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This paper studies ML systems that interactively learn from users acrossmultiple subpopulations with heterogeneous data distributions. The primaryobjective is to provide specialized services for different user groups whilealso predicting user preferences. Once the users select a service based on howwell the service anticipated their preference, the services subsequently adaptand refine themselves based on the user data they accumulate, resulting in aniterative, alternating minimization process between users and services(learning dynamics). Employing such tailored approaches has two mainchallenges: (i) Unknown user preferences: Typically, data on user preferencesare unavailable without interaction, and uniform data collection across a largeand diverse user base can be prohibitively expensive. (ii) Suboptimal LocalSolutions: The total loss (sum of loss functions across all users and allservices) landscape is not convex even if the individual losses on a singleservice are convex, making it likely for the learning dynamics to get stuck inlocal minima. The final outcome of the aforementioned learning dynamics is thusstrongly influenced by the initial set of services offered to users, and is notguaranteed to be close to the globally optimal outcome. In this work, wepropose a randomized algorithm to adaptively select very few users to collectpreference data from, while simultaneously initializing a set of services. Weprove that under mild assumptions on the loss functions, the expected totalloss achieved by the algorithm right after initialization is within a factor ofthe globally optimal total loss with complete user preference data, and thisfactor scales only logarithmically in the number of services. Our theory iscomplemented by experiments on real as well as semi-synthetic datasets.

Initializing Services in Interactive ML Systems for Diverse Users