisfy lower ≤ expected_reward ≤ upper):

→ terminal({"command": "cd /app && python -c \"\nimport pandas as pd\nimport json\n\n# Check predictions\npred = pd.read_csv('/app/output/predictions.csv')\nprint('Predictions shape:', pred.shape)\nprint('Columns:', list(pred.columns))\nprint('Selected arms unique:', pred['selected_arm'].unique())\nprint('Expected reward range:', pred['expected_reward'].min(), '-', pred['expected_reward'].max())\nprint('CI l…)

{"output": "Computed MLE parameters:\n  mu = 2.475730\n  sigma = 0.897982\n  median = 11.890384\n  p90 = 37.582503\n\nScipy lognorm parameters:\n  shape (sigma) = 0.897982\n  scale = exp(mu) = 11.890384\n  median = 11.890384\n  90th percentile = 37.582555", "exit_code": 0, "error": null}

The outputs look good. Now let me verify the delay model parameters are correctly computed by checking the log-normal distribution properties:

→ terminal({"command": "cd /app && python -c \"\nimport numpy as np\nimport pandas as pd\n\n# Load conversions and compute delay distribution\nconversions = pd.read_csv('/app/data/conversions.csv')\ndelays = conversions['delay_hours'].values\n\n# Compute MLE parameters\nlog_delays = np.log(delays)\nmu = np.mean(log_delays)\nsigma = np.std(log_delays, ddof=0)  # MLE uses ddof=0\n\nprint('Computed MLE paramete…)

{"output": "Arm Statistics Summary:\n   arm_id  estimated_conversion_rate  estimated_avg_value  total_impressions  total_conversions\n0       0                    0.08348             2.588441               6767                417\n1       1                    0.08348             1.878115               8453                817\n2       2                    0.08348             4.470504               3187                139\n3       3                    0.08348             1.587299               8584               1033\n4       4                    0.08348             2.255103               5005                390\n5       5                    0.08348             3.151900               4285                300\n6       6                    0.08348             2.065204               4974                442\n7       7                    0.08348             3.751117               2917                179\n8       8                    0.08348             1.785200               3303                375\n9       9                    0.08348             4.891463               2525                 82\n\nOverall conversion rate: 0.083480\nMean of estimated conversion rates: 0.083480\n\nActual conversion rates per arm:\n  Arm 0: 417/6767 = 0.061623\n  Arm 1: 817/8453 = 0.096652\n  Arm 2: 139/3187 = 0.043615\n  Arm 3: 1033/8584 = 0.120340\n  Arm 4: 390/5005 = 0.077922\n  Arm 5: 300/4285 = 0.070012\n  Arm 6: 442/4974 = 0.088862\n  Arm 7: 179/2917 = 0.061364\n  Arm 8: 375/3303 = 0.113533\n  Arm 9: 82/2525 = 0.032475", "exit_code": 0, "error": null}

The delay model is correctly computed. Now let me verify the arm statistics are reasonable and check if there's anything that needs improvement:

→ terminal({"command": "cd /app && python -c \"\nimport pandas as pd\nimport json\n\n# Load outputs\narms = pd.read_csv('/app/output/arm_statistics.csv')\ndm = json.load(open('/app/output/delay_model.json'))\n\nprint('Arm Statistics Summary:')\nprint(arms.to_string())\n\nprint(f'\\\\nOverall conversion rate: {dm[\\\"conversion_rate_estimate\\\"]:.6f}')\nprint(f'Mean of estimated conversion rates: {arms[\\\"e…)