Decision making is the ability to select the best alternative from a set of candidates based on their respective values. When the value depends on uncertain future events, this task becomes more complicated. The question is then whether to wait for more information before making a decision or to stop and make a decision based on uncertain information. This has been addressed in previous work, when the information (events) could be represented as discrete random variables. However, there are real world domains where this assumption is incorrect. Thus, in this paper, we propose a novel framework and algorithms designed to cope with the challenge posed when future events are represented as continuous random variables. More specifically, we define a mathematical representation to model the utility functions of the candidates and introduce optimal and approximate algorithms to compute the best time to stop, and make a decision in order to optimize the utility. We evaluate our model and algorithms theoretically and empirically, and measure their performance in terms of the gain they achieve and their runtime. Our experiment demonstrates that there is no significant difference between the quality of the decision reached by the two algorithms, while the runtime of the optimal algorithm is much higher than that of the approximate algorithm.
- Continuous variables