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We call this distinction thediscrimination risk. We prove that a higher discrimination risk can amplify the unfairness of a machine learning model applied totheimputed data.

In practical situations, the clustering result must be stable against points missing in the input data so that we can make trustworthy andconsistentdecisions.

If A is (",0)- di erentiallyprivate, thenA is " Yis (", )- di B : Y anyrandomB Ais (", )- di erA is thenthealgoB Ais - z CDP. Proof.Algorithm1 isthedesiredsamplerAPo.Itis (", ) - di erentiallyprivatesinceA is (", ) - di erentially private.

The publicly verifiable record of the randomization is available athttps://www.

Werecallthisresult from [4] (see Theorem 7 thereinformoredetails).

Theorem B.1 (Performance difference bound for Model-based RL). Mi denote the inconsistency between the learned dynamics PMi and the true dynamics, i.e. ϵ For L1 L3, with the performance gap approximation of M1 and π1, we apply Lemma C.2, and Here, dπMi denotes the distribution of state-action pair induced by policy π under the dynamical modelMi. Theorem B.3 (Refined bound with constraints). Let µ and v be two probability distributions on the configuration space X, according to LemmaC.1,thenwehaveDTV(µ Under these definitions, we can yield the following intermediate outcome by applying the results from B.2and B.1 Here, we take the time-varying linear quadratic regulator as an instance for illustrating the rationality of our assumption on α.

In the first model, we are givenn i.i.d.

In the first model, we are givenn i.i.d.

There is no universally agreed upon definition of adversarial risk.