We study the sample complexity (i.e., the number of comparisons needed) bounds

Given an input query, a recommendation model is trained using user feedback data (e.g., click data) to output a ranked list of items. In real-world systems, besides accuracy, an important consideration for a new model is novelty of its top-k recommendations w.r.t. an existing deployed model. However, novelty of top-k items is a difficult goal to optimize a model for, since it involves a non-differentiable sorting operation on the model's predictions. Moreover, novel items, by definition, do not have any user feedback data. Given the semantic capabilities of large language models, we address these problems using a reinforcement learning (RL) formulation where large language models provide feedback for the novel items. However, given millions of candidate items, the sample complexity of a standard RL algorithm can be prohibitively high. To reduce sample complexity, we reduce the top-k list reward to a set of item-wise rewards and reformulate the state space to consist of tuples such that the action space is reduced to a binary decision; and show that this reformulation results in a significantly lower complexity when the number of items is large. We evaluate the proposed algorithm on improving novelty for a query-ad recommendation task on a large-scale search engine. Compared to supervised finetuning on recent pairs, the proposed RL-based algorithm leads to significant novelty gains with minimal loss in recall. We obtain similar results on the ORCAS query-webpage matching dataset and a product recommendation dataset based on Amazon reviews.

In this paper, we address the top-$K$ ranking problem with a monotone adversary. We consider the scenario where a comparison graph is randomly generated and the adversary is allowed to add arbitrary edges. The statistician's goal is then to accurately identify the top-$K$ preferred items based on pairwise comparisons derived from this semi-random comparison graph. The main contribution of this paper is to develop a weighted maximum likelihood estimator (MLE) that achieves near-optimal sample complexity, up to a $\log^2(n)$ factor, where n denotes the number of items under comparison. This is made possible through a combination of analytical and algorithmic innovations. On the analytical front, we provide a refined $\ell_\infty$ error analysis of the weighted MLE that is more explicit and tighter than existing analyses. It relates the $\ell_\infty$ error with the spectral properties of the weighted comparison graph. Motivated by this, our algorithmic innovation involves the development of an SDP-based approach to reweight the semi-random graph and meet specified spectral properties. Additionally, we propose a first-order method based on the Matrix Multiplicative Weight Update (MMWU) framework. This method efficiently solves the resulting SDP in nearly-linear time relative to the size of the semi-random comparison graph.

A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the top-k items as the most prominent special case. The score of a given item is defined as the probability that it beats a randomly chosen other item. Finding an exact ranking typically requires a prohibitively large number of comparisons, but in practice, approximate rankings are often adequate. Accordingly, we study the problem of finding approximate rankings from pairwise comparisons. We analyze an active ranking algorithm that counts the number of comparisons won, and decides whether to stop or which pair of items to compare next, based on confidence intervals computed from the data collected in previous steps. We show that this algorithm succeeds in recovering approximate rankings using a number of comparisons that is close to optimal up to logarithmic factors. We also present numerical results, showing that in practice, approximation can drastically reduce the number of comparisons required to estimate a ranking.

We study the active learning problem of top-$k$ ranking from multi-wise comparisons under the popular multinomial logit model. Our goal is to identify the top-$k$ items with high probability by adaptively querying sets for comparisons and observing the noisy output of the most preferred item from each comparison. To achieve this goal, we design a new active ranking algorithm without using any information about the underlying items' preference scores. We also establish a matching lower bound on the sample complexity even when the set of preference scores is given to the algorithm. These two results together show that the proposed algorithm is nearly instance optimal (similar to instance optimal [FLN03], but up to polylog factors). Our work extends the existing literature on rank aggregation in three directions. First, instead of studying a static problem with fixed data, we investigate the top-$k$ ranking problem in an active learning setting. Second, we show our algorithm is nearly instance optimal, which is a much stronger theoretical guarantee. Finally, we extend the pairwise comparison to the multi-wise comparison, which has not been fully explored in ranking literature.