Towards minimax optimal algorithms for Active Simple Hypothesis Testing

• URL: http://arxiv.org/abs/2504.19014v1
• Date: Sat, 26 Apr 2025 20:03:53 GMT
• Title: Towards minimax optimal algorithms for Active Simple Hypothesis Testing
• Authors: Sushant Vijayan,
• Abstract summary: We study the Active Simple Hypothesis Testing (ASHT) problem, a simpler variant of the Fixed Budget Best Arm Identification problem.<n>We provide novel game theoretic formulation of the upper bounds of the ASHT problem.<n>We propose an approximately optimal algorithm that is computationally tractable compared to prior work.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We study the Active Simple Hypothesis Testing (ASHT) problem, a simpler variant of the Fixed Budget Best Arm Identification problem. In this work, we provide novel game theoretic formulation of the upper bounds of the ASHT problem. This formulation allows us to leverage tools of differential games and Partial Differential Equations (PDEs) to propose an approximately optimal algorithm that is computationally tractable compared to prior work. However, the optimal algorithm still suffers from a curse of dimensionality and instead we use a novel link to Blackwell Approachability to propose an algorithm that is far more efficient computationally. We show that this new algorithm, although not proven to be optimal, is always better than static algorithms in all instances of ASHT and is numerically observed to attain the optimal exponent in various instances.

Related papers

• Faster WIND: Accelerating Iterative Best-of-$N$ Distillation for LLM Alignment [81.84950252537618]
  This paper reveals a unified game-theoretic connection between iterative BOND and self-play alignment.<n>We establish a novel framework, WIN rate Dominance (WIND), with a series of efficient algorithms for regularized win rate dominance optimization.
  arXiv  Detail & Related papers  (2024-10-28T04:47:39Z)
• Fast Screening Rules for Optimal Design via Quadratic Lasso Reformulation [0.135975510645475]
  In this work, we derive safe screening rules that can be used to discard inessential samples. The new tests are much faster to compute, especially for problems involving a parameter space of high dimension. We show how an existing homotopy algorithm to compute the regularization path of the lasso method can be reparametrized with respect to the squared $ell_$-penalty.
  arXiv  Detail & Related papers  (2023-10-13T08:10:46Z)
• Provably Faster Algorithms for Bilevel Optimization [54.83583213812667]
  Bilevel optimization has been widely applied in many important machine learning applications. We propose two new algorithms for bilevel optimization. We show that both algorithms achieve the complexity of $mathcalO(epsilon-1.5)$, which outperforms all existing algorithms by the order of magnitude.
  arXiv  Detail & Related papers  (2021-06-08T21:05:30Z)
• Lower Bounds and Optimal Algorithms for Smooth and Strongly Convex Decentralized Optimization Over Time-Varying Networks [79.16773494166644]
  We consider the task of minimizing the sum of smooth and strongly convex functions stored in a decentralized manner across the nodes of a communication network. We design two optimal algorithms that attain these lower bounds. We corroborate the theoretical efficiency of these algorithms by performing an experimental comparison with existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-06-08T15:54:44Z)
• Minimax Optimization with Smooth Algorithmic Adversaries [59.47122537182611]
  We propose a new algorithm for the min-player against smooth algorithms deployed by an adversary. Our algorithm is guaranteed to make monotonic progress having no limit cycles, and to find an appropriate number of gradient ascents.
  arXiv  Detail & Related papers  (2021-06-02T22:03:36Z)
• An Asymptotically Optimal Primal-Dual Incremental Algorithm for Contextual Linear Bandits [129.1029690825929]
  We introduce a novel algorithm improving over the state-of-the-art along multiple dimensions. We establish minimax optimality for any learning horizon in the special case of non-contextual linear bandits.
  arXiv  Detail & Related papers  (2020-10-23T09:12:47Z)
• 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)
• Optimal and Practical Algorithms for Smooth and Strongly Convex Decentralized Optimization [21.555331273873175]
  We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. We propose two new algorithms for this decentralized optimization problem and equip them with complexity guarantees.
  arXiv  Detail & Related papers  (2020-06-21T11:23:20Z)
• Stochastic Optimization for Regularized Wasserstein Estimators [10.194798773447879]
  We introduce an algorithm to solve a regularized version of the problem of Wasserstein estimators gradient, with a time per step which is sublinear in the natural dimensions. We show that this algorithm can be extended to other tasks, including estimation of Wasserstein barycenters.
  arXiv  Detail & Related papers  (2020-02-20T12:04:05Z)

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.