Online Learning via Offline Greedy: Applications in Market Design and Optimization

Niazadeh, Rad; Golrezaei, Negin; Wang, Joshua; Susan, Fransisca; Badanidiyuru, Ashwinkumar

doi:10.2139/ssrn.3613756

Cited by 5 publications

(4 citation statements)

References 53 publications

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“…Note that in the discrete setting, (Roughgarden and Wang 2018) studied the non-monotone (discrete) submodular maximization over the hypercube and gave an algorithm which guarantees the tight (1/2)-approximation and O( √ T ) regret. Recently and independently, (Niazadeh et al 2020) have provided an (1/2, O( √ T log T ))-regret algorithm for DR-submodular maximization over the hypercube. Their algorithm is built on an interesting framework that transform offline greedy algorithms to online ones using Blackwell approachability.…”

Section: Online Settingmentioning

confidence: 99%

Online Non-Monotone DR-Submodular Maximization

Thắng¹,

Srivastav²

2021

AAAI

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In this paper, we study fundamental problems of maximizing DR-submodular continuous functions that have real-world applications in the domain of machine learning, economics, operations research and communication systems. It captures a subclass of non-convex optimization that provides both theoretical and practical guarantees. Here, we focus on minimizing regret for online arriving non-monotone DR-submodular functions over down-closed and general convex sets. First, we present an online algorithm that achieves a 1/e-approximation ratio with the regret of O(T^{3/4}) for maximizing DR-submodular functions over any down-closed convex set. Note that, the approximation ratio of 1/e matches the best-known guarantee for the offline version of the problem. Next, we give an online algorithm that achieves an approximation guarantee (depending on the search space) for the problem of maximizing non-monotone continuous DR-submodular functions over a general convex set (not necessarily down-closed). To best of our knowledge, no prior algorithm with approximation guarantee was known for non-monotone DR-submodular maximization in the online setting. Finally we run experiments to verify the performance of our algorithms on problems arising in machine learning domain with the real-world datasets.

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Section: Online Settingmentioning

confidence: 99%

Online Non-Monotone DR-Submodular Maximization

Thắng¹,

Srivastav²

2021

AAAI

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“…Since their major focus is pricing instead of ranking, the design of the algorithm deviates signi cantly from ours. Niazadeh et al (2020) consider the online learning problem of Asadpour et al (2020) and focus on the maximization of the sum of a sequence of submodular functions, subject to a permutation of the inputs. It is closely connected to product ranking.…”

Section: Online Learning and Multi-armed Banditmentioning

confidence: 99%

Revenue Maximization and Learning in Products Ranking

Chen

Yang

2020

Preprint

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We consider the revenue maximization problem for an online retailer who plans to display a set of products di ering in their prices and qualities and rank them in order. The consumers have random attention spans and view the products sequentially before purchasing a "satis cing" product or leaving the platform emptyhanded when the attention span gets exhausted. Our framework extends the cascade model in two directions: the consumers have random attention spans instead of xed ones and the rm maximizes revenues instead of clicking probabilities. We show a nested structure of the optimal product ranking as a function of the attention span when the attention span is xed and design a 1/𝑒-approximation algorithm accordingly for the random attention spans. When the conditional purchase probabilities are not known and may depend on consumer and product features, we devise an online learning algorithm that achieves Õ ( √ 𝑇 ) regret relative to the approximation algorithm, despite of the censoring of information: the attention span of a customer who purchases an item is not observable. Numerical experiments demonstrate the outstanding performance of the approximation and online learning algorithms.

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“…Other structures that have been studied include imposing upper bounds on the average rewards of arms (Gupta et al 2019) and imposing lower and upper bounds on the realized rewards of the arms (Bubeck et al 2019). There are also papers that study structural information in (i) contextual multi-armed bandit problems (e.g., Slivkins (2011) and Balseiro et al (2019)) and (ii) combinatorial decision-making (e.g., Streeter and Golovin (2008), Zhang et al (2019), and Niazadeh et al (2020)).…”

Section: Related Workmentioning

confidence: 99%

Optimal Learning for Structured Bandits

Parys¹,

Golrezaei²

2020

Preprint

Self Cite

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We study structured multi-armed bandits, which is the problem of online decisionmaking under uncertainty in the presence of structural information. In this problem, the decision-maker needs to discover the best course of action despite observing only uncertain rewards over time. The decision-maker is aware of certain structural information regarding the reward distributions and would like to minimize his regret by exploiting this information, where the regret is its performance difference against a benchmark policy which knows the best action ahead of time. In the absence of structural information, the classical upper confidence bound (UCB) and Thomson sampling algorithms are well known to suffer only minimal regret. As recently pointed out by Russo and Van Roy (2018) and Lattimore and Szepesvari (2017), neither algorithms is, however, capable of exploiting structural information which is commonly available in practice. We propose a novel learning algorithm which we call "DUSA" whose worstcase regret matches the information-theoretic regret lower bound up to a constant factor and can handle a wide range of structural information. Our algorithm DUSA solves a dual counterpart of regret lower bound at the empirical reward distribution and follows the suggestion made by the dual problem. Our proposed algorithm is the first computationally viable learning policy for structured bandit problems that suffers asymptotic minimal regret.

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Online Learning via Offline Greedy: Applications in Market Design and Optimization

Cited by 5 publications

References 53 publications

Online Non-Monotone DR-Submodular Maximization

Online Non-Monotone DR-Submodular Maximization

Revenue Maximization and Learning in Products Ranking

Optimal Learning for Structured Bandits

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