Choice models are essential for understanding decision-making processes in domains like online advertising, product recommendations, and assortment optimization. The Multinomial Logit (MNL) model is particularly versatile in selecting products or advertisements for display. However, challenges arise with unknown MNL parameters and delayed feedback, requiring sellers to learn customers' choice behavior and make dynamic decisions with biased knowledge due to delays. We address these challenges by developing an algorithm that handles delayed feedback, balancing exploration and exploitation using confidence bounds and optimism. We first consider a censored setting where a threshold for considering feedback is imposed by business requirements. Our algorithm demonstrates a $\tilde{O}(\sqrt{NT})$ regret, with a matching lower bound up to a logarithmic term. Furthermore, we extend our analysis to environments with non-thresholded delays, achieving a $\tilde{O}(\sqrt{NT})$ regret. To validate our approach, we conduct experiments that confirm the effectiveness of our algorithm.

We study online learning with the general notion of transductive regret, that is regret with modification rules applying to expert sequences (as opposed to single experts) that are representable by weighted finite-state transducers. We show how transductive regret generalizes existing notions of regret, including: (1) external regret; (2) internal regret; (3) swap regret; and (4) conditional swap regret. We present a general and efficient online learning algorithm for minimizing transductive regret. We further extend that to design efficient algorithms for the time-selection and sleeping expert settings. A by-product of our study is an algorithm for swap regret, which, under mild assumptions, is more efficient than existing ones, and a substantially more efficient algorithm for time selection swap regret.

We consider the problem of online learning in the linear contextual bandits setting, but in which there are also strong individual fairness constraints governed by an unknown similarity metric. These constraints demand that we select similar actions or individuals with approximately equal probability [?], which may be at odds with optimizing reward, thus modeling settings where profit and social policy are in tension. We assume we learn about an unknown Mahalanobis similarity metric from only weak feedback that identifies fairness violations, but does not quantify their extent. This is intended to represent the interventions of a regulator who "knows unfairness when he sees it" but nevertheless cannot enunciate a quantitative fairness metric over individuals. Our main result is an algorithm in the adversarial context setting that has a number of fairness violations that depends only logarithmically on T, while obtaining an optimal O( T) regret bound to the best fair policy.

V ov95, CBL06] and online convex optimization [Haz16, Ora19] have been developed. Until the labels of all examples of X have been predicted: The learning algorithm picks a point x X and makes a prediction z R about its label.

In this work we study the problem of actively learning binary classifiers from a given concept class, i.e., learning by utilizing unlabeled data and submitting targeted queries about their labels to a domain expert. We evaluate the quality of our solutions by considering the learning curves they induce, i.e., the rate of

In Euclidean space, OCO boasts a robust theoretical foundation and numerous real-world applications, such as online load balancing (Molinaro, 2017), optimal control (Li et al., 2019), revenue maximization (Lin et al., 2019), and portfolio management (Jézéquel et al., 2022).

In this paper, we propose an online convex optimization approach with two different levels of adaptivity. On a higher level, our approach is agnostic to the unknown types and curvatures of the online functions, while at a lower level, it can exploit the unknown niceness of the environments and attain problem-dependent guarantees.