FraPPE: Fast and Efficient Preference-based Pure Exploration

• URL: http://arxiv.org/abs/2508.16487v1
• Date: Fri, 22 Aug 2025 16:02:06 GMT
• Title: FraPPE: Fast and Efficient Preference-based Pure Exploration
• Authors: Udvas Das, Apurv Shukla, Debabrota Basu,
• Abstract summary: We propose an efficient algorithm to optimally track the existing lower bound for arbitrary preference cones.<n>We prove that our proposed PrePEx algorithm, FraPPE, achieves the optimal sample complexity.
• Score: 17.53646399595373
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Preference-based Pure Exploration (PrePEx) aims to identify with a given confidence level the set of Pareto optimal arms in a vector-valued (aka multi-objective) bandit, where the reward vectors are ordered via a (given) preference cone $\mathcal{C}$. Though PrePEx and its variants are well-studied, there does not exist a computationally efficient algorithm that can optimally track the existing lower bound for arbitrary preference cones. We successfully fill this gap by efficiently solving the minimisation and maximisation problems in the lower bound. First, we derive three structural properties of the lower bound that yield a computationally tractable reduction of the minimisation problem. Then, we deploy a Frank-Wolfe optimiser to accelerate the maximisation problem in the lower bound. Together, these techniques solve the maxmin optimisation problem in $\mathcal{O}(KL^{2})$ time for a bandit instance with $K$ arms and $L$ dimensional reward, which is a significant acceleration over the literature. We further prove that our proposed PrePEx algorithm, FraPPE, asymptotically achieves the optimal sample complexity. Finally, we perform numerical experiments across synthetic and real datasets demonstrating that FraPPE achieves the lowest sample complexities to identify the exact Pareto set among the existing algorithms.

Related papers

• Closing the Approximation Gap of Partial AUC Optimization: A Tale of Two Formulations [121.39938773554523]
  The Area Under the ROC Curve (AUC) is a pivotal evaluation metric in real-world scenarios with both class imbalance and decision constraints.<n>We present two simple instance-wise minimax reformulations to close the approximation gap of PAUC optimization.<n>The resulting algorithms enjoy a linear per-iteration computational complexity w.r.t. the sample size and a convergence rate of $O(-2/3)$ for typical one-way and two-way PAUCs.
  arXiv  Detail & Related papers  (2025-12-01T02:52:33Z)
• Efficiently Solving Discounted MDPs with Predictions on Transition Matrices [6.199300239433395]
  We study Discounted Markov Decision Processes (DMDPs) under a generative model.<n>We propose a novel framework to investigate how a prediction on the transition matrix can enhance the sample efficiency in solving DMDPs.
  arXiv  Detail & Related papers  (2025-02-21T09:59:46Z)
• Span-Agnostic Optimal Sample Complexity and Oracle Inequalities for Average-Reward RL [6.996002801232415]
  We study the sample complexity of finding an $varepsilon$-optimal policy in Markov Decision Processes (MDPs) with a generative model.<n>We develop the first algorithms matching the optimal span-based complexity without $H$ knowledge.
  arXiv  Detail & Related papers  (2025-02-16T19:10:55Z)
• Stochastic Optimization for Non-convex Problem with Inexact Hessian Matrix, Gradient, and Function [99.31457740916815]
  Trust-region (TR) and adaptive regularization using cubics have proven to have some very appealing theoretical properties. We show that TR and ARC methods can simultaneously provide inexact computations of the Hessian, gradient, and function values.
  arXiv  Detail & Related papers  (2023-10-18T10:29:58Z)
• Explicit Second-Order Min-Max Optimization Methods with Optimal Convergence Guarantee [86.05440220344755]
  We propose and analyze inexact regularized Newton-type methods for finding a global saddle point of emphcon unconstrained min-max optimization problems. We show that the proposed methods generate iterates that remain within a bounded set and that the iterations converge to an $epsilon$-saddle point within $O(epsilon-2/3)$ in terms of a restricted function.
  arXiv  Detail & Related papers  (2022-10-23T21:24:37Z)
• Best Policy Identification in Linear MDPs [70.57916977441262]
  We investigate the problem of best identification in discounted linear Markov+Delta Decision in the fixed confidence setting under a generative model. The lower bound as the solution of an intricate non- optimization program can be used as the starting point to devise such algorithms.
  arXiv  Detail & Related papers  (2022-08-11T04:12:50Z)
• Optimal and Efficient Dynamic Regret Algorithms for Non-Stationary Dueling Bandits [27.279654173896372]
  We study the problem of emphdynamic regret minimization in $K$-armed Dueling Bandits under non-stationary or time varying preferences. This is an online learning setup where the agent chooses a pair of items at each round and observes only a relative binary win-loss' feedback for this pair.
  arXiv  Detail & Related papers  (2021-11-06T16:46:55Z)
• 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)
• 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)
• Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandits [99.70167985955352]
  We study the problem of zero-order optimization of a strongly convex function. We consider a randomized approximation of the projected gradient descent algorithm. Our results imply that the zero-order algorithm is nearly optimal in terms of sample complexity and the problem parameters.
  arXiv  Detail & Related papers  (2020-06-14T10:42:23Z)
• Stochastic Proximal Gradient Algorithm with Minibatches. Application to Large Scale Learning Models [2.384873896423002]
  We develop and analyze minibatch variants of gradient algorithm for general composite objective functions with nonsmooth components. We provide complexity for constant and variable stepsize iteration policies obtaining that, for minibatch size $N$, after $mathcalO(frac1Nepsilon)$ $epsilon-$subity is attained in expected quadratic distance to optimal solution.
  arXiv  Detail & Related papers  (2020-03-30T10:43:56Z)

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.