Nested Elimination: A Simple Algorithm for Best-Item Identification from Choice-Based Feedback

• URL: http://arxiv.org/abs/2307.09295v1
• Date: Thu, 13 Jul 2023 05:05:30 GMT
• Title: Nested Elimination: A Simple Algorithm for Best-Item Identification from Choice-Based Feedback
• Authors: Junwen Yang, Yifan Feng
• Abstract summary: We study the problem of best-item identification from choice-based feedback. In this problem, a company sequentially and adaptively shows display sets to a population of customers and collects their choices. We propose an elimination-based algorithm, namely Nested Elimination (NE), which is inspired by the nested structure implied by the information-theoretic lower bound.
• Score: 8.043586007062858
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study the problem of best-item identification from choice-based feedback. In this problem, a company sequentially and adaptively shows display sets to a population of customers and collects their choices. The objective is to identify the most preferred item with the least number of samples and at a high confidence level. We propose an elimination-based algorithm, namely Nested Elimination (NE), which is inspired by the nested structure implied by the information-theoretic lower bound. NE is simple in structure, easy to implement, and has a strong theoretical guarantee for sample complexity. Specifically, NE utilizes an innovative elimination criterion and circumvents the need to solve any complex combinatorial optimization problem. We provide an instance-specific and non-asymptotic bound on the expected sample complexity of NE. We also show NE achieves high-order worst-case asymptotic optimality. Finally, numerical experiments from both synthetic and real data corroborate our theoretical findings.

Related papers

• Optimal Decision Tree and Adaptive Submodular Ranking with Noisy Outcomes [9.321976218862542]
  In pool-based active learning, the learner is given an unlabeled data set and aims to efficiently learn the unknown hypothesis by querying the labels of the data points. This can be formulated as the classical Optimal Decision Tree (ODT) problem: Given a set of tests, a set of hypotheses, and an outcome for each pair of test and hypothesis, our objective is to find a low-cost testing procedure (i.e., decision tree) that identifies the true hypothesis. In this work, we study a fundamental variant of the ODT problem in which some test outcomes are noisy, even in the more general
  arXiv  Detail & Related papers  (2023-12-23T21:47:50Z)
• Optimal Multi-Distribution Learning [88.3008613028333]
  Multi-distribution learning seeks to learn a shared model that minimizes the worst-case risk across $k$ distinct data distributions. We propose a novel algorithm that yields an varepsilon-optimal randomized hypothesis with a sample complexity on the order of (d+k)/varepsilon2.
  arXiv  Detail & Related papers  (2023-12-08T16:06:29Z)
• Dual-Directed Algorithm Design for Efficient Pure Exploration [9.728332815218181]
  We consider pure-exploration problems in the context of sequential adaptive experiments with a finite set of alternatives. We formulate the problem complexity measure as a maximin optimization problem for the static fixed-budget, fixed-confidence, and posterior convergence rate settings. Our algorithm attains optimality in $varepsilon$-best-arm identification (or ranking and selection with a probability of good selection guarantee) and thresholding bandits.
  arXiv  Detail & Related papers  (2023-10-30T07:29:17Z)
• Faster Stochastic Variance Reduction Methods for Compositional MiniMax Optimization [50.10952609321302]
  compositional minimax optimization is a pivotal challenge across various machine learning domains. Current methods of compositional minimax optimization are plagued by sub-optimal complexities or heavy reliance on sizable batch sizes. This paper introduces a novel method, called Nested STOchastic Recursive Momentum (NSTORM), which can achieve the optimal sample complexity of $O(kappa3 /epsilon3 )$.
  arXiv  Detail & Related papers  (2023-08-18T14:57:21Z)
• Debiasing Conditional Stochastic Optimization [15.901623717313493]
  We study the conditional causal optimization (CSO) problem which covers a variety of applications including portfolio selection, reinforcement learning, robust learning, etc. We develop new algorithms for the finite variant variant CSO problem that significantly improve upon existing results. We believe that our technique has the potential to be a useful tool for addressing similar challenges in other optimization problems.
  arXiv  Detail & Related papers  (2023-04-20T19:19:55Z)
• Symmetric Tensor Networks for Generative Modeling and Constrained Combinatorial Optimization [72.41480594026815]
  Constrained optimization problems abound in industry, from portfolio optimization to logistics. One of the major roadblocks in solving these problems is the presence of non-trivial hard constraints which limit the valid search space. In this work, we encode arbitrary integer-valued equality constraints of the form Ax=b, directly into U(1) symmetric networks (TNs) and leverage their applicability as quantum-inspired generative models.
  arXiv  Detail & Related papers  (2022-11-16T18:59:54Z)
• Optimal Clustering with Bandit Feedback [57.672609011609886]
  This paper considers the problem of online clustering with bandit feedback. It includes a novel stopping rule for sequential testing that circumvents the need to solve any NP-hard weighted clustering problem as its subroutines. We show through extensive simulations on synthetic and real-world datasets that BOC's performance matches the lower boundally, and significantly outperforms a non-adaptive baseline algorithm.
  arXiv  Detail & Related papers  (2022-02-09T06:05:05Z)
• Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias [27.06618125828978]
  We consider the problem of learning the causal MAG of a system from observational data in the presence of latent variables and selection bias. We propose a novel computationally efficient constraint-based method that is sound and complete. We provide experimental results to compare the proposed approach with the state of the art on both synthetic and real-world structures.
  arXiv  Detail & Related papers  (2021-10-22T19:49:59Z)
• Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness [68.97830259849086]
  Most datasets only capture a simpler subproblem and likely suffer from spurious features. We study adversarial robustness - a local generalization property - to reveal hard, model-specific instances and spurious features. Unlike in other applications, where perturbation models are designed around subjective notions of imperceptibility, our perturbation models are efficient and sound. Surprisingly, with such perturbations, a sufficiently expressive neural solver does not suffer from the limitations of the accuracy-robustness trade-off common in supervised learning.
  arXiv  Detail & Related papers  (2021-10-21T07:28:11Z)
• Local policy search with Bayesian optimization [73.0364959221845]
  Reinforcement learning aims to find an optimal policy by interaction with an environment. Policy gradients for local search are often obtained from random perturbations. We develop an algorithm utilizing a probabilistic model of the objective function and its gradient.
  arXiv  Detail & Related papers  (2021-06-22T16:07:02Z)
• Online Model Selection for Reinforcement Learning with Function Approximation [50.008542459050155]
  We present a meta-algorithm that adapts to the optimal complexity with $tildeO(L5/6 T2/3)$ regret. We also show that the meta-algorithm automatically admits significantly improved instance-dependent regret bounds.
  arXiv  Detail & Related papers  (2020-11-19T10:00:54Z)
• Adaptive Sampling for Best Policy Identification in Markov Decision Processes [79.4957965474334]
  We investigate the problem of best-policy identification in discounted Markov Decision (MDPs) when the learner has access to a generative model. The advantages of state-of-the-art algorithms are discussed and illustrated.
  arXiv  Detail & Related papers  (2020-09-28T15:22:24Z)
• Bloom Origami Assays: Practical Group Testing [90.2899558237778]
  Group testing is a well-studied problem with several appealing solutions. Recent biological studies impose practical constraints for COVID-19 that are incompatible with traditional methods. We develop a new method combining Bloom filters with belief propagation to scale to larger values of n (more than 100) with good empirical results.
  arXiv  Detail & Related papers  (2020-07-21T19:31:41Z)
• Ranking a set of objects: a graph based least-square approach [70.7866286425868]
  We consider the problem of ranking $N$ objects starting from a set of noisy pairwise comparisons provided by a crowd of equal workers. We propose a class of non-adaptive ranking algorithms that rely on a least-squares intrinsic optimization criterion for the estimation of qualities.
  arXiv  Detail & Related papers  (2020-02-26T16:19:09Z)
• Optimal Clustering from Noisy Binary Feedback [75.17453757892152]
  We study the problem of clustering a set of items from binary user feedback. We devise an algorithm with a minimal cluster recovery error rate. For adaptive selection, we develop an algorithm inspired by the derivation of the information-theoretical error lower bounds.
  arXiv  Detail & Related papers  (2019-10-14T09:18:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.