In many platforms, user arrivals exhibit a self-reinforcing behavior: future user arrivals are likely to have preferences similar to users who were satisfied in the past.

Motivated by the application of real-time pricing in e-commerce platforms, we consider the problem of revenue-maximization in a setting where the seller can leverage contextual information describing the customer's history and the product's type to predict her valuation of the product. However, her true valuation is unobservable to the seller, only binary outcome in the form of success-failure of a transaction is observed. Unlike in usual contextual bandit settings, the optimal price/arm given a covariate in our setting is sensitive to the detailed characteristics of the residual uncertainty distribution. We develop a semi-parametric model in which the residual distribution is non-parametric and provide the first algorithm which learns both regression parameters and residual distribution with Õ(p n) regret. We empirically test a scalable implementation of our algorithm and observe good performance.

This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein perturbations of the empirical measure) of the absolute regression errors. The inner maximization is solved in closed form resulting in a regularization penalty involves the norm of the gradient.

In many platforms, user arrivals exhibit a self-reinforcing behavior: future user arrivals are likely to have preferences similar to users who were satisfied in the past.

Consider a player that in each of T rounds chooses one of K arms.

In this paper, we consider online learning in generalized linear contextual bandits where rewards are not immediately observed. Instead, rewards are available to the decision maker only after some delay, which is unknown and stochastic, even though a decision must be made at each time step for an incoming set of contexts. We study the performance of upper confidence bound (UCB) based algorithms adapted to this delayed setting. In particular, we design a delay-adaptive algorithm, which we call Delayed UCB, for generalized linear contextual bandits using UCB-style exploration and establish regret bounds under various delay assumptions. In the important special case of linear contextual bandits, we further modify this algorithm and establish a tighter regret bound under the same delay assumptions. Our results contribute to the broad landscape of contextual bandits literature by establishing that UCB algorithms, which are widely deployed in modern recommendation engines, can be made robust to delays.

Consider a player that in each of T rounds chooses one of K arms.

In this paper, we consider online learning in generalized linear contextual bandits where rewards are not immediately observed. Instead, rewards are available to the decision maker only after some delay, which is unknown and stochastic, even though a decision must be made at each time step for an incoming set of contexts. We study the performance of upper confidence bound (UCB) based algorithms adapted to this delayed setting. In particular, we design a delay-adaptive algorithm, which we call Delayed UCB, for generalized linear contextual bandits using UCB-style exploration and establish regret bounds under various delay assumptions. In the important special case of linear contextual bandits, we further modify this algorithm and establish a tighter regret bound under the same delay assumptions. Our results contribute to the broad landscape of contextual bandits literature by establishing that UCB algorithms, which are widely deployed in modern recommendation engines, can be made robust to delays.

Motivated by the application of real-time pricing in e-commerce platforms, we consider the problem of revenue-maximization in a setting where the seller can leverage contextual information describing the customer's history and the product's type to predict her valuation of the product. However, her true valuation is unobservable to the seller, only binary outcome in the form of success-failure of a transaction is observed. Unlike in usual contextual bandit settings, the optimal price/arm given a covariate in our setting is sensitive to the detailed characteristics of the residual uncertainty distribution. We develop a semi-parametric model in which the residual distribution is non-parametric and provide the first algorithm which learns both regression parameters and residual distribution with Õ(p n) regret. We empirically test a scalable implementation of our algorithm and observe good performance.