We show that, surprisingly, the notion of optimal finite-time regret is not a uniquely defined property in this context and that, in general, it is decoupled from the asymptotic rate. We discuss alternative choices and propose a notion of finite-time optimality that we argue is meaningful .

In addition, current offline RL benchmarks test agents on the exact same environment where the data was collected.

We need to prove the following two inequalities. Thus, the inequality ( 19) holds trivially. Note that f p w, Z q " x M In this section, we will show that the MIQP presented in ( 4) is at least as hard to solve as a 0 1 Quadratic Program. It should be noted that MIQP ( 4) is stated for a fixed X. The Mixed Integer Quadratic Program (MIQP) ( 4) is NP-hard. " 0. Other cases will be at least as difficult as this case.

In this paper, we study the problem of fair sparse regression on a biased dataset where bias depends upon a hidden binary attribute. The presence of a hidden attribute adds an extra layer of complexity to the problem by combining sparse regression and clustering with unknown binary labels. The corresponding optimization problem is combinatorial, but we propose a novel relaxation of it as an invex optimization problem. To the best of our knowledge, this is the first invex relaxation for a combinatorial problem. We show that the inclusion of the debi-asing/fairness constraint in our model has no adverse effect on the performance. Rather, it enables the recovery of the hidden attribute.

Importantly, an item cannot be recommended twice to the same user. The probabilities that a user likes each item are unknown.

During initial iterations of training in most Reinforcement Learning (RL) algorithms, agents perform a significant number of random exploratory steps.