Efficient Algorithms for Online Decision Problems

  • Adam Kalai
  • Santosh Vempala
Conference paper

DOI: 10.1007/978-3-540-45167-9_4

Volume 2777 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Kalai A., Vempala S. (2003) Efficient Algorithms for Online Decision Problems. In: Schölkopf B., Warmuth M.K. (eds) Learning Theory and Kernel Machines. Lecture Notes in Computer Science, vol 2777. Springer, Berlin, Heidelberg

Abstract

In an online decision problem, one makes a sequence of decisions without knowledge of the future. Tools from learning such as Weighted Majority and its many variants [4, 13, 18] demonstrate that online algorithms can perform nearly as well as the best single decision chosen in hindsight, even when there are exponentially many possible decisions. However, the naive application of these algorithms is inefficient for such large problems. For some problems with nice structure, specialized efficient solutions have been developed [3, 6, 10, 16, 17].

We show that a very simple idea, used in Hannan’s seminal 1957 paper [9], gives efficient solutions to all of these problems. Essentially, in each period, one chooses the decision that worked best in the past. To guarantee low regret, it is necessary to add randomness. Surprisingly, this simple approach gives additive ε regret per period, efficiently. We present a simple general analysis and several extensions, including a (1+ε)-competitive algorithm as well as a lazy one that rarely switches between decisions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Adam Kalai
    • 1
  • Santosh Vempala
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA