Error-Tolerant E-Discovery Protocols

We consider the multi-party classification problem introduced by Dong, Hartline, and Vijayaraghavan (2022) in the context of electronic discovery (e-discovery). Based on a request for production from the requesting party, the responding party is required to provide documents that are responsive to the request except for those that are legally privileged. Our goal is to find a protocol that verifies that the responding party sends almost all responsive documents while minimizing the disclosure of non-responsive documents. We provide protocols in the challenging non-realizable setting, where the instance may not be perfectly separated by a linear classifier. We demonstrate empirically that our protocol successfully manages to find almost all relevant documents, while incurring only a small disclosure of non-responsive documents. We complement this with a theoretical analysis of our protocol in the single-dimensional setting, and other experiments on simulated data which suggest that the non-responsive disclosure incurred by our protocol may be unavoidable.

Algorithmic Robust Forecast Aggregation

Forecast aggregation combines the predictions of multiple forecasters to improve accuracy. However, the lack of knowledge about forecasters' information structure hinders optimal aggregation. Given a family of information structures, robust forecast aggregation aims to find the aggregator with minimal worst-case regret compared to the omniscient aggregator. Previous approaches for robust forecast aggregation rely on heuristic observations and parameter tuning. We propose an algorithmic framework for robust forecast aggregation. Our framework provides efficient approximation schemes for general information aggregation with a finite family of possible information structures. In the setting considered by Arieli et al. (2018) where two agents receive independent signals conditioned on a binary state, our framework also provides efficient approximation schemes by imposing Lipschitz conditions on the aggregator or discrete conditions on agents' reports. Numerical experiments demonstrate the effectiveness of our method by providing a nearly optimal aggregator in the setting considered by Arieli et al. (2018).