HAVER: Instance-Dependent Error Bounds for Maximum Mean Estimation and Applications to Q-Learning

• URL: http://arxiv.org/abs/2411.00405v1
• Date: Fri, 01 Nov 2024 07:05:11 GMT
• Title: HAVER: Instance-Dependent Error Bounds for Maximum Mean Estimation and Applications to Q-Learning
• Authors: Tuan Ngo Nguyen, Kwang-Sung Jun,
• Abstract summary: We study the problem of estimating the emphvalue of the largest mean among $K$ distributions via samples from them. We propose a novel algorithm called HAVER and analyze its mean squared error.
• Score: 11.026588768210601
• License:
• Abstract: We study the problem of estimating the \emph{value} of the largest mean among $K$ distributions via samples from them (rather than estimating \emph{which} distribution has the largest mean), which arises from various machine learning tasks including Q-learning and Monte Carlo tree search. While there have been a few proposed algorithms, their performance analyses have been limited to their biases rather than a precise error metric. In this paper, we propose a novel algorithm called HAVER (Head AVERaging) and analyze its mean squared error. Our analysis reveals that HAVER has a compelling performance in two respects. First, HAVER estimates the maximum mean as well as the oracle who knows the identity of the best distribution and reports its sample mean. Second, perhaps surprisingly, HAVER exhibits even better rates than this oracle when there are many distributions near the best one. Both of these improvements are the first of their kind in the literature, and we also prove that the naive algorithm that reports the largest empirical mean does not achieve these bounds. Finally, we confirm our theoretical findings via numerical experiments including bandits and Q-learning scenarios where HAVER outperforms baseline methods.

Related papers

• An Upper Confidence Bound Approach to Estimating the Maximum Mean [0.0]
  We study estimation of the maximum mean using an upper confidence bound (UCB) approach. We establish statistical guarantees, including strong consistency, mean squared errors, and central limit theorems (CLTs) for both estimators.
  arXiv  Detail & Related papers  (2024-08-08T02:53:09Z)
• RaBitQ: Quantizing High-Dimensional Vectors with a Theoretical Error Bound for Approximate Nearest Neighbor Search [16.389851096504277]
  We propose a new randomized quantization method named RaBitQ, which quantizes $D$-dimensional vectors into $D$-bit strings. RaBitQ guarantees a sharp theoretical error bound and provides good empirical accuracy at the same time. In addition, we introduce efficient implementations of RaBitQ, supporting to estimate the distances with bitwise operations or SIMD-based operations.
  arXiv  Detail & Related papers  (2024-05-21T04:55:04Z)
• Best Arm Identification with Fixed Budget: A Large Deviation Perspective [54.305323903582845]
  We present sred, a truly adaptive algorithm that can reject arms in it any round based on the observed empirical gaps between the rewards of various arms. In particular, we present sred, a truly adaptive algorithm that can reject arms in it any round based on the observed empirical gaps between the rewards of various arms.
  arXiv  Detail & Related papers  (2023-12-19T13:17:43Z)
• 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)
• Partial identification of kernel based two sample tests with mismeasured data [5.076419064097733]
  Two-sample tests such as the Maximum Mean Discrepancy (MMD) are often used to detect differences between two distributions in machine learning applications. We study the estimation of the MMD under $epsilon$-contamination, where a possibly non-random $epsilon$ proportion of one distribution is erroneously grouped with the other. We propose a method to estimate these bounds, and show that it gives estimates that converge to the sharpest possible bounds on the MMD as sample size increases.
  arXiv  Detail & Related papers  (2023-08-07T13:21:58Z)
• Learning to Estimate Without Bias [57.82628598276623]
  Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
  arXiv  Detail & Related papers  (2021-10-24T10:23:51Z)
• Ensemble Bootstrapping for Q-Learning [15.07549655582389]
  We introduce a new bias-reduced algorithm called Ensemble Bootstrapped Q-Learning (EBQL) EBQL-like updates yield lower MSE when estimating the maximal mean of a set of independent random variables. We show that there exist domains where both over and under-estimation result in sub-optimal performance.
  arXiv  Detail & Related papers  (2021-02-28T10:19:47Z)
• Large-Scale Methods for Distributionally Robust Optimization [53.98643772533416]
  We prove that our algorithms require a number of evaluations gradient independent of training set size and number of parameters. Experiments on MNIST and ImageNet confirm the theoretical scaling of our algorithms, which are 9--36 times more efficient than full-batch methods.
  arXiv  Detail & Related papers  (2020-10-12T17:41:44Z)
• Breaking the Sample Size Barrier in Model-Based Reinforcement Learning with a Generative Model [50.38446482252857]
  This paper is concerned with the sample efficiency of reinforcement learning, assuming access to a generative model (or simulator) We first consider $gamma$-discounted infinite-horizon Markov decision processes (MDPs) with state space $mathcalS$ and action space $mathcalA$. We prove that a plain model-based planning algorithm suffices to achieve minimax-optimal sample complexity given any target accuracy level.
  arXiv  Detail & Related papers  (2020-05-26T17:53:18Z)
• Computationally efficient sparse clustering [67.95910835079825]
  We provide a finite sample analysis of a new clustering algorithm based on PCA. We show that it achieves the minimax optimal misclustering rate in the regime $|theta infty$.
  arXiv  Detail & Related papers  (2020-05-21T17:51:30Z)

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.