Mechanism Design for Collaborative Normal Mean Estimation
Authors: Yiding Chen, Jerry Zhu, Kirthevasan Kandasamy
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study collaborative normal mean estimation, where m strategic agents collect i.i.d samples from a normal distribution N(µ, σ2) at a cost. They all wish to estimate the mean µ. By sharing data with each other, agents can obtain better estimates while keeping the cost of data collection small. To facilitate this collaboration, we wish to design mechanisms that encourage agents to collect a sufficient amount of data and share it truthfully, so that they are all better off than working alone. In naive mechanisms, such as simply pooling and sharing all the data, an individual agent might find it beneficial to under-collect and/or fabricate data, which can lead to poor social outcomes. We design a novel mechanism that overcomes these challenges via two key techniques: first, when sharing the others data with an agent, the mechanism corrupts this dataset proportional to how much the data reported by the agent differs from the others; second, we design minimax optimal estimators for the corrupted dataset. Our mechanism, which is Nash incentive compatible and individually rational, achieves a social penalty (sum of all agents estimation errors and data collection costs) that is at most a factor 2 of the global minimum. When applied to high dimensional (non-Gaussian) distributions with bounded variance, this mechanism retains these three properties, but with slightly weaker results. Finally, in two special cases where we restrict the strategy space of the agents, we design mechanisms that essentially achieve the global minimum. |
| Researcher Affiliation | Academia | Yiding Chen UW-Madison ychen695@wisc.edu Xiaojin Zhu UW-Madison jerryzhu@cs.wisc.edu Kirthevasan Kandasamy UW-Madison kandasamy@cs.wisc.edu |
| Pseudocode | Yes | Algorithm 1 MC3D |
| Open Source Code | No | The paper does not provide any statements about releasing open-source code or links to a code repository. |
| Open Datasets | No | The paper is theoretical and focuses on mechanism design and analysis. It does not mention using any datasets for training or empirical evaluation. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical evaluation on datasets, thus no dataset splits for training, validation, or testing are mentioned. |
| Hardware Specification | No | The paper is theoretical and does not describe any experiments that would require specific hardware. Therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not describe any software implementation details with version numbers. |
| Experiment Setup | No | The paper is theoretical and focuses on mechanism design and analysis. It does not describe an experimental setup with hyperparameters or training configurations. |