Month: August 2004

A fictitious play approach to large-scale optimization

  • Marina A. Epelman
  • Theodore Lambert
  • Robert L. Smith
    • Categories Game Theory, Optimization of Simulated Systems Tags ,

    In this paper we investigate the properties of the sampled version of the fictitious play algorithm, familiar from game theory, for games with identical payoffs, and propose a heuristic based on fictitious play as a solution procedure for discrete optimization problems of the form $\max\{u(y):y=(y^1,\ldots,y^n)\in\setY^1\times\cdots\times\setY^n\}$, i.e., in which the feasible region is a Cartesian product … Read more

    Aggregation in Stochastic Dynamic Programming

  • Marina A. Epelman
  • Theodore Lambert
  • Robert L. Smith
    • Categories Dynamic Programming Tags , ,

    We present a general aggregation method applicable to all finite-horizon Markov decision problems. States of the MDP are aggregated into macro-states based on a pre-selected collection of “distinguished” states which serve as entry points into macro-states. The resulting macro-problem is also an MDP, whose solution approximates an optimal solution to the original problem. The aggregation … Read more