Efficient Algorithms for Minimax Decisions Under Tree-Structured Incompleteness

Thijs van Ommen, Wouter M. Koolen, Peter D. Grünwald

Abstract: 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.