{ "seed": 2092, "environment": { "score_states": 21, "max_refinements": 5, "transition": "score increases one grid step with p=0.10+0.75*(1-score)", "payoff": "score" }, "math_check": { "max_bellman_residual": 0.0, "delta_gt_cost_matches_policy": true, "value_at_initial_state_by_cost": { "0.0": 0.19714903424072264, "0.02": 0.09714903424072266, "0.03": 0.047149034240722656, "0.035": 0.02214903424072262, "0.038": 0.009432143371582019, "0.04": 0.0037074088745117084, "0.045": 0.0, "0.1": 0.0 } }, "predictions": { "P1_initial_continue_decreases_with_cost": { "predicted": "monotone non-increasing", "costs": [ 0.0, 0.02, 0.03, 0.035, 0.038, 0.04, 0.045, 0.1 ], "observed_continue": [ true, true, true, true, true, true, false, false ], "observed_threshold_score": [ 1.0, 0.6, 0.35, 0.2, 0.15, 0.1, 0.0, 0.0 ], "confirmed": true }, "P2_stopping_boundary_is_upper_score_region_and_moves_lower_with_cost": { "predicted": "stop for sufficiently high score; boundary non-increasing in cost", "boundary_monotone_each_cost": [ true, true, true, true, true, true, true, true ], "finite_boundaries": [ 1.0, 0.6, 0.35, 0.2, 0.15, 0.1, 0.0, 0.0 ], "confirmed": true }, "P3_bellman_value_decreases_with_cost": { "predicted": "non-increasing value and exact max recursion", "values": [ 0.19714903424072264, 0.09714903424072266, 0.047149034240722656, 0.02214903424072262, 0.009432143371582019, 0.0037074088745117084, 0.0, 0.0 ], "residuals": [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], "confirmed": true } }, "simulation_cost_0.038": { "adaptive": { "calls": 3.62601, "quality": 0.14725649999999998, "objective": 0.009468120000000002, "pass_at_0.75": 0.0, "stop_state_mean": 2.94513 }, "fixed": { "1": { "calls": 1.0, "quality": 0.042446500000000005, "objective": 0.004446500000000005, "pass_at_0.75": 0.0, "stop_state_mean": 0.84893 }, "3": { "calls": 3.0, "quality": 0.12281, "objective": 0.00881000000000001, "pass_at_0.75": 0.0, "stop_state_mean": 2.4562 }, "5": { "calls": 5.0, "quality": 0.1969025, "objective": 0.0069025000000000015, "pass_at_0.75": 0.0, "stop_state_mean": 3.93805 } } }, "simulation_cost_sweep": { "0.0": { "adaptive": { "calls": 5.0, "quality": 0.19711666666666666, "objective": 0.19711666666666666, "pass_at_0.75": 0.0, "stop_state_mean": 3.9423333333333335 } }, "0.02": { "adaptive": { "calls": 5.0, "quality": 0.197255, "objective": 0.09725500000000001, "pass_at_0.75": 0.0, "stop_state_mean": 3.9451 } }, "0.03": { "adaptive": { "calls": 5.0, "quality": 0.19720166666666666, "objective": 0.04720166666666668, "pass_at_0.75": 0.0, "stop_state_mean": 3.9440333333333335 } }, "0.035": { "adaptive": { "calls": 4.603133333333333, "quality": 0.18343333333333334, "objective": 0.022323666666666662, "pass_at_0.75": 0.0, "stop_state_mean": 3.6686666666666667 } }, "0.038": { "adaptive": { "calls": 3.6234333333333333, "quality": 0.14737166666666665, "objective": 0.009681200000000001, "pass_at_0.75": 0.0, "stop_state_mean": 2.947433333333333 } }, "0.04": { "adaptive": { "calls": 2.3984666666666667, "quality": 0.09983500000000001, "objective": 0.0038963333333333385, "pass_at_0.75": 0.0, "stop_state_mean": 1.9967 } }, "0.045": { "adaptive": { "calls": 0.0, "quality": 0.0, "objective": 0.0, "pass_at_0.75": 0.0, "stop_state_mean": 0.0 } }, "0.1": { "adaptive": { "calls": 0.0, "quality": 0.0, "objective": 0.0, "pass_at_0.75": 0.0, "stop_state_mean": 0.0 } } }, "worked": true }