Making Online Decisions with Bounded Memory

  • Chi-Jen Lu
  • Wei-Fu Lu
Conference paper

DOI: 10.1007/978-3-642-24412-4_21

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6925)
Cite this paper as:
Lu CJ., Lu WF. (2011) Making Online Decisions with Bounded Memory. In: Kivinen J., Szepesvári C., Ukkonen E., Zeugmann T. (eds) Algorithmic Learning Theory. ALT 2011. Lecture Notes in Computer Science, vol 6925. Springer, Berlin, Heidelberg

Abstract

We study the online decision problem in which there are T steps to play and n actions to choose. For this problem, several algorithms achieve an optimal regret of \(O(\sqrt{T \ln n})\), but they all require about Tn states, which one may not be able to afford when n and T are very large. We are interested in such large scale problems, and we would like to understand what an online algorithm can achieve with only a bounded number of states. We provide two algorithms, both with mn − 1 states, for a parameter m, which achieve regret of O(m + (T/m)ln (mn)) and \(O(n \sqrt{m} +T/\sqrt{m})\), respectively. We also show that any online algorithm with mn − 1 states must suffer a regret of Ω(T/m), which is close to what our algorithms achieve.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Chi-Jen Lu
    • 1
  • Wei-Fu Lu
    • 2
  1. 1.Institute of Information ScienceAcademia SinicaTaipeiTaiwan
  2. 2.Department of Computer Science and Information EngineeringAsia UniversityTaiwan

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