On Best-Arm Identification with a Fixed Budget in Non-Parametric Multi-Armed Bandits

• URL: http://arxiv.org/abs/2210.00895v1
• Date: Fri, 30 Sep 2022 10:55:40 GMT
• Title: On Best-Arm Identification with a Fixed Budget in Non-Parametric Multi-Armed Bandits
• Authors: Antoine Barrier (UMPA-ENSL, LMO, CELESTE), Aur\'elien Garivier (UMPA-ENSL, LIP), Gilles Stoltz (LMO, CELESTE)
• Abstract summary: We consider general, possibly non-parametric, models D for distributions over the arms. We propose upper bounds on the average log-probability of misidentifying the optimal arm based on information-theoretic quantities.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We lay the foundations of a non-parametric theory of best-arm identification in multi-armed bandits with a fixed budget T. We consider general, possibly non-parametric, models D for distributions over the arms; an overarching example is the model D = P(0,1) of all probability distributions over [0,1]. We propose upper bounds on the average log-probability of misidentifying the optimal arm based on information-theoretic quantities that correspond to infima over Kullback-Leibler divergences between some distributions in D and a given distribution. This is made possible by a refined analysis of the successive-rejects strategy of Audibert, Bubeck, and Munos (2010). We finally provide lower bounds on the same average log-probability, also in terms of the same new information-theoretic quantities; these lower bounds are larger when the (natural) assumptions on the considered strategies are stronger. All these new upper and lower bounds generalize existing bounds based, e.g., on gaps between distributions.

Related papers

• Gradual Domain Adaptation via Manifold-Constrained Distributionally Robust Optimization [0.4732176352681218]
  This paper addresses the challenge of gradual domain adaptation within a class of manifold-constrained data distributions. We propose a methodology rooted in Distributionally Robust Optimization (DRO) with an adaptive Wasserstein radius. Our bounds rely on a newly introduced it compatibility measure, which fully characterizes the error propagation dynamics along the sequence.
  arXiv  Detail & Related papers  (2024-10-17T22:07:25Z)
• Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beat [49.1574468325115]
  This paper presents explicit non-asymptotic bounds on the forward diffusion error in total variation (TV) We parametrise multi-modal data distributions in terms of the distance $R$ to their furthest modes and consider forward diffusions with additive and multiplicative noise.
  arXiv  Detail & Related papers  (2024-08-25T10:28:31Z)
• Score-based generative models are provably robust: an uncertainty quantification perspective [4.396860522241307]
  We show that score-based generative models (SGMs) are provably robust to the multiple sources of error in practical implementation. Our primary tool is the Wasserstein uncertainty propagation (WUP) theorem. We show how errors due to (a) finite sample approximation, (b) early stopping, (c) score-matching objective choice, (d) score function parametrization, and (e) reference distribution choice, impact the quality of the generative model.
  arXiv  Detail & Related papers  (2024-05-24T17:50:17Z)
• A General Recipe for the Analysis of Randomized Multi-Armed Bandit Algorithms [16.114012813668932]
  We revisit two famous bandit algorithms, Minimum Empirical Divergence (MED) and Thompson Sampling (TS) We prove that MED is optimal for all these models, but also provide a simple regret analysis of some TS algorithms for which the optimality is already known.
  arXiv  Detail & Related papers  (2023-03-10T16:43:48Z)
• Beyond the Best: Estimating Distribution Functionals in Infinite-Armed Bandits [40.71199236098642]
  In the infinite-armed bandit problem, each arm's average reward is sampled from an unknown distribution. We consider a general class of distribution functionals beyond the maximum, and propose unified meta algorithms for both the offline and online settings.
  arXiv  Detail & Related papers  (2022-11-01T18:20:10Z)
• Targeted Separation and Convergence with Kernel Discrepancies [61.973643031360254]
  kernel-based discrepancy measures are required to (i) separate a target P from other probability measures or (ii) control weak convergence to P. In this article we derive new sufficient and necessary conditions to ensure (i) and (ii) For MMDs on separable metric spaces, we characterize those kernels that separate Bochner embeddable measures and introduce simple conditions for separating all measures with unbounded kernels.
  arXiv  Detail & Related papers  (2022-09-26T16:41:16Z)
• From Optimality to Robustness: Dirichlet Sampling Strategies in Stochastic Bandits [0.0]
  We study a generic Dirichlet Sampling (DS) algorithm, based on pairwise comparisons of empirical indices computed with re-sampling of the arms' observations. We show that different variants of this strategy achieve provably optimal regret guarantees when the distributions are bounded and logarithmic regret for semi-bounded distributions with a mild quantile condition.
  arXiv  Detail & Related papers  (2021-11-18T14:34:21Z)
• Robust Learning of Optimal Auctions [84.13356290199603]
  We study the problem of learning revenue-optimal multi-bidder auctions from samples when the samples of bidders' valuations can be adversarially corrupted or drawn from distributions that are adversarially perturbed. We propose new algorithms that can learn a mechanism whose revenue is nearly optimal simultaneously for all true distributions'' that are $alpha$-close to the original distribution in Kolmogorov-Smirnov distance.
  arXiv  Detail & Related papers  (2021-07-13T17:37:21Z)
• Distributional Reinforcement Learning via Moment Matching [54.16108052278444]
  We formulate a method that learns a finite set of statistics from each return distribution via neural networks. Our method can be interpreted as implicitly matching all orders of moments between a return distribution and its Bellman target. Experiments on the suite of Atari games show that our method outperforms the standard distributional RL baselines.
  arXiv  Detail & Related papers  (2020-07-24T05:18:17Z)
• Lower bounds in multiple testing: A framework based on derandomized proxies [107.69746750639584]
  This paper introduces an analysis strategy based on derandomization, illustrated by applications to various concrete models. We provide numerical simulations of some of these lower bounds, and show a close relation to the actual performance of the Benjamini-Hochberg (BH) algorithm.
  arXiv  Detail & Related papers  (2020-05-07T19:59:51Z)
• Distributionally Robust Bayesian Quadrature Optimization [60.383252534861136]
  We study BQO under distributional uncertainty in which the underlying probability distribution is unknown except for a limited set of its i.i.d. samples. A standard BQO approach maximizes the Monte Carlo estimate of the true expected objective given the fixed sample set. We propose a novel posterior sampling based algorithm, namely distributionally robust BQO (DRBQO) for this purpose.
  arXiv  Detail & Related papers  (2020-01-19T12:00:33Z)

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.