In this section, we focus on the reason why GNNs are poorly calibrated. It is inspired by the observation in [12] that modern neural networks can overfit to NLL without overfitting to the accuracy.

Based ontheprinciple ofoptimism inthefaceofuncertainty(OFU) [56,49,10],OFU-RL achievestheglobal optimality by ensuring that the optimistically biased value is close to the real value in the long run. Based on Thompson Sampling [62], Posterior Sampling RL (PSRL) [57, 42, 43] explores by greedily optimizing the policy in an MDP which is sampled from the posterior distribution over MDPs.

Proposition 1 is a part of the following proposition. We shall prove this proposition in the end of this section. The proof is the extension of [18, Exercises 3.11] to the transductive and multi-layer setting. See also the proof of [20, Theorem 3]. Therefore, itissufficient that we first prove the proposition by assuming P(s) = IN for alls = 2,...,t and then replaceX with By definition, the transductive Rademacher variable of parameterp = 1/2 equals to the (inductive) Rademacher variable.

Weimplement our approach using TensorFlow[1]forefficient GPU-based computation and also use some components of TensorFlow Probability [4]2.

We also report the accuracy of the base and smooth classifier (binary attr.).