08:45 AM - 09:10 AM
Developing robust solutions via preference robust optimization
We present the latest framework of preference robust optimization that can be used to generate robust solutions while only partial information about risk preference is available. This resolves to a great extent the issue of risk underestimation due to an incorrect assumption of one's preference system, which has not been well addressed in the setting of robust optimization. Our framework allows ones to specify their preference systems qualitatively using terms from risk axioms and comparisons between risky payoffs. We show how preference robust optimization problems can be solved as convex programs, and demonstrate the value of robust solutions in the context of portfolio selection.
09:10 AM - 09:35 AM
The Wasserstein metric and the distributionally robust TSP
Recent research on the robust and stochastic Euclidean travelling salesman problem has seen many different approaches for describing the region of uncertainty, such as taking convex combinations of observed demand vectors or imposing constraints on the moments of the spatial demand distribution. In this paper, we consider a distributionally robust version of the Euclidean travelling salesman problem in which we compute the worst-case spatial distribution of demand against all distributions whose Wasserstein distance to an observed demand distribution is bounded from above. This constraint allows us to circumvent common overestimation that arises when other procedures are used.
09:35 AM - 10:00 AM
"Dice"-sion Making under Uncertainty: When Can a Random Decision Reduce Risk?
Consider an Ellsberg experiment in which one can win by calling the color (red or blue) of the ball that will be drawn from an urn in which the two colored balls are of unknown proportions. It is actually well known (yet rarely advertised) that delegating the selection of the color to a fair sided coin can completely eradicate the ambiguity about the odds of winning hence has the potential of reducing the amount of perceived risk. In this talk, we explore what are conditions under which a decision maker that employs a risk measure should have his action depend on the outcome of a random device such as a coin or a dice. We find that in the absence of distributional ambiguity, deterministic decisions are optimal if both the risk measure and the feasible region are convex, or alternatively if the risk measure is mixture-quasiconcave. Several classes of risk measures, such as mean (semi-)deviation and mean (semi-)moment measures, fail to be mixture-quasiconcave and can therefore give rise to problems in which the decision maker might benefit from a randomizated policy. Under distributional ambiguity, on the other hand, we show that for any ambiguity averse risk measure there always exists a decision problem (with a non-convex, e.g., mixed-integer, feasible region) in which a randomized decision strictly dominates all deterministic decisions. This is joint work with D. Kuhn and W. Wiesemann.