Information Gathering with Peers: Submodular Optimization with Peer-Prediction Constraints

TL;DR

This paper addresses optimal information gathering from data providers using submodular optimization with peer-prediction incentives, proposing greedy algorithms with theoretical guarantees and validating them in a crowd sensing testbed.

Contribution

It introduces a novel formulation combining submodular maximization with peer-prediction constraints and develops greedy algorithms with performance bounds.

Findings

The problem is hard to approximate within a constant factor.

Proposed greedy algorithms perform well under certain conditions.

Algorithms are validated on a realistic crowd sensing testbed.

Abstract

We study a problem of optimal information gathering from multiple data providers that need to be incentivized to provide accurate information. This problem arises in many real world applications that rely on crowdsourced data sets, but where the process of obtaining data is costly. A notable example of such a scenario is crowd sensing. To this end, we formulate the problem of optimal information gathering as maximization of a submodular function under a budget constraint, where the budget represents the total expected payment to data providers. Contrary to the existing approaches, we base our payments on incentives for accuracy and truthfulness, in particular, {\em peer-prediction} methods that score each of the selected data providers against its best peer, while ensuring that the minimum expected payment is above a given threshold. We first show that the problem at hand is hard to approximate within a constant factor that is not dependent on the properties of the payment function. However, for given topological and analytical properties of the instance, we construct two greedy algorithms, respectively called PPCGreedy and PPCGreedyIter, and establish theoretical bounds on their performance w.r.t. the optimal solution. Finally, we evaluate our methods using a realistic crowd sensing testbed.