Modern recommendation systems can be broadly divided into two key stages: the ranking stage, where the system predicts various user engagements (e.g., click-through rate, like rate, follow rate, watch time), and the value model stage, which aggregates these predictive scores through a function (e.g., a linear combination defined by a weight vector) to measure the value of each content by a single numerical score. Both stages play roughly equally important roles in real industrial systems; however, how to optimize the model weights for the second stage still lacks systematic study. This paper focuses on optimizing the second stage through auto-tuning technology. Although general auto-tuning systems and solutions - both from established production practices and open-source solutions - can address this problem, they typically require weeks or even months to identify a feasible solution. Such prolonged tuning processes are unacceptable in production environments for recommendation systems, as suboptimal value models can severely degrade user experience. An effective auto-tuning solution is required to identify a viable model within 2-3 days, rather than the extended timelines typically associated with existing approaches. In this paper, we introduce a practical auto-tuning system named HyperZero that addresses these time constraints while effectively solving the unique challenges inherent in modern recommendation systems. Moreover, this framework has the potential to be expanded to broader tuning tasks within recommendation systems.

We study the sample complexity (i.e., the number of comparisons needed) bounds for actively ranking a set of $n$ items from multi-wise comparisons. Here, a multi-wise comparison takes $m$ items as input and returns a (noisy) result about the best item (the winner feedback) or the order of these items (the full-ranking feedback). We consider two basic ranking problems: top-$k$ items selection and full ranking. Unlike previous works that study ranking from multi-wise comparisons, in this paper, we do not require any parametric model or assumption and work on the fundamental setting where each comparison returns the correct result with probability $1$ or a certain probability larger than $\frac{1}{2}$. This paper helps understand whether and to what degree utilizing multi-wise comparisons can reduce the sample complexity for the ranking problems compared to ranking from pairwise comparisons. Specifically, under the winner feedback setting, one can reduce the sample complexity for top-$k$ selection up to an $m$ factor and that for full ranking up to a $\log{m}$ factor. Under the full-ranking feedback setting, one can reduce the sample complexity for top-$k$ selection up to an $m$ factor and that for full ranking up to an $m\log{m}$ factor. We also conduct numerical simulations to confirm our theoretical results.

This paper studies the sample complexity (aka number of comparisons) bounds for the active best-$k$ items selection from pairwise comparisons. From a given set of items, the learner can make pairwise comparisons on every pair of items, and each comparison returns an independent noisy result about the preferred item. At any time, the learner can adaptively choose a pair of items to compare according to past observations (i.e., active learning). The learner’s goal is to find the (approximately) best-$k$ items with a given confidence, while trying to use as few comparisons as possible. In this paper, we study two problems: (i) finding the probably approximately correct (PAC) best-$k$ items and (ii) finding the exact best-$k$ items, both under strong stochastic transitivity and stochastic triangle inequality. For PAC best-$k$ items selection, we first show a lower bound and then propose an algorithm whose sample complexity upper bound matches the lower bound up to a constant factor. For the exact best-$k$ items selection, we first prove a worst-instance lower bound. We then propose two algorithms based on our PAC best items selection algorithms: one works for $k=1$ and is sample complexity optimal up to a loglog factor, and the other works for all values of $k$ and is sample complexity optimal up to a log factor.

This paper studies the problem of identifying any $k$ distinct arms among the top $\rho$ fraction (e.g., top 5%) of arms from a finite or infinite set with a probably approximately correct (PAC) tolerance $\epsilon$. We consider two cases: (i) when the threshold of the top arms’ expected rewards is known and (ii) when it is unknown. We prove lower bounds for the four variants (finite or infinite arms, and known or unknown threshold), and propose algorithms for each. Two of these algorithms are shown to be sample complexity optimal (up to constant factors) and the other two are optimal up to a log factor. Results in this paper provide up to $\rho n/k$ reductions compared with the “$k$-exploration” algorithms that focus on finding the (PAC) best $k$ arms out of $n$ arms. We also numerically show improvements over the state-of-the-art.

This paper studies the problem of finding the exact ranking from noisy comparisons. A noisy comparison over a set of $m$ items produces a noisy outcome about the most preferred item, and reveals some information about the ranking. By repeatedly and adaptively choosing items to compare, we want to fully rank the items with a certain confidence, and use as few comparisons as possible. Different from most previous works, in this paper, we have three main novelties: (i) compared to prior works, our upper bounds (algorithms) and lower bounds on the sample complexity (aka number of comparisons) require the minimal assumptions on the instances, and are not restricted to specific models; (ii) we give lower bounds and upper bounds on instances with \textit{unequal} noise levels; and (iii) this paper aims at the \textit{exact} ranking without knowledge on the instances, while most of the previous works either focus on approximate rankings or study exact ranking but require prior knowledge. We first derive lower bounds for pairwise ranking (i.e., compare two items each time), and then propose (nearly) \textit{optimal} pairwise ranking algorithms. We further make extensions to listwise ranking (i.e., comparing multiple items each time). Numerical results also show our improvements against the state of the art.