Cost-Aware Cascading Bandits

Gan, Chao; Zhou, Ruida; Yang, Jing; Shen, Cong

doi:10.1109/tsp.2020.3001388

Cited by 12 publications

(4 citation statements)

References 16 publications

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“…They also consider the position in the cascading model and generalize the reward function meeting some common constraints. Gan et al [9] propose a cost-aware cascading bandits model. When agents pull an arm, the agent deserves not only a reward but also a cost.…”

Section: Related Workmentioning

confidence: 99%

Conservative Contextual Combinatorial Cascading Bandit

Wang¹,

Zhao²,

Li³

et al. 2021

Preprint

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Conservative mechanism is a desirable property in decisionmaking problems which balance the tradeoff between the exploration and exploitation. We propose the novel conservative contextual combinatorial cascading bandit (C 4 -bandit), a cascading online learning game which incorporates the conservative mechanism. At each time step, the learning agent is given some contexts and has to recommend a list of items but not worse than the base strategy and then observes the reward by some stopping rules. We design the C 4 -UCB algorithm to solve the problem and prove its n-step upper regret bound for two situations: known baseline reward and unknown baseline reward. The regret in both situations can be decomposed into two terms: (a) the upper bound for the general contextual combinatorial cascading bandit; and (b) a constant term for the regret from the conservative mechanism. We also improve the bound of the conservative contextual combinatorial bandit as a by-product. Experiments on synthetic data demonstrate its advantages and validate our theoretical analysis.

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Section: Related Workmentioning

confidence: 99%

Conservative Contextual Combinatorial Cascading Bandit

Wang¹,

Zhao²,

Li³

et al. 2021

Preprint

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“…Another application would be a movie recommendation system which sequentially presents options from different genres to a user, till he/she picks one; and then uses this feedback to learn the subset of genres that the user likes. Such a feedback model has also recently received significant attention in the Online Learning community under the moniker 'cascading bandits' [22]- [24], with applications in opportunistic spectrum access, network routing, recommendation systems, and dynamic treatment allocation.…”

Section: Introductionmentioning

confidence: 99%

Neoliberalism and Majoritarian Politics

Mirza¹

2022

Mumbai / Bombay

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In this paper, we introduce a variation of the group testing problem where each test is specified by an ordered subset of items, and returns the first defective item in the specified order. We refer to this as cascaded group testing and the goal is to identify a small set of K defective items amongst a collection of size N , using as few tests as possible. For the adaptive testing regime, we show that a simple scheme is able to find all defective items in at most K tests, which is optimal. For the non-adaptive setting, we first come up with a necessary and sufficient condition for any collection of tests to be feasible for recovering all the defectives. Using this, we are able to show that any feasible non-adaptive strategy requires at least Ω(K 2 ) tests. In terms of achievability, it is easy to show that a collection of O(K 2 log(N/K)) randomly constructed tests is feasible. We show via carefully constructed explicit designs that one can do significantly better. We provide two simple schemes for K = 1, 2 which only require one and two tests respectively irrespective of the number of items N . Note that this is in contrast to standard binary group testing, where at least Ω(log N ) tests are required. The case of K ≥ 3 is more challenging and here we come up with an iterative design which requires only poly(log log N ) tests.

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“…The goal is to minimize the total expected loss over certain time horizon. With this objective, the design of the sequential decision strategy and the corresponding theoretical analysis have been extensively investigated [1][2][3][4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Optimal Stochastic Nonconvex Optimization with Bandit Feedback

Zhao,

Lai

2021

Preprint

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In this paper, we analyze the continuous armed bandit problems for nonconvex cost functions under certain smoothness and sublevel set assumptions. We first derive an upper bound on the expected cumulative regret of a simple bin splitting method. We then propose an adaptive bin splitting method, which can significantly improve the performance. Furthermore, a minimax lower bound is derived, which shows that our new adaptive method achieves locally minimax optimal expected cumulative regret.

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Cost-Aware Cascading Bandits

Cited by 12 publications

References 16 publications

Conservative Contextual Combinatorial Cascading Bandit

Conservative Contextual Combinatorial Cascading Bandit

Neoliberalism and Majoritarian Politics

Optimal Stochastic Nonconvex Optimization with Bandit Feedback

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