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Wesummarize all unidentifiable situations that are discovered in the causal inference literature. Then, we develop a constrained optimization problem forbounding thePCfairness, whichismotivatedbythemethod proposed in[2]forbounding confounded causaleffects. Thekeyideaistoparameterize thecausal model using so-called response-function variables, whose distribution captures all randomness encoded in the causal model, so that we can explicitly traverse all possible causal models to find thetightest possible bounds.

Numerical results demonstrate significant regret reductions by our method, in comparison with several baselines in a range of multi-armed and linear bandit problems.

Each dataset contains miscellaneous series, categorized into six domains (micro, industry, macro, finance, demographic, other). Thus, atime series regression dataset consists ofT input-target pairs: {(X1,y1),...,(XT,yT). For each synthesized training set withT samples, we synthesize100T samples as the testing set. D.3 Models The NN we use has six fully-connected layers with ReLU activation function and three residual connections. D.4 Results There are three methods tobe compared.