Grant: Discovery Grants Program - Individual

This research proposal is in the field of decision making under uncertainty. More specifically we focus on improving the decision making in adversarial, stochastic and/or partially observable situations. Decision policies heavily depend on the quality of the evaluation of the cost function, which is the main source of uncertainty. In these problems, the actual limitation often lies in the approximation of cost which is typically discontinuous, non-convex, stochastic and time-consuming to compute (it is difficult to evaluate due to a limited ability to predict the future of all possible events.). In most problems the actual challenge is often more about being able to compute a ``good`` approximation of the cost value rather than making the decision itself. Given that values are approximated, computing regret between two uncertain values can be misleading. The assumption underlying this project is that both the approximation of the cost and the decision policy are intertwined. The more reliable the information gathered from the cost function, the more trivial the decision policy becomes for practitioners. The opposite is also true. If the information is unreliable, the best decision can be impossible to identify. One consequence of the previous statement is that as the information becomes less reliable, minimizing regret rather than cost could be a better idea. The link between the quality of the approximation and the specific decision policy to use is intuitive yet remain relatively unexplored. Our research program focusses on the impact of the approximation of the cost function on decision making under uncertainties. Considering the importance of making good decisions in an uncertain environment, the long term goal of this proposal is to provide an adversarial decision making platform that will vastly improve decision making processes for companies and researchers by studying the link between the bias induced from the approximation of a cost function and its impact on different decision policies. More specifically, we will first (1) evaluate the impact of different cost functions (discontinuous, non-convex, stochastic, time-consuming, etc.) on existing decision policies that require an adversarial decision. Second, we will (2) improve and create new decision policies. Third, we will (3) study the interaction between the approximation of the cost function and decision policies. The current litterature considers the approximation of the cost function independently from the decision policy. The decision policy is an initial assumption that cannot change. This proposal intends to show that, depending on the quality of the approximation cost function, the decision policy may differ.