We consider the classic cake-cutting problem of producing fair allocations for n agents, in the Robertson-Webb query model.

In collaborative data sharing and machine learning, multiple parties aggregate their data resources to train a machine learning model with better model performance. However, as the parties incur data collection costs, they are only willing to do so when guaranteed incentives, such as fairness and individual rationality. Existing frameworks assume that all parties join the collaboration simultaneously, which does not hold in many real-world scenarios. Due to the long processing time for data cleaning, difficulty in overcoming legal barriers, or unawareness, the parties may join the collaboration at different times. In this work, we propose the following perspective: As a party who joins earlier incurs higher risk and encourages the contribution from other wait-and-see parties, that party should receive a reward of higher value for sharing data earlier. To this end, we propose a fair and time-aware data sharing framework, including novel time-aware incentives. We develop new methods for deciding reward values to satisfy these incentives. We further illustrate how to generate model rewards that realize the reward values and empirically demonstrate the properties of our methods on synthetic and real-world datasets.

We revisit the classical problem of designing Budget-Feasible Mechanisms (BFMs) for submodular valuation functions, which has been extensively studied since the seminal paper of Singer [FOCS'10] due to its wide applications in crowdsourcing and social marketing. We propose TripleEagle, a novel algorithmic framework for designing BFMs, based on which we present several simple yet effective BFMs that achieve better approximation ratios than the state-of-the-art work for both monotone and non-monotone submodular valuation functions. Moreover, our BFMs are the first in the literature to achieve linear complexities while ensuring obvious strategyproofness, making them more practical than the previous BFMs. We conduct extensive experiments to evaluate the empirical performance of our BFMs, and the experimental results strongly demonstrate the efficiency and effectiveness of our approach.

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

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.