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

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

doi:10.1145/3465456.3467571

Cited by 11 publications

(13 citation statements)

References 8 publications

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“…A multi-linear DR-submodular function is a DRsubmodular function, and we additionally require it to be a multi-variable polynomial with the degree of each variable not exceeding 1. We propose the algorithm BanditMLSM for the bandit maximization of this function class and reach the (1 − 1/e)-regret of O(T 2/3 ), which is far better than the O(T 5/6 ) (1 − 1/e)-regret bound achieved on the general bandit DR-submodular maximization problem (Niazadeh et al, 2021). Multi-linear DR-submodular function captures the property of the multi-linear extension of a submodular set function.…”

Section: Introductionmentioning

confidence: 88%

“…They obtained an O(T 4/5 ) (1 − 1/e)-regret in this situation. A recent work (Niazadeh et al, 2021) uses a Blackwell algorithm to turn offline greedy algorithms into online regret minimization algorithms. As an application, they reproduced the O(T 2/3 ) (1 − 1/e)-regret for the cardinality constraint.…”

Section: Introductionmentioning

confidence: 99%

“…They prove a O(T 4/5 ) (1 − 1/e)-regret upper bound. For the bandit sequential submodular maximization, the existing work proves an O(T 2/3 ) regret with a suboptimal 1/2 approximation ratio (Niazadeh et al, 2021).…”

mentioning

confidence: 99%

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Streaming Algorithms for Monotone DR-Submodular Maximization Under a Knapsack Constraint on the Integer Lattice

Tan

Zhang

et al. 2021

Parallel Architectures, Algorithms and Programming

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We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm BanditMLSM that attains O(T 2/3 log T ) of (1 − 1/e)-regret. Then we reduce submodular bandit with partition matroid constraint and bandit sequential monotone maximization to the online bandit learning of the monotone multi-linear DR-submodular functions, attaining O(T 2/3 log T ) of (1−1/e)-regret in both problems, which improve the existing results. To the best of our knowledge, we are the first to give a sublinear regret algorithm for the submodular bandit with partition matroid constraint. A special case of this problem is studied by Streeter et al. (2009). They prove a O(T 4/5 ) (1 − 1/e)-regret upper bound. For the bandit sequential submodular maximization, the existing work proves an O(T 2/3 ) regret with a suboptimal 1/2 approximation ratio (Niazadeh et al., 2021).

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Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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Streaming Algorithms for Monotone DR-Submodular Maximization Under a Knapsack Constraint on the Integer Lattice

Tan

Zhang

et al. 2021

Parallel Architectures, Algorithms and Programming

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“…A few examples of combinatorial optimization problems where finding an exact optimum is intractable are various settings of submodular optimization, the traveling salesman problem, or clustering. Many such problems have been studied in an online setting with full-information or bandit feedback [Kakade et al, 2007, Streeter and Golovin, 2008, Niazadeh et al, 2021, Nie et al, 2022.…”

Section: Introductionmentioning

confidence: 99%

Lower Bounds for $γ$-Regret via the Decision-Estimation Coefficient

Glasgow¹,

Rakhlin²

2023

Preprint

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In this note, we give a new lower bound for the γ-regret in bandit problems, the regret which arises when comparing against a benchmark that is γ times the optimal solution, i.e., Reg γ (T ) = T t=1 γ maxπ f (π) − f (πt). The γ-regret arises in structured bandit problems where finding an exact optimum of f is intractable. Our lower bound is given in terms of a modification of the constrained Decision-Estimation Coefficient (DEC) of Foster et al. [2023] (and closely related to the original offset DEC of Foster et al. [2021]), which we term the γ-DEC. When restricted to the traditional regret setting where γ = 1, our result removes the logarithmic factors in the lower bound of Foster et al. [2023].

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“…Choice modeling allows firms to model consumers' preferences and decisions. It can help with important operational decisions, including demand forecasting (e.g., McFadden et al (1977), McGill and Van Ryzin (1999)), inventory planning (e.g., , Gaur and Honhon (2006), Aouad et al (2019)), assortment optimization (e.g., Talluri and Van Ryzin (2004), Rusmevichientong et al (2010), Davis et al (2014), Golrezaei et al (2014)), and product ranking optimization (e.g., Derakhshan et al (2020), Niazadeh et al (2021), ). Among choice models, parametric choice models -and in particular random utility maximization models -have received the most attention by far.…”

Section: Introductionmentioning

confidence: 99%

Active Learning for Non-Parametric Choice Models

Susan¹,

Golrezaei²,

Emamjomeh-Zadeh³

et al. 2022

Preprint

Self Cite

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We study the problem of actively learning a non-parametric choice model based on consumers' decisions. We present a negative result showing that such choice models may not be identifiable. To overcome the identifiability problem, we introduce a directed acyclic graph (DAG) representation of the choice model, which in a sense captures as much information about the choice model as could information-theoretically be identified. We then consider the problem of learning an approximation to this DAG representation in an active-learning setting. We design an efficient active-learning algorithm to estimate the DAG representation of the non-parametric choice model, which runs in polynomial time when the set of frequent rankings is drawn uniformly at random. Our algorithm learns the distribution over the most popular items of frequent preferences by actively and repeatedly offering assortments of items and observing the item chosen. We show that our algorithm can better recover a set of frequent preferences on both a synthetic and publicly available dataset on consumers' preferences, compared to the corresponding non-active learning estimation algorithms. This demonstrates the value of our algorithm and active-learning approaches more generally.

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

Abstract: Link to the full version of the paper: https://papers.ssrn.com/abstract=3613756. CCS Concepts: • Theory of computation → Online learning algorithms; Computational pricing and auctions; Approximation algorithms analysis; • Applied computing → Operations research.

Cited by 11 publications

References 8 publications

Streaming Algorithms for Monotone DR-Submodular Maximization Under a Knapsack Constraint on the Integer Lattice

Streaming Algorithms for Monotone DR-Submodular Maximization Under a Knapsack Constraint on the Integer Lattice

Lower Bounds for $γ$-Regret via the Decision-Estimation Coefficient

Active Learning for Non-Parametric Choice Models

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