Rising Rested Bandits: Lower Bounds and Efficient Algorithms

• URL: http://arxiv.org/abs/2411.14446v2
• Date: Tue, 26 Nov 2024 22:39:42 GMT
• Title: Rising Rested Bandits: Lower Bounds and Efficient Algorithms
• Authors: Marco Fiandri, Alberto Maria Metelli, Francesco Trov`o,
• Abstract summary: This paper is in the field of sequential Multi-Armed Bandits (MABs) We study a particular case of the rested bandits in which the arms' expected reward is monotonically non-decreasing and concave. We empirically compare our algorithms with state-of-the-art methods for non-stationary MABs over several synthetically generated tasks and an online model selection problem for a real-world dataset.
• Score: 15.390680055166769
• License:
• Abstract: This paper is in the field of stochastic Multi-Armed Bandits (MABs), i.e. those sequential selection techniques able to learn online using only the feedback given by the chosen option (a.k.a. $arm$). We study a particular case of the rested bandits in which the arms' expected reward is monotonically non-decreasing and concave. We study the inherent sample complexity of the regret minimization problem by deriving suitable regret lower bounds. Then, we design an algorithm for the rested case $\textit{R-ed-UCB}$, providing a regret bound depending on the properties of the instance and, under certain circumstances, of $\widetilde{\mathcal{O}}(T^{\frac{2}{3}})$. We empirically compare our algorithms with state-of-the-art methods for non-stationary MABs over several synthetically generated tasks and an online model selection problem for a real-world dataset

Related papers

• Combinatorial Stochastic-Greedy Bandit [79.1700188160944]
  We propose a novelgreedy bandit (SGB) algorithm for multi-armed bandit problems when no extra information other than the joint reward of the selected set of $n$ arms at each time $tin [T]$ is observed. SGB adopts an optimized-explore-then-commit approach and is specifically designed for scenarios with a large set of base arms.
  arXiv  Detail & Related papers  (2023-12-13T11:08:25Z)
• Variance-Dependent Regret Bounds for Linear Bandits and Reinforcement Learning: Adaptivity and Computational Efficiency [90.40062452292091]
  We present the first computationally efficient algorithm for linear bandits with heteroscedastic noise. Our algorithm is adaptive to the unknown variance of noise and achieves an $tildeO(d sqrtsum_k = 1K sigma_k2 + d)$ regret. We also propose a variance-adaptive algorithm for linear mixture Markov decision processes (MDPs) in reinforcement learning.
  arXiv  Detail & Related papers  (2023-02-21T00:17:24Z)
• Complexity Analysis of a Countable-armed Bandit Problem [9.163501953373068]
  We study the classical problem of minimizing the expected cumulative regret over a horizon of play $n$. We propose algorithms that achieve a rate-optimal finite-time instance-dependent regret of $mathcalOleft( log n right)$ when $K=2$. While the order of regret and complexity of the problem suggests a great degree of similarity to the classical MAB problem, properties of the performance bounds and salient aspects of algorithm design are quite distinct from the latter.
  arXiv  Detail & Related papers  (2023-01-18T00:53:46Z)
• Stochastic Rising Bandits [40.32303434592863]
  We study a particular case of the rested and restless bandits in which the arms' expected payoff is monotonically non-decreasing. This characteristic allows designing specifically crafted algorithms that exploit the regularity of the payoffs to provide tight regret bounds. We empirically compare our algorithms with state-of-the-art methods for non-stationary MABs over several synthetically generated tasks and an online model selection problem for a real-world dataset.
  arXiv  Detail & Related papers  (2022-12-07T17:30:45Z)
• Stochastic Contextual Dueling Bandits under Linear Stochastic Transitivity Models [25.336599480692122]
  We consider the regret minimization task in a dueling bandits problem with context information. We propose a computationally efficient algorithm, $texttCoLSTIM$, which makes its choice based on imitating the feedback process. Our experiments demonstrate its superiority over state-of-art algorithms for special cases of CoLST models.
  arXiv  Detail & Related papers  (2022-02-09T17:44:19Z)
• Recurrent Submodular Welfare and Matroid Blocking Bandits [22.65352007353614]
  A recent line of research focuses on the study of the multi-armed bandits problem (MAB) We develop new algorithmic ideas that allow us to obtain a $ (1 - frac1e)$-approximation for any matroid. A key ingredient is the technique of correlated (interleaved) scheduling.
  arXiv  Detail & Related papers  (2021-01-30T21:51:47Z)
• Restless-UCB, an Efficient and Low-complexity Algorithm for Online Restless Bandits [61.490254407420906]
  We study the online restless bandit problem, where the state of each arm evolves according to a Markov chain. We propose Restless-UCB, a learning policy that follows the explore-then-commit framework.
  arXiv  Detail & Related papers  (2020-11-05T05:16:04Z)
• Nearly Dimension-Independent Sparse Linear Bandit over Small Action Spaces via Best Subset Selection [71.9765117768556]
  We consider the contextual bandit problem under the high dimensional linear model. This setting finds essential applications such as personalized recommendation, online advertisement, and personalized medicine. We propose doubly growing epochs and estimating the parameter using the best subset selection method.
  arXiv  Detail & Related papers  (2020-09-04T04:10:39Z)
• Stochastic Bandits with Linear Constraints [69.757694218456]
  We study a constrained contextual linear bandit setting, where the goal of the agent is to produce a sequence of policies. We propose an upper-confidence bound algorithm for this problem, called optimistic pessimistic linear bandit (OPLB)
  arXiv  Detail & Related papers  (2020-06-17T22:32:19Z)
• Model Selection in Contextual Stochastic Bandit Problems [51.94632035240787]
  We develop a meta-algorithm that selects between base algorithms. We show through a lower bound that even when one of the base algorithms has $O(sqrtT)$ regret, in general it is impossible to get better than $Omega(sqrtT)$ regret.
  arXiv  Detail & Related papers  (2020-03-03T18:46:34Z)

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.