SlowGuess/NeurIPS_2023_OCR huggingface dataset:
In this section, we conduct an ablation test to demonstrate the importance of the CEM to this task. To that end, we implement a naive adversarial task sampler. The first  $\mathcal{M} = 100$  tasks are sampled from the original distribution  $D$ , and the naive sampler memorizes the  $\alpha \mathcal{M}$  lowest-return tasks, and samples randomly from them for the rest of the training.
As displayed in Table 3, switching to the naive sampler decreases the CVaR returns significantly.
Table 3: Ablation test:  ${\mathrm{{CVaR}}}_{0.05}$  return,compared to the naive sampler baseline.
HalfCheetah Body	HalfCheetah 10D-task
(a)	(b)	(c)
VariBAD	835 ± 30	1126 ± 6	1536 ± 39	988 ± 13
Naive sampler	839 ± 20	1056 ± 34	1340 ± 57	978 ± 12
RoML (VariBAD)	935 ± 17	1227 ± 13	1697 ± 24	999 ± 20
E Supervised Meta-Learning
Below we provide the complete details for the toy Sine Regression experiment of Section 6.3. The input in the problem is  $x \in [0,2\pi)$ , the desired output is  $y = A\sin (\omega x + b)$ , and the task is defined by the parameters  $\tau = (A,b,\omega)$ , distributed uniformly over  $\Omega = [0.1,5] \times [0,2\pi ] \times [0.3,3]$ . Similarly to Finn et al. [2017], the model is fine-tuned for each task via a gradient-descent optimization step over 10 samples  $\{(x_{i},y_{i})\}_{i = 1}^{10}$ , and is tested on another set of 10 samples. The goal is to find model weights that adapt quickly to new task data.
CVaR-ML and RoML are implemented with robustness level of  $\alpha = 0.05$ , on top of MAML. For the CEM of RoML, we re-parameterize the uniform task distribution using Beta distributions (see CEM details below).
As shown in Fig. 13, RoML learns to focus on tasks (sine functions) with high amplitudes and slightly increased frequencies, without changing the phase distribution. Fig. 14 displays the test losses over 30 seeds, after meta-training for 10000 tasks. Similarly to the MRL experiments, again RoML achieves better CVaR losses than both CVaR-ML and the baseline.
(b)  $\mathrm{CVaR}_{0.05}$
Figure 14: Sine Regression: Mean and CVaR losses over 10000 test tasks, against the number of tuning gradient-steps at test time. The  $95\%$  confidence intervals are calculated over 30 seeds.
CEM implementation details: In comparison to Finn et al. [2017], we added the sine frequency as a third parameter in the task space, since the original problem was to simplistic to pose a mean/CVaR tradeoff. The tasks are distributed uniformly, and we reparameterize them for the CEM using the Beta distribution, similarly to Appendix D.2:  $\tau = \{\tau_{j}\}_{j=1}^{3}$ ,  $\tau_{j} \sim \text{Beta}(2\phi_{j}, 2 - 2\phi_{j})$ . On top of this, we add a linear transformation from the Beta distribution domain  $[0,1]$  to the actual task range ([0.1, 5] for amplitude,  $[0,2\pi]$  for phase and [0.3, 3] for frequency). Note that the original uniform distribution is recovered by  $\phi_{0} = (0.5,0.5,0.5)$ . The parameter  $\phi_{j} \in [0,1]$ , which is controlled by the CEM, equals the expected task  $\mathbb{E}_{\tau \sim D_{\phi}}[\tau_{j}]$ . The other hyper-parameters of RoML are set to  $\beta = 0.2$  (CEM quantile) and  $\nu = 0$  (no regularization).