Before revision:  On the positive side, we provide an online algorithm that achieves a competitive ratio of O(\log N) and O(\log T) , but also a stronger competitive ratio of O(\log k) in settings where the value of any agent for her most preferred item is no more than k times her average value .
After revision:  On the positive side, we provide an online algorithm whose competitive ratio is parameterized by the multiplicative errors in these predictions. The algorithm achieves a competitive ratio of O(\log N) and O(\log T) , but also a stronger competitive ratio of O(\log k) in settings where the value of any agent for her most preferred item is no more than k times her average value .