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Competitive Online Optimization under Inventory Constraints

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Published:26 March 2019Publication History
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Abstract

This paper studies online optimization under inventory (budget) constraints. While online optimization is a well-studied topic, versions with inventory constraints have proven difficult. We consider a formulation of inventory-constrained optimization that is a generalization of the classic one-way trading problem and has a wide range of applications. We present a new algorithmic framework, \textsfCR-Pursuit, and prove that it achieves the minimal competitive ratio among all deterministic algorithms (up to a problem-dependent constant factor) for inventory-constrained online optimization. Our algorithm and its analysis not only simplify and unify the state-of-the-art results for the standard one-way trading problem, but they also establish novel bounds for generalizations including concave revenue functions. For example, for one-way trading with price elasticity, the \textsfCR-Pursuit algorithm achieves a competitive ratio that is within a small additive constant (i.e., 1/3) to the lower bound of ln 0+1, where 0 is the ratio between the maximum and minimum base prices.

References

  1. Jacob D Abernethy, Elad Hazan, and Alexander Rakhlin. 2009. Competing in the dark: An efficient algorithm for bandit linear optimization. (2009).Google ScholarGoogle Scholar
  2. H. Akhavan-Hejazi and H. Mohsenian-Rad. 2014. Optimal Operation of Independent Storage Systems in Energy and Reserve Markets With High Wind Penetration. IEEE Transactions on Smart Grid , Vol. 5, 2 (March 2014), 1088--1097.Google ScholarGoogle ScholarCross RefCross Ref
  3. Susanne Albers. 2003. Online algorithms: a survey. Mathematical Programming , Vol. 97, 1--2 (2003), 3--26.Google ScholarGoogle ScholarCross RefCross Ref
  4. Lachlan Andrew, Siddharth Barman, Katrina Ligett, Minghong Lin, Adam Meyerson, Alan Roytman, and Adam Wierman. 2013. A tale of two metrics: Simultaneous bounds on competitiveness and regret. In Conference on Learning Theory. 741--763.Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Antonios Antoniadis, Neal Barcelo, Michael Nugent, Kirk Pruhs, Kevin Schewior, and Michele Scquizzato. 2016. Chasing convex bodies and functions. In Latin American Symposium on Theoretical Informatics. Springer, 68--81.Google ScholarGoogle ScholarCross RefCross Ref
  6. Sanjeev Arora, Elad Hazan, and Satyen Kale. 2012. The Multiplicative Weights Update Method: a Meta-Algorithm and Applications. Theory of Computing , Vol. 8, 1 (2012), 121--164.Google ScholarGoogle ScholarCross RefCross Ref
  7. Peter Auer, Nicolo Cesa-Bianchi, Yoav Freund, and Robert E Schapire. 1995. Gambling in a rigged casino: The adversarial multi-armed bandit problem. In IEEE FOCS . 322. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Yossi Azar, Niv Buchbinder, Hubert Chan, Shahar Chen, Ilan Reuven Cohen, Anupam Gupta, Zhiyi Huang, Ning Kang, Viswanath Nagarajan, Joseph Naor, and Debmalya Panigrahi. 2016. Online Algorithms for Covering and Packing Problems with Convex Objectives. In 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) . 148--157.Google ScholarGoogle Scholar
  9. Moshe Babaioff, Nicole Immorlica, David Kempe, and Robert Kleinberg. 2008. Online auctions and generalized secretary problems. ACM SIGecom Exchanges , Vol. 7, 2 (2008). Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Nikhil Bansa, Martin Böhm, Marek Eliávs , Grigorios Koumoutsos, and Seeun William Umboh. 2018. Nested convex bodies are chaseable. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms. 1253--1260. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Nikhil Bansal, Niv Buchbinder, and Joseph Seffi Naor. 2012. A primal-dual randomized algorithm for weighted paging. Journal of the ACM (JACM) , Vol. 59, 4 (2012). Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Nikhil Bansal, Anupam Gupta, Ravishankar Krishnaswamy, Kirk Pruhs, Kevin Schewior, and Cliff Stein. 2015. A 2-competitive algorithm for online convex optimization with switching costs. In LIPIcs-Leibniz International Proceedings in Informatics , Vol. 40. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.Google ScholarGoogle Scholar
  13. H. Bogucka, M. Parzy, P. Marques, J. W. Mwangoka, and T. Forde. 2012. Secondary spectrum trading in TV white spaces. IEEE Communications Magazine , Vol. 50, 11 (November 2012), 121--129.Google ScholarGoogle ScholarCross RefCross Ref
  14. Allan Borodin, Nathan Linial, and Michael E Saks. 1992. An optimal on-line algorithm for metrical task system. Journal of the ACM (JACM) , Vol. 39, 4 (1992), 745--763. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Sébastien Bubeck, Nicolo Cesa-Bianchi, et almbox. 2012. Regret analysis of stochastic and nonstochastic multi-armed bandit problems. Foundations and Trends® in Machine Learning , Vol. 5, 1 (2012), 1--122.Google ScholarGoogle ScholarCross RefCross Ref
  16. Niv Buchbinder and Joseph Naor. 2005. Online primal-dual algorithms for covering and packing problems. In European Symposium on Algorithms. Springer, 689--701. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Niv Buchbinder, Joseph Seffi Naor, et almbox. 2009. The design of competitive online algorithms via a primal--dual approach. Foundations and Trends® in Theoretical Computer Science , Vol. 3, 2--3 (2009), 93--263. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Niangjun Chen, Anish Agarwal, Adam Wierman, Siddharth Barman, and Lachlan LH Andrew. 2015. Online convex optimization using predictions. In ACM SIGMETRICS Performance Evaluation Review , Vol. 43. 191--204. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Francis YL Chin, Bin Fu, Jiuling Guo, Shuguang Han, Jueliang Hu, Minghui Jiang, Guohui Lin, Hing-Fung Ting, Luping Zhang, Yong Zhang, et almbox. 2015. Competitive algorithms for unbounded one-way trading. Theoretical Computer Science , Vol. 607 (2015), 35--48. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. YS Chow, Sigaiti Moriguti, Herbert Robbins, and SM Samuels. 1964. Optimal selection based on relative rank (the "secretary problem"). Israel Journal of mathematics , Vol. 2, 2 (1964), 81--90.Google ScholarGoogle Scholar
  21. Peter Damaschke, Phuong Hoai Ha, and Philippas Tsigas. 2009. Online search with time-varying price bounds. Algorithmica , Vol. 55, 4 (2009), 619--642. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Nikhil R. Devanur and Kamal Jain. 2012. Online Matching with Concave Returns. In Proceedings of the Forty-fourth Annual ACM Symposium on Theory of Computing (STOC '12). ACM, 137--144. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Ran El-Yaniv, Amos Fiat, Richard M Karp, and Gordon Turpin. 2001. Optimal search and one-way trading online algorithms. Algorithmica , Vol. 30, 1 (2001), 101--139.Google ScholarGoogle ScholarCross RefCross Ref
  24. Moran Feldman and Rico Zenklusen. 2018. The submodular secretary problem goes linear. SIAM J. Comput. , Vol. 47, 2 (2018), 330--366.Google ScholarGoogle ScholarCross RefCross Ref
  25. Amos Fiat. 1998. Online Algorithms: The State of the Art (Lecture Notes in Computer Science). (1998). Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Amos Fiat and Manor Mendel. 2003. Better algorithms for unfair metrical task systems and applications. SIAM J. Comput. , Vol. 32, 6 (2003), 1403--1422. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. Amos Fiat, Yuval Rabani, and Yiftach Ravid. 1990. Competitive k-server algorithms. (1990).Google ScholarGoogle Scholar
  28. Joel Friedman and Nathan Linial. 1993. On convex body chasing. Discrete & Computational Geometry , Vol. 9, 3 (1993), 293--321. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Hiroshi Fujiwara, Kazuo Iwama, and Yoshiyuki Sekiguchi. 2011. Average-case competitive analyses for one-way trading. Journal of Combinatorial Optimization , Vol. 21, 1 (2011), 83--107. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Edward F Grove. 1991. The harmonic online k-server algorithm is competitive. In Proceedings of the twenty-third annual ACM symposium on Theory of computing. 260--266. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. Linqi Guo, John Pang, and Anwar Walid. {n. d.}. Dynamic service function chaining in SDN-enabled networks with middleboxes. In 2016 IEEE 24th International Conference on Network Protocols (ICNP) . 1--10.Google ScholarGoogle Scholar
  32. Linqi Guo, John Pang, and Anwar Walid. 2018. Joint Placement and Routing of Network Function Chains in Data Centers. In IEEE INFOCOM . 612--620.Google ScholarGoogle Scholar
  33. Mohammad Taghi Hajiaghayi, Robert Kleinberg, and Tuomas Sandholm. 2007. Automated online mechanism design and prophet inequalities. In AAAI, Vol. 7. 58--65. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Elad Hazan, Amit Agarwal, and Satyen Kale. 2007. Logarithmic regret algorithms for online convex optimization. Machine Learning , Vol. 69, 2--3 (2007), 169--192. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. Sham M Kakade, Michael Kearns, Yishay Mansour, and Luis E Ortiz. 2004. Competitive algorithms for VWAP and limit order trading. In Proceedings of ACM EC . 189--198. Google ScholarGoogle ScholarDigital LibraryDigital Library
  36. Anna R Karlin, Mark S Manasse, Larry Rudolph, and Daniel D Sleator. 1988. Competitive snoopy caching. Algorithmica , Vol. 3, 1--4 (1988), 79--119. Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. Jiayin Li, Meikang Qiu, Zhong Ming, Gang Quan, Xiao Qin, and Zonghua Gu. 2012. Online optimization for scheduling preemptable tasks on IaaS cloud systems. J. Parallel and Distrib. Comput. , Vol. 72, 5 (2012), 666--677. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. Yingying Li, Guannan Qu, and Na Li. 2018. Using Predictions in Online Optimization with Switching Costs: A Fast Algorithm and A Fundamental Limit. In IEEE Annual American Control Conference (ACC) . 3008--3013.Google ScholarGoogle Scholar
  39. Minghong Lin, Adam Wierman, Lachlan LH Andrew, and Eno Thereska. 2013. Dynamic right-sizing for power-proportional data centers. IEEE/ACM Transactions on Networking (TON) , Vol. 21, 5 (2013), 1378--1391. Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. Minghong Lin, Adam Wierman, Alan Roytman, Adam Meyerson, and Lachlan LH Andrew. 2012. Online optimization with switching cost. ACM SIGMETRICS Performance Evaluation Review , Vol. 40, 3 (2012), 98--100. Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. Julian Lorenz, Konstantinos Panagiotou, and Angelika Steger. 2009. Optimal algorithms for k-search with application in option pricing. Algorithmica , Vol. 55, 2 (2009), 311--328. Google ScholarGoogle ScholarDigital LibraryDigital Library
  42. Lian Lu, Jinlong Tu, Chi-Kin Chau, Minghua Chen, and Xiaojun Lin. 2013b. Online Energy Generation Scheduling for Microgrids with Intermittent Energy Sources and Co-Generation. Proceedings of ACM Sigmetrics (2013). Google ScholarGoogle ScholarDigital LibraryDigital Library
  43. Tan Lu, Minghua Chen, and Lachlan LH Andrew. 2013a. Simple and effective dynamic provisioning for power-proportional data centers. IEEE Transactions on Parallel and Distributed Systems , Vol. 24, 6 (2013), 1161--1171. Google ScholarGoogle ScholarDigital LibraryDigital Library
  44. Jacob Mattingley, Yang Wang, and Stephen Boyd. 2011. Receding horizon control. IEEE Control Systems , Vol. 31, 3 (2011), 52--65.Google ScholarGoogle ScholarCross RefCross Ref
  45. Hanna Michalska and David Q Mayne. 1993. Robust receding horizon control of constrained nonlinear systems. IEEE transactions on automatic control , Vol. 38, 11 (1993), 1623--1633.Google ScholarGoogle Scholar
  46. John ZF Pang, Hu Fu, Won I Lee, and Adam Wierman. 2017a. The Efficiency of Open Access in Platforms for Networked Cournot Markets. In Proceedings of IEEE INFOCOM .Google ScholarGoogle ScholarCross RefCross Ref
  47. John ZF Pang, Linqi Guo, and Steven H Low. 2017b. Optimal load control for frequency regulation under limited control coverage. In IREP Symposium . 1--7.Google ScholarGoogle Scholar
  48. L. Qian, F. Ye, L. Gao, X. Gan, T. Chu, X. Tian, X. Wang, and M. Guizani. 2011. Spectrum Trading in Cognitive Radio Networks: An Agent-Based Model under Demand Uncertainty. IEEE Transactions on Communications , Vol. 59, 11 (November 2011), 3192--3203.Google ScholarGoogle ScholarCross RefCross Ref
  49. Xiaoqi Ren, Palma London, Juba Ziani, and Adam Wierman. 2018. Datum: Managing Data Purchasing and Data Placement in a Geo-Distributed Data Market. IEEE/ACM Transactions on Networking , Vol. 26, 2 (2018), 893--905. Google ScholarGoogle ScholarDigital LibraryDigital Library
  50. Aviad Rubinstein. 2016. Beyond matroids: Secretary problem and prophet inequality with general constraints. In Proceedings of the forty-eighth annual ACM symposium on Theory of Computing . 324--332. Google ScholarGoogle ScholarDigital LibraryDigital Library
  51. Karl H Schlag. 1998. Why imitate, and if so, how?: A boundedly rational approach to multi-armed bandits. Journal of Economic Theory , Vol. 78, 1 (1998), 130--156.Google ScholarGoogle ScholarCross RefCross Ref
  52. S. Shafiee, A. Bhuiya, A. U. Haque, H. Zareipour, and A. M. Knight. 2018. Economic Assessment of Energy Storage Systems in Alberta's Energy and Operating Reserve Markets. In 2018 IEEE/PES Transmission and Distribution Conference and Exposition . 1--5.Google ScholarGoogle Scholar
  53. Shai Shalev-Shwartz and Sham M Kakade. 2009. Mind the duality gap: Logarithmic regret algorithms for online optimization. In Advances in Neural Information Processing Systems. 1457--1464. Google ScholarGoogle ScholarDigital LibraryDigital Library
  54. Lin Yang, Mohammad H Hajiesmaili, Hanling Yi, and Minghua Chen. June 2017. Online Offering Strategies for Storage-Assisted Renewable Power Producer in Hour-Ahead Market. In Proceedings of ACM SIGMETRICS .Google ScholarGoogle Scholar
  55. Hanling Yi*, Qiulin Lin*, and Minghua Chen. 2019. Balancing Cost and Dissatisfaction in Online EV Charging under Real-time Pricing. In IEEE INFOCOM . (The first two authors contribute equally to the work.).Google ScholarGoogle Scholar
  56. Wenming Zhang, Yinfeng Xu, Feifeng Zheng, and Yucheng Dong. 2012. Optimal algorithms for online time series search and one-way trading with interrelated prices. Journal of combinatorial optimization , Vol. 23, 2 (2012), 159--166. Google ScholarGoogle ScholarDigital LibraryDigital Library
  57. Ying Zhang, Mohammad H Hajiesmaili, Sinan Cai, Minghua Chen, and Qi Zhu. 2018. Peak-aware online economic dispatching for microgrids. IEEE Transactions on Smart Grid , Vol. 9, 1 (2018), 323--335.Google ScholarGoogle ScholarCross RefCross Ref

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