Recently, there has been a marked increase in interest regarding the generalization capabilities of unregularized gradient-based learning methods.

Recently, there has been a marked increase in interest regarding the generalization capabilities of unregularized gradient-based learning methods.

We study reinforcement learning in episodic inhomogeneous MDPs with adversarial full-information rewards and the unknown transition kernel. We consider the linear mixture MDPs whose transition kernel is a linear mixture model and choose the dynamic regret as the performance measure.

Step 2. The deduction in Step 1 can be iterated repeatedly due to the symmetry of

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]).