In this paper we consider the dynamic assortment selection problem under an uncapacitated multinomial-logit (MNL) model. By carefully analyzing a revenue potential function, we show that a trisection based algorithm achieves an item-independent regret bound of O(sqrt(T log log T), which matches information theoretical lower bounds up to iterated logarithmic terms. Our proof technique draws tools from the unimodal/convex bandit literature as well as adaptive confidence parameters in minimax multi-armed bandit problems.

We study the contextual linear bandit problem, a version of the standard stochastic multi-armed bandit (MAB) problem where a learner sequentially selects actions to maximize a reward which depends also on a user provided per-round context. Though the context is chosen arbitrarily or adversarially, the reward is assumed to be a stochastic function of a feature vector that encodes the context and selected action. Our goal is to devise private learners for the contextual linear bandit problem.

Your Out-of-Distribution Detection Method is Not Robust!

We propose and study the known-compensation multi-arm bandit (KCMAB) problem, where a system controller offers a set of arms to many short-term players for $T$ steps. In each step, one short-term player arrives to the system. Upon arrival, the player greedily selects an arm with the current best average reward and receives a stochastic reward associated with the arm. In order to incentivize players to explore other arms, the controller provides proper payment compensation to players. The objective of the controller is to maximize the total reward collected by players while minimizing the compensation. We first give a compensation lower bound $\Theta(\sum_i {\Delta_i\log T\over KL_i})$, where $\Delta_i$ and $KL_i$ are the expected reward gap and Kullback-Leibler (KL) divergence between distributions of arm $i$ and the best arm, respectively. We then analyze three algorithms to solve the KCMAB problem, and obtain their regrets and compensations. We show that the algorithms all achieve $O(\log T)$ regret and $O(\log T)$ compensation that match the theoretical lower bound. Finally, we use experiments to show the behaviors of those algorithms.

Linear contextual bandits represent a fundamental class of models with numerous real-world applications, and it is critical to developing algorithms that can effectively manage noise with unknown variance, ensuring provable guarantees for both worst-case constant-variance noise and deterministic reward scenarios.

Adap-tivity to the problem's structure is essential in order to obtain optimal regret upper

Two key features make correlation clustering quite suitable in real-world applications.

The agent pulls an arm and observes the corresponding return provided by the environment.

In contextual dynamic pricing, a seller sequentially prices goods based on contextual information.