{ "seed": 1037, "math": { "weak_duality": { "trials": 1000, "max_violation": 0.0, "min_gap": 5.94276364219283, "mean_gap": 43.103476950363415 }, "stability_sweep": [ { "rho": 0.001, "predicted_multiplier": 0.8, "mean_abs_load_imbalance": 11.272, "max_abs_load_imbalance": 38, "final_price_difference": 0.03 }, { "rho": 0.005, "predicted_multiplier": 0.0, "mean_abs_load_imbalance": 16.248, "max_abs_load_imbalance": 52, "final_price_difference": -0.010000000000000134 }, { "rho": 0.01, "predicted_multiplier": -1.0, "mean_abs_load_imbalance": 200.0, "max_abs_load_imbalance": 200, "final_price_difference": -1.0 }, { "rho": 0.02, "predicted_multiplier": -3.0, "mean_abs_load_imbalance": 200.0, "max_abs_load_imbalance": 200, "final_price_difference": -2.0 }, { "rho": 0.04, "predicted_multiplier": -7.0, "mean_abs_load_imbalance": 200.0, "max_abs_load_imbalance": 200, "final_price_difference": 4.0 } ], "zero_price_prediction": { "initial_greedy_counts": [ 70, 30 ], "final_prices": [ 0.8000000000000004, 0.6 ], "final_counts": [ 70, 30 ], "predicted": "overloaded expert gets positive price and its routed load falls" } }, "mini_experiment": { "baseline_greedy": { "mean_accepted_utility": 60.41729494485572, "mean_overflow_tokens": 63.698, "mean_load_variance": 1434.546, "final_prices": null, "mean_dual_gap": null, "p95_dual_gap": null }, "dual_rho_0.001": { "mean_accepted_utility": 74.85044840824874, "mean_overflow_tokens": 10.404, "mean_load_variance": 56.474, "final_prices": [ 0.9670000000000005, 0.5760000000000003, 0.2670000000000001, 0.011 ], "mean_dual_gap": 2.3516214654459953, "p95_dual_gap": 8.073226189641645 }, "dual_rho_0.01": { "mean_accepted_utility": 72.63663640056988, "mean_overflow_tokens": 12.844, "mean_load_variance": 66.31, "final_prices": [ 1.0500000000000003, 0.6999999999999993, 0.3399999999999996, 0.12000000000000002 ], "mean_dual_gap": 4.5823267279012665, "p95_dual_gap": 12.897556184530256 }, "dual_rho_0.1": { "mean_accepted_utility": 21.845974808291007, "mean_overflow_tokens": 95.746, "mean_load_variance": 3058.686, "final_prices": [ 9.600000000000001, 8.881784197001252e-16, 3.200000000000001, 6.400000000000001 ], "mean_dual_gap": 618.5238928336585, "p95_dual_gap": 674.9308881975837 } } }