{ "seed": 2136, "theory": { "action": "uniform box, Q(u)=-||u||^2", "kappa": 2.0 }, "scaling_checks": { "1": { "N": [ 4, 8, 16, 32, 64, 128, 256 ], "mean_deficit": [ 0.06640631588755148, 0.022636377682861506, 0.006528169534484174, 0.0017875689851673177, 0.0004578994655922372, 0.00012140445360598402, 3.023320829182972e-05 ], "observed_loglog_slope": -1.8650658444171606, "predicted_loglog_slope": -2.0, "observed_doubling_ratio_mean": 0.2789022582354856, "predicted_doubling_ratio": 0.25, "doubling_ratios": [ 0.34087687865703326, 0.28839285268803383, 0.27382392196230904, 0.2561576472806041, 0.2651334249734538, 0.2490288238514796 ] }, "2": { "N": [ 4, 8, 16, 32, 64, 128, 256 ], "mean_deficit": [ 0.25821817408976405, 0.13893883213603778, 0.0750868579475538, 0.038825207082835766, 0.019679357675239758, 0.009771275682382357, 0.00492897792583224 ], "observed_loglog_slope": -0.9544596505812625, "predicted_loglog_slope": -1.0, "observed_doubling_ratio_mean": 0.5172332435833921, "predicted_doubling_ratio": 0.5, "doubling_ratios": [ 0.5380675958452817, 0.5404310428781693, 0.5170706052176821, 0.5068706429112597, 0.49652411646933037, 0.504435458178629 ] } }, "scheduler_scaling_check": { "beta": 0.9, "C_hat": 1.2554489046264004, "C_exact_asymptotic": 1.2732395447351628, "C_hat_over_C_exact": 0.9860272639329131, "epsilons": [ 0.04, 0.02, 0.01, 0.005 ], "scheduled_N": [ 314, 628, 1256, 2511 ], "measured_mean_delta": [ 0.004022013260628948, 0.0020138474084132286, 0.0010023714128676862, 0.0005102458916812143 ], "measured_delta_over_1_minus_beta": [ 0.04022013260628949, 0.02013847408413229, 0.010023714128676864, 0.005102458916812144 ], "expected_value_proxy_at_schedule": [ 0.040549030087107106, 0.020274515043553553, 0.010137257521776777, 0.005070647330685635 ], "mean_expected_proxy_over_epsilon": 1.01382668066754, "observed_loglog_N_vs_epsilon_slope": -0.9998276693139629, "predicted_loglog_N_vs_epsilon_slope": -1.0, "fraction_meeting_epsilon_bound": 0.0 }, "mini_comparison": [ { "method": "fixed_N=8", "mean_evaluations": 8, "mean_delta": 0.16419592083685855, "mean_value_error_proxy": 1.6419592083685857, "fraction_value_proxy_le_eps": 0.007666666666666666 }, { "method": "fixed_N=32", "mean_evaluations": 32, "mean_delta": 0.04499299744646731, "mean_value_error_proxy": 0.4499299744646731, "fraction_value_proxy_le_eps": 0.03766666666666667 }, { "method": "fixed_N=118", "mean_evaluations": 118, "mean_delta": 0.012764775954553246, "mean_value_error_proxy": 0.1276477595455325, "fraction_value_proxy_le_eps": 0.136 }, { "method": "fixed_N=128", "mean_evaluations": 128, "mean_delta": 0.011785689513341488, "mean_value_error_proxy": 0.11785689513341491, "fraction_value_proxy_le_eps": 0.14933333333333335 }, { "method": "adaptive_scheduler", "mean_evaluations": 117.86833333333334, "mean_delta": 0.016230854836525168, "mean_value_error_proxy": 0.16230854836525171, "fraction_value_proxy_le_eps": 0.129, "pool_min": 8, "pool_median": 128.0, "pool_max": 128 } ] }