Efficient Algorithms for Minimax Decisions Under Tree-Structured Incompleteness

  • Thijs van OmmenEmail author
  • Wouter M. Koolen
  • Peter D. Grünwald
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11726)


When decisions must be based on incomplete (coarsened) observations and the coarsening mechanism is unknown, a minimax approach offers the best guarantees on the decision maker’s expected loss. Recent work has derived mathematical conditions characterizing minimax optimal decisions, but also found that computing such decisions is a difficult problem in general. This problem is equivalent to that of maximizing a certain conditional entropy expression. In this work, we present a highly efficient algorithm for the case where the coarsening mechanism can be represented by a tree, whose vertices are outcomes and whose edges are coarse observations.


Coarse data Incomplete observations Minimax decision making Maximum entropy 



This research was supported by Vici grant 639.073.04 and Veni grant 639.021.439 from the Netherlands Organization for Scientific Research (NWO).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Thijs van Ommen
    • 1
    Email author
  • Wouter M. Koolen
    • 2
  • Peter D. Grünwald
    • 2
    • 3
  1. 1.Utrecht UniversityUtrechtThe Netherlands
  2. 2.Centrum Wiskunde & InformaticaAmsterdamThe Netherlands
  3. 3.Leiden UniversityLeidenThe Netherlands

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