Brown Bag Seminar: Costly acquisition of observations in decision making

Abstract: In resource-constrained environments where frequent sampling can be expensive or impractical, a trade off between cost and observations occurs in the decision making process. We incorporate this aspect within the mathematical modelling of single agent optimisation problems as well as non-cooperative games, with the latter modelled by a mean-field game (MFG). To obtain optimal policies for a single agent, we propose an algorithm based on a penalty scheme to avoid numerical instabilities. To compute an approximate Nash equilibrium for the MFG, we employ entropy regularisation to demonstrate a contraction result for an iterative scheme. We then conclude with some simple numerical experiments.

In resource-constrained environments where frequent sampling can be expensive or impractical, a trade off between cost and observations occurs in the decision making process. We incorporate this aspect within the mathematical modelling of single agent optimisation problems as well as non-cooperative games, with the latter modelled by a mean-field game (MFG). To obtain optimal policies for a single agent, we propose an algorithm based on a penalty scheme to avoid numerical instabilities. To compute an approximate Nash equilibrium for the MFG, we employ entropy regularisation to demonstrate a contraction result for an iterative scheme. We then conclude with some simple numerical experiments.