Brief

This research paper delves into the theoretical aspects of interpolation and aggregation within regression models. The authors introduce the concept of $\gamma$-graph dimension as a key factor for understanding learnability across various aggregation techniques. They demonstrate that a simple median-based aggregation of three interpolating hypotheses achieves optimal performance, surpassing traditional proper learning methods. The paper also highlights that certain hypothesis classes can only be learned through infinite aggregation or non-interpolating rules, indicating limitations of finite interpolating aggregations. AI

A new paper published on arXiv details an algorithm for learning optimal linear contracts from data. The Empirical Utility Maximization (EUM) algorithm can achieve an \(\\varepsilon\)-approximation of the best possible linear contract with high probability, using a sample complexity of \(O(\ln(1/\delta) / \varepsilon^2)\). This sample complexity is proven to be optimal, matching existing lower bounds and establishing uniform convergence guarantees. AI