Recently a multi-agent variant of the classical multi-armed bandit was proposed to tackle fairness issues in online learning. Inspired by a long line of work in social choice and economics, the goal is to optimize the Nash social welfare instead of the total utility. Unfortunately previous algorithms either are not efficient or achieve sub-optimal regret in terms of the number of rounds. We propose a new efficient algorithm with lower regret than even previous inefficient ones. We also complement our efficient algorithm with an inefficient approach with regret that matches the lower bound for one agent. The experimental findings confirm the effectiveness of our efficient algorithm compared to the previous approaches.

In this work, we study the problem of privately maximizing a submodular function in the streaming setting. Extensive work has been done on privately maximizing submodular functions in the general case when the function depends upon the private data of individuals. However, when the size of the data stream drawn from the domain of the objective function is large or arrives very fast, one must privately optimize the objective within the constraints of the streaming setting. We establish fundamental differentially private baselines for this problem and then derive better trade-offs between privacy and utility for the special case of decomposable submodular functions. A submodular function is decomposable when it can be written as a sum of submodular functions; this structure arises naturally when each summand function models the utility of an individual and the goal is to study the total utility of the whole population as in the well-known Combinatorial Public Projects Problem. Finally, we complement our theoretical analysis with experimental corroboration.

This paper studies the problem of clustering in metric spaces while preserving the privacy of individual data. Specifically, we examine differentially private variants of the k-medians and Euclidean k-means problems. We present polynomial algorithms with constant multiplicative error and lower additive error than the previous state-of-the-art for each problem. Additionally, our algorithms use a clustering algorithm without differential privacy as a black-box. This allows practitioners to control the trade-off between runtime and approximation factor by choosing a suitable clustering algorithm to use.

The field of algorithms has seen a push for fairness, or the removal of inherent bias, in recent history. In data summarization, where a much smaller subset of a data set is chosen to represent the whole of the data, fairness can be introduced by guaranteeing each "demographic group" a specific portion of the representative subset. Specifically, this paper examines this fair variant of the k-centers problem, where a subset of the data with cardinality k is chosen to minimize distance to the rest of the data. Previous papers working on this problem presented both a 3-approximation algorithm with a super-linear runtime and a linear-time algorithm whose approximation factor is exponential in the number of demographic groups. This paper combines the best of each algorithm by presenting a linear-time algorithm with a guaranteed 3-approximation factor and provides empirical evidence of both the algorithm’s runtime and effectiveness.