While this setup has enjoyed a lot of attention in the applied community, there hasn't be theoretical work that even formalizes the desired guarantees.

Let k, d, r2 N, r k, d, 2 (0,1/2). Let d, k, r2 N, r d, k, >0.

However, because they are not identifiable without any assumptions, various assumptions have been utilized to evaluate the joint probabilities of potential outcomes, e.g., the assumption of monotonicity (Pearl, 2009; Tian and Pearl, 2000), the independence between potential outcomes (Robins and Richardson, 2011), the condition of gain equality (Li and Pearl, 2019), and the specific functional relationshipsbetween cause and effect (Pearl, 2009). Unlike existing identification conditions, in order to evaluate the joint probabilities of potential outcomeswithoutsuch assumptions,this paper proposestwo types of novel identification conditions using covariate information. In addition, when the joint probabilities of potential outcomes are identifiable through the proposed conditions, the estimation problem of the joint probabilities of potential outcomes reduces to that of singular models and thus they can not be evaluated by standard statistical estimation methods. To solve the problem,this paper proposes a new statisticalestimationmethod based on the augmented Lagrangianmethod and shows the asymptoticnormality of the proposed estimators. Given space constraints, the proofs, the details on the statistical estimationmethod, some numerical experiments, and the case study are provided in the supplementary material.

Among these forms, scene graphs are powerful structured representations of the images that encode objects and their interactions.

However, vanilla Adam remains exceptionally popular anditworkswellinpractice.

Contextual multinomial logit (MNL) bandits capture many real-world assortment recommendation problems such as online retailing/advertising. However, prior work has only considered (generalized) linear value functions, which greatly limits its applicability. Motivated by this fact, in this work, we consider contextual MNL bandits with a general value function class that contains the ground truth, borrowing ideas from a recent trend of studies on contextual bandits. Specifically, we consider both the stochastic and the adversarial settings, and propose a suite of algorithms, each with different computation-regret trade-off. When applied to the linear case, our results not only are the first ones with no dependence on a certain problem-dependent constant that can be exponentially large, but also enjoy other advantages such as computational efficiency, dimension-free regret bounds, or the ability to handle completely adversarial contexts and rewards.