1{
  2  "seed": 1037,
  3  "math": {
  4    "weak_duality": {
  5      "trials": 1000,
  6      "max_violation": 0.0,
  7      "min_gap": 5.94276364219283,
  8      "mean_gap": 43.103476950363415
  9    },
 10    "stability_sweep": [
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 12        "rho": 0.001,
 13        "predicted_multiplier": 0.8,
 14        "mean_abs_load_imbalance": 11.272,
 15        "max_abs_load_imbalance": 38,
 16        "final_price_difference": 0.03
 17      },
 18      {
 19        "rho": 0.005,
 20        "predicted_multiplier": 0.0,
 21        "mean_abs_load_imbalance": 16.248,
 22        "max_abs_load_imbalance": 52,
 23        "final_price_difference": -0.010000000000000134
 24      },
 25      {
 26        "rho": 0.01,
 27        "predicted_multiplier": -1.0,
 28        "mean_abs_load_imbalance": 200.0,
 29        "max_abs_load_imbalance": 200,
 30        "final_price_difference": -1.0
 31      },
 32      {
 33        "rho": 0.02,
 34        "predicted_multiplier": -3.0,
 35        "mean_abs_load_imbalance": 200.0,
 36        "max_abs_load_imbalance": 200,
 37        "final_price_difference": -2.0
 38      },
 39      {
 40        "rho": 0.04,
 41        "predicted_multiplier": -7.0,
 42        "mean_abs_load_imbalance": 200.0,
 43        "max_abs_load_imbalance": 200,
 44        "final_price_difference": 4.0
 45      }
 46    ],
 47    "zero_price_prediction": {
 48      "initial_greedy_counts": [
 49        70,
 50        30
 51      ],
 52      "final_prices": [
 53        0.8000000000000004,
 54        0.6
 55      ],
 56      "final_counts": [
 57        70,
 58        30
 59      ],
 60      "predicted": "overloaded expert gets positive price and its routed load falls"
 61    }
 62  },
 63  "mini_experiment": {
 64    "baseline_greedy": {
 65      "mean_accepted_utility": 60.41729494485572,
 66      "mean_overflow_tokens": 63.698,
 67      "mean_load_variance": 1434.546,
 68      "final_prices": null,
 69      "mean_dual_gap": null,
 70      "p95_dual_gap": null
 71    },
 72    "dual_rho_0.001": {
 73      "mean_accepted_utility": 74.85044840824874,
 74      "mean_overflow_tokens": 10.404,
 75      "mean_load_variance": 56.474,
 76      "final_prices": [
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 78        0.5760000000000003,
 79        0.2670000000000001,
 80        0.011
 81      ],
 82      "mean_dual_gap": 2.3516214654459953,
 83      "p95_dual_gap": 8.073226189641645
 84    },
 85    "dual_rho_0.01": {
 86      "mean_accepted_utility": 72.63663640056988,
 87      "mean_overflow_tokens": 12.844,
 88      "mean_load_variance": 66.31,
 89      "final_prices": [
 90        1.0500000000000003,
 91        0.6999999999999993,
 92        0.3399999999999996,
 93        0.12000000000000002
 94      ],
 95      "mean_dual_gap": 4.5823267279012665,
 96      "p95_dual_gap": 12.897556184530256
 97    },
 98    "dual_rho_0.1": {
 99      "mean_accepted_utility": 21.845974808291007,
100      "mean_overflow_tokens": 95.746,
101      "mean_load_variance": 3058.686,
102      "final_prices": [
103        9.600000000000001,
104        8.881784197001252e-16,
105        3.200000000000001,
106        6.400000000000001
107      ],
108      "mean_dual_gap": 618.5238928336585,
109      "p95_dual_gap": 674.9308881975837
110    }
111  }
112}