| الملخص: |
Abstract: In batch policy evaluation the goal is to predict the value of a policy given some historical data. A specific example, which motivated the approach pursued in this thesis, is to predict the probability of putting a natural wildfire out given some specific configuration of dispatched resources, such as helicopters, planes, trucks, and firefighters of various kinds. The general structure of problems like this is that the more resources are deployed, the higher success rate we expect to see: the response is a monotone function of the resources dispatched. In this thesis, we investigate the question of what are the best ways of estimating success probabilities of policies in problems that exhibit such a monotone structure. In particular, viewing the problem as a multiobjective optimization problem where the optimization variables are parameters describing the estimators and the objectives correspond to different problem-instances (in the wildfire application these correspond to different conditions under which the fire may happen), we propose various ways of optimizing estimation accuracy. More specifically, when resource levels are discrete and one-dimensional (or totally ordered) and focusing on minimum variance point estimation and unbiased estimators, it is found that natural optimization objectives lead to convex optimization problems that can be solved efficiently. One of the main contributions of the thesis is the careful experimental comparison of the various optimization objectives with Monte-Carlo simulations. As a second main contribution, a similar investigation is carried out for comparing alternative strategies that produce interval estimates. |
