From PAC to Instance-Optimal Sample Complexity in the Plackett-Luce Model

We consider PAC learning for identifying a good item from subset-wise samples in \pl\, probability models, with instance-dependent sample complexity performance. For the setting where subsets of a fixed size can be tested and top-ranked feedback is made available to the learner each time, we give the first $(\epsilon,\delta)$-PAC best item algorithm with an instance-dependent sample complexity bound. The algorithm relies on a wrapper that uses a weaker PAC algorithm with worst-case performance guarantees to adapt to the hardness of the input instance. The sample complexity is shown to be multiplicatively better depending on the length of rank-ordered feedback available in each subset play. We also give a new fixed-budget best-item algorithm for the \pl\, model along with an error bound. Numerical results of simulations of the algorithms are reported.