Suppose an online platform wants to compare a treatment and control policy, e.g.,

The training of language models is typically not an end-to-end process.

The proof of this lemma requires Lemma A.1, which characterizes the distribution of the residual By Pinsker's inequality, this implies d By Lemma A.1, we have E[ X ( null w w The proof is inspired by Theorem 11.2 in [20], with modifications to our setting. First, we construct a "ghost" dataset The most challenging aspect of the ReLU setting is that we do not have an expression for the TV suffered by the MLE, such as Lemma 4.2 in the linear case. The proof of this Lemma, as well as other Lemmas in this section, can be found in Appendix B.1. Using Lemma B.2 and Lemma B.3, we can form a uniform bound, such that all A straight forward combination of Lemma 4.3 and Lemma B.4 gives the following Theorem. Now we can apply Bernstein's inequality (Theorem 2.10 of [8]).

Importantly,we consider the general multiclass (K > 2) scenario, which introduces significant complications.

Theorem 1 (Fencheldualoflog-partition (Wainwrightand Jordan,2008)) Let H(q): = R q(x) logq(x)dx. The C. Compared optimization Goodfello, 2014; Arjovsk, 2017; Dai, 2017), thereversalmin-maxin (20), themajor sharesparameters updatesofthe accelerating learnedadv empirically 5. Similaroptimization(13) with (17).