There have been many recent advances on provably efficient Reinforcement Learning (RL) in problems with rich observation spaces. However, all these works share a strong realizability assumption about the optimal value function of the true MDP . Such realizability assumptions are often too strong to hold in practice. In this work, we consider the more realistic setting of agnostic RL with rich observation spaces and a fixed class of policies Π that may not contain any near-optimal policy. We provide an algorithm for this setting whose error is bounded in terms of the rank d of the underlying MDP .

For many applications, variables in the data can be gathered into semantically meaningful groups, where useful insights are at group level. For example, in finance, one may be interested in how a financial situation influences different industries (i.e.

While this may seem of mostly theoretical interest, in this work, we show that it can be used in practice to the benefit of BNNs.

In practice, however, they are very efficient.

As per standard batch variational techniques, we use stochastic gradients to simultaneously optimize a lower bound on the log evidence with respect to both model parameters and a variational approximation of the states' posterior distribution.

In Appendix D we provide the proofs for Theorem 7. In Appendix E we include some useful results for the sake of completeness. Informally, we expect that there is one sign flip (i.e., The top left, top right and bottom left figures show the scaling of the minimax rates of GLM (cf. To begin with the analysis of the estimator in Figure 2, the following lemma is a simple, yet key tool for the proof. It establishes the variance of the random gain S . The proof relies on a sort of self-bounding property (cf.