Prophet inequality concerns a basic optimal stopping problem and states that simple threshold stopping policies -- i.e., accepting the first reward larger than a certain threshold -- can achieve tight

Machine Learning critically relies on the assumption that the training data is representative of the unseen instances a learner faces at test time.

Contract theory studies the setting where a principal seeks to design a contract for rewarding an agent on the basis of the uncertain outcomes caused by the agent's private actions [

We consider a novel dynamic pricing and learning setting where in addition to setting prices of products in sequential rounds, the seller also ex-ante commits to'advertising schemes'. That is, in the beginning of each round the seller can decide what kind of signal they will provide to the buyer about the product's quality upon realization. Using the popular Bayesian persuasion framework to model the effect of these signals on the buyers' valuation and purchase responses, we formulate the problem of finding an optimal design of the advertising scheme along with a pricing scheme that maximizes the seller's expected revenue. Without any apriori knowledge of the buyers' demand function, our goal is to design an online algorithm that can use past purchase responses to adaptively learn the optimal pricing and advertising strategy. We study the regret of the algorithm when compared to the optimal clairvoyant price and advertising scheme.

We introduce and study the problem of detecting whether an agent is updating their prior beliefs given new evidence in an optimal way that is Bayesian, or whether they are biased towards their own prior. In our model, biased agents form posterior beliefs that are a convex combination of their prior and the Bayesian posterior, where the more biased an agent is, the closer their posterior is to the prior. Since we often cannot observe the agent's beliefs directly, we take an approach inspired by information design . Specifically, we measure an agent's bias by designing a signaling scheme and observing the actions the agent takes in response to different signals, assuming that the agent maximizes their own expected utility. Our goal is to detect bias with a minimum number of signals. Our main results include a characterization of scenarios where a single signal suffices and a computationally efficient algorithm to compute optimal signaling schemes.

To thrive in those environments, the agent needs to influence other agents so their actions become more helpful and less harmful. Research in computational economics distills two ways to influence others directly: by providing tangible goods ( mechanism design) and by providing information ( information design). This work investigates information design problems for a group of RL agents. The main challenges are two-fold. One is the information provided will immediately affect the transition of the agent trajectories, which introduces additional non-stationarity. The other is the information can be ignored, so the sender must provide information that the receiver is willing to respect.