Asynchronous active recommendation systems

We consider the following abstraction of recommendation systems. There are players and objects, and each player has an arbitrary binary preference grade ("likes" or "dislikes") for each object. The preferences are unknown at start. A player can find his grade for an object by "probing" it, but each probe incurs cost. The goal of a recommendation algorithm is to find the preferences of the players while minimizing cost. To save on cost, players post the results of their probes on a public "billboard" (writing and reading from the billboard is free). In asynchronous systems, an adversary controls the order in which players probe. Active algorithms get to tell players which objects to probe when they are scheduled. In this paper we present the first low-overhead algorithms that can provably reconstruct the preferences of players under asynchronous scheduling. "Low overhead" means that the probing cost is only a polylogarithmic factor over the best possible cost; and by "provably" we mean that the algorithm works with high probability (over internal coin tosses) for all inputs, assuming that each player gets some minimal number of probing opportunities. We present algorithms in this model for exact and approximate preference reconstruction.