- Replicable Studying of Massive-Margin Halfspaces(arXiv)
Writer : Alkis Kalavasis, Amin Karbasi, Kasper Green Larsen, Grigoris Velegkas, Felix Zhou
Summary : We offer environment friendly replicable algorithms for the issue of studying large-margin halfspaces. Our outcomes enhance upon the algorithms supplied by Impagliazzo, Lei, Pitassi, and Sorrell [STOC, 2022]. We design the primary dimension-independent replicable algorithms for this process which runs in polynomial time, is correct, and has strictly improved pattern complexity in comparison with the one achieved by Impagliazzo et al. [2022] with respect to all of the related parameters. Furthermore, our first algorithm has pattern complexity that’s optimum with respect to the accuracy parameter ε. We additionally design an SGD-based replicable algorithm that, in some parameters’ regimes, achieves higher pattern and time complexity than our first algorithm. Departing from the requirement of polynomial time algorithms, utilizing the DP-to-Replicability discount of Bun, Gaboardi, Hopkins, Impagliazzo, Lei, Pitassi, Sorrell, and Sivakumar [STOC, 2023], we present how you can receive a replicable algorithm for large-margin halfspaces with improved pattern complexity with respect to the margin parameter τ, however operating time doubly exponential in 1/τ2 and worse pattern complexity dependence on ε than one in every of our earlier algorithms. We then design an improved algorithm with higher pattern complexity than all three of our earlier algorithms and operating time exponential in 1/τ2.
