SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Table 3: Policy Noise: Success rates (and standard error) for BC in PMObstacle, for 1000 episodes (left) and 10 episodes (right) of data, under learned policy noise. Rows correspond to injecting gaussian policy noise  $(\sigma_p)$  into the expert of increasing variance, and columns correspond to injecting system noise during evaluation. Left: For large datasets, unlike system noise in Table 2, more policy noise during training often produces the worst models (columns top to bottom). Right: For small datasets, adding policy noise produces large variance in performance across runs. Importantly, the datasets in each row have the same observed state diversity as the corresponding row in Table 2, but performance is almost universally lower in both sub-tables here, supporting the idea that state diversity is a coarse metric for success.
σs=0.01	σs=0.02	σs=0.03	σs=0.04	σs=0.01	σs=0.02	σs=0.03	σs=0.04
SCRIPTED	100	100	99	96
σp=0.01	96.3(2.2)	99.3(0.5)	97.7(0.3)	93.3(1.0)	99.7(0.3)	98.0(1.2)	96.7(0.5)	96.3(1.4)
σp=0.02	98.0(0.5)	98.3(0.5)	97.7(0.7)	94.7(1.0)	99.3(0.5)	98.7(1.1)	96.0(2.2)	94.7(1.7)
σp=0.03	98.0(0.8)	96.7(1.0)	98.3(1.0)	96.3(0.7)	95.0(2.1)	97.7(0.5)	97.7(0.5)	93.3(2.2)
σp=0.04	98.7(0.5)	99.0(0.5)	97.3(0.3)	95.0(0.8)	100.0(0.0)	99.7(0.3)	99.0(0.8)	93.7(3.1)
Table 4: System Noise + Policy Noise: Success rates (and standard error) for BC in PMObstacle, for 1000 episodes (left) and 10 episodes (right) of data, under learned policy noise for a fixed amount of system noise  $(\sigma_{p} = 0.03)$ . Here we see how system noise improves the robustness of the model to added policy noise.
σs=0.05	σs=0.1	σs=0.2	σs=0.3	σs=0.4
σs=0.05	55.7(5.3)	50.0(5.4)	27.0(3.9)	12.0(2.4)	7.3(2.2)
σs=0.1	69.7(5.5)	69.0(3.7)	57.3(6.0)	50.3(6.0)	22.7(3.5)
σs=0.2	67.7(9.6)	68.7(12.6)	82.0(3.4)	74.3(2.7)	50.3(1.7)
σs=0.3	47.0(4.9)	53.3(5.9)	54.3(3.0)	50.7(4.3)	38.7(7.3)
σs=0.4	31.3(5.0)	37.7(8.2)	48.3(9.7)	49.0(8.7)	44.0(5.3)
Table 5: System Noise, 200ep: Success rates for BC in Square, for 200 episodes of data, under system noise. Rows correspond to injecting gaussian system noise  $(\sigma_s)$  into the dataset of increasing variance, and columns correspond to injecting noise during evaluation. The diagonal in both sub-tables represents evaluating in distribution. In both sub-tables we see how policies with low data coverage (low system noise) generalize the worst to increasing noise at test time. More system noise during training generally produces the best models (columns top to bottom).
σs=0.05	σs=0.1	σs=0.2	σs=0.3	σs=0.4
σs=0.05	40.0(1.2)	33.7(3.1)	16.7(1.4)	4.3(1.0)	2.0(0.5)
σs=0.1	42.3(4.0)	39.7(3.8)	31.3(3.7)	19.7(3.1)	10.0(1.6)
σs=0.2	70.0(7.0)	73.7(5.4)	69.7(0.7)	55.3(1.2)	27.0(2.2)
σs=0.3	57.3(3.1)	58.7(3.1)	64.7(1.4)	60.7(0.3)	44.7(2.2)
σs=0.4	30.0(7.0)	33.7(6.4)	39.7(5.7)	39.7(6.5)	36.7(6.9)
Table 6: System Noise, 50ep: Success rates for BC in Square, for 50 episodes of data, under system noise. Rows correspond to injecting gaussian system noise  $(\sigma_s)$  into the dataset of increasing variance, and columns correspond to injecting noise during evaluation. The diagonal in both sub-tables represents evaluating in distribution. In both sub-tables we see how policies with low data coverage (low system noise) generalize the worst to increasing noise at test time. More system noise during training generally produces the best models (columns top to bottom).
σs=0.05	σs=0.1	σs=0.2	σs=0.3	σs=0.4
σp=0.005	69.0(3.7)	59.0(3.7)	34.0(1.7)	20.7(2.4)	7.0(1.6)
σp=0.01	80.7(3.7)	78.0(4.2)	57.7(2.4)	38.0(1.7)	23.0(2.2)
σp=0.02	62.3(7.8)	71.7(6.1)	73.0(3.9)	65.3(2.8)	43.3(3.6)
Table 7: Policy Noise, 200ep: Success rates for BC in Square, for 200 episodes of data, under learned policy noise. Rows correspond to injecting gaussian policy noise  $(\sigma_p)$  into the dataset of increasing variance, and columns correspond to injecting noise during evaluation. In the high data regime, we see that more policy noise tends to improve performance (columns top to bottom), since the noise is unbiased so with enough samples from the scripted policy, the model will recover an unbiased policy.
σs=0.05	σs=0.1	σs=0.2	σs=0.3	σs=0.4
σp=0.005	32.7(3.8)	30.3(3.2)	18.0(3.6)	7.0(0.8)	5.7(1.2)
σp=0.01	61.3(4.3)	59.0(6.7)	48.3(3.7)	29.7(1.7)	19.3(1.4)
σp=0.02	57.7(3.2)	58.3(3.1)	49.3(0.5)	41.3(0.5)	28.3(2.4)
Table 8: Policy Noise, 50ep: Success rates for BC in Square, for 50 episodes of data, under learned policy noise. Rows correspond to injecting gaussian policy noise  $(\sigma_p)$  into the dataset of increasing variance, and columns correspond to injecting noise during evaluation. As the amount of data is reduced, there is a significant drop in performance for added policy noise in the dataset, along with higher performance variation compared to 200eps, since the policy can no longer recover an unbiased policy.