Near-Optimal Primal-Dual Algorithms for Quantity-Based Network Revenue Management

Sun, Rui; Wang, Xinshang; Zhou, Zijie

doi:10.48550/arxiv.2011.06327

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…Our algorithm is motivated by the traditional online gradient descent (OGD) algorithm (Hazan, 2016). The OGD algorithm applies a linear update rule according to the gradient information at the current period and has been shown to work well in the stationary setting, even when the distribution is unknown (Lu et al, 2020;Sun et al, 2020;Li et al, 2020). However, the update in OGD only involves historical information and for the non-stationary setting, we have to incorporate the prior estimates of the future time periods.…”

Section: Main Results and Contributionsmentioning

confidence: 99%

Online Stochastic Optimization with Wasserstein Based Non-stationarity

Jiashuo¹,

Li²,

Zhang³

2020

Preprint

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We consider a general online stochastic optimization problem with multiple budget constraints over a horizon of finite time periods. In each time period, a reward function and multiple cost functions are revealed, and the decision maker needs to specify an action from a convex and compact action set to collect the reward and consume the budget. Each cost function corresponds to the consumption of one budget. In each time period, the reward function and the cost functions are drawn from an unknown distribution, which is non-stationary across time. The objective of the decision maker is to maximize the cumulative reward subject to the budget constraints. This formulation captures a wide range of applications including online linear programming and network revenue management, among others. In this paper, we consider two settings:(i) a data-driven setting where the true distribution is unknown but a prior estimate (possibly inaccurate) is available; (ii) an uninformative setting where the true distribution is completely unknown. We propose a unified Wasserstein-distance based measure to quantify the inaccuracy of the prior estimate in setting (i) and the non-stationarity of the system in setting (ii). We show that the proposed measure leads to a necessary and sufficient condition for the attainability of a sublinear regret in both settings. For setting (i), we propose an informative gradient descent algorithm. The algorithm takes a primal-dual perspective and it integrates the prior information of the underlying distributions into an online gradient descent procedure in the dual space. The algorithm also naturally extends to the uninformative setting (ii). Under both settings, we show the corresponding algorithm achieves a regret of optimal order. In numerical experiments, we demonstrate how the proposed algorithms can be naturally integrated with the re-solving technique to further boost the empirical performance.

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Section: Main Results and Contributionsmentioning

confidence: 99%

Online Stochastic Optimization with Wasserstein Based Non-stationarity

Jiashuo¹,

Li²,

Zhang³

2020

Preprint

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“…We note that the expected-instance relaxations have been adopted successfully in several other problems to obtain a bound on an integer program [10,13,20,40]. Here, we aim to construct a scheduling algorithm that obtains a total reward close to the optimal value of EI(T), which implies an approximation to RI(T) due to Lemma 1.…”

Section: Proof Of Theorem 1 For Algorithmmentioning

confidence: 99%

Online scheduling and routing with end-to-end deadline constraints in multihop wireless networks

Tsanikidis

Ghaderi

2022

Proceedings of the Twenty-Third International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Netw

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Scheduling packets with end-to-end deadline constraints in multihop networks is an important problem that has been notoriously difficult to tackle. Recently, there has been progress on this problem in the worst-case traffic setting, with the objective of maximizing the number of packets delivered within their deadlines. Specifically, the proposed algorithms were shown to achieve Ω(1/log(𝐿)) fraction of the optimal objective value if the minimum link capacity in the network is C min = Ω(log(𝐿)), where 𝐿 is the maximum length of a packet's route in the network (which is bounded by the packet's maximum deadline). However, such guarantees can be quite pessimistic due to the strict worst-case traffic assumption and may not accurately reflect real-world settings. In this work, we aim to address this limitation by exploring whether it is possible to design algorithms that achieve a constant fraction of the optimal value while relaxing the worst-case traffic assumption. We provide a positive answer by demonstrating that in stochastic traffic settings, such as i.i.d. packet arrivals, near-optimal, (1 − 𝜖)-approximation algorithms can be designed if C min = Ω log(𝐿/𝜖 ) 𝜖 2. To the best of our knowledge, this is the first result that shows this problem can be solved near-optimally under nontrivial assumptions on traffic and link capacity. We further present extended simulations using real network traces with non-stationary traffic, which demonstrate that our algorithms outperform worst-case-based algorithms in practical settings.

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“…Their regrets are proved to be bounded by O( √ n), O( √ n log n), and O(log n log log n) respectively. Recent developments based on Li and Ye (2021) include Balseiro et al (2022), Sun et al (2020), and Chen et al (2021) that improve revenue management by adopting the dual-policy based algorithms; Jiang and Zhang (2020) that discusses the performance when the resource capacity does not scale up linearly with n; and Kerimov et al (2020) that improves the matching problem in the discrete form, widely applied in kidney exchange platforms and carpooling platforms. Hence, suppose we can further generalize the results for those three algorithms, we may find a handful of promising applications.…”

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confidence: 99%

Online Regenerative Learning

Shen¹

2022

Preprint

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We study a type of Online Linear Programming (OLP) problem that maximizes the objective function with stochastic inputs. The performance of various algorithms that analyze this type of OLP is well studied when the stochastic inputs follow some i.i.d distribution. The two central questions to ask are: (i) can the algorithms achieve the same efficiency if the stochastic inputs are not i.i.d but still stationary, and (ii) how can we modify our algorithms if we know the stochastic inputs are trendy, hence not stationary. We answer the first question by analyzing a regenerative type of input and show the regrets of two popular algorithms are bounded by the same orders as their i.i.d counterparts. We discuss the second question in the context of linearly growing inputs and propose a trend-adaptive algorithm. We provide numerical simulations to illustrate the performance of our algorithms under both regenerative and trendy inputs.

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Near-Optimal Primal-Dual Algorithms for Quantity-Based Network Revenue Management

Cited by 5 publications

References 21 publications

Online Stochastic Optimization with Wasserstein Based Non-stationarity

Online Stochastic Optimization with Wasserstein Based Non-stationarity

Online scheduling and routing with end-to-end deadline constraints in multihop wireless networks

Online Regenerative Learning

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