Preference Ambiguity Averse Decision Making Using Robust Optimization and Sensitivity Analysis

In this work, we study decision making with personalized stochastic optimization models. The methods, we propose, develop custom-tailored stochastic optimization models for a specific decision maker, while preserving the robustness of an optimal decision as expressions of the decision maker’s attitude towards ambiguity. We present an optimization model using a novel robust preference relationship — reference-based almost stochastic dominance (RSD). We use decision maker’s utility function as a reference to individualize constraints of stochastic dominance. The concept of RSD addresses the two problems in utility-based decision making: (i) ambiguity and inaccuracy in characterizing the decision maker’s individual risk attitude, (ii) over-conservativeness of stochastic dominance representing general properties of risk aversion. The RSD rule reveals the maximum dominance level quantifying the robustness of the decision maker’s preference between alternative choices. We develop an approximation model using Bernstein polynomials, show the asymptotic convergence of its optimal value and set of optimal solutions to the true counterparts as the degree of Bernstein polynomials increases, and analyze the convergence rate of its feasible region. We next develop a cut-generation algorithm to solve the approximation model. Finally, we further adapt this cut-generation algorithm to seek a valid option most robustly preferable to a random benchmark. The effectiveness and computational complexity of the model are illustrated using a portfolio optimization problem. We study the sensitivity of the personalized stochastic optimization models with regards to risk entangled with the decision maker’s ambiguous preference itself. We present a bi-objective stochastic optimization model —expected utility and sensitivity-averse maximization (ESM), incorporating classical risk-aversion and sensitivity analysis with regards to decision maker’s preference. Unlike classical sensitivity analysis approaches which are post-analyses after optimization, ESM incorporates sensitivity analysis in the optimization procedure in terms of the second objective function. It thus allows to produce solutions which are both risk-averse in the classical sense and sensitivity-averse with regards to ambiguity in the decision maker’s preference. ESM adapts the sensitivity measure (SMU) from the general Bayesian sensitivity analysis to build connection between classical expected utility maximization and the sensitivity aversion. We develop two solution methods of ESM. A mixed-integer reformulation is given for a preference maximizer decision maker, while a linear programming reformulation for a risk-averse decision maker. The effect of ESM is illustrated using a homeland security budget allocation problem.Ph.D.Industrial and Systems Engineering, College of Engineering & Computer ScienceUniversity of Michigan-Dearbornhttp://deepblue.lib.umich.edu/bitstream/2027.42/168149/1/Gevorg Stepanyan Final Dissertation.pdfDescription of Gevorg Stepanyan Final Dissertation.pdf : Dissertatio

Foraging as an evidence accumulation process

A canonical foraging task is the patch-leaving problem, in which a forager must decide to leave a current resource in search for another. Theoretical work has derived optimal strategies for when to leave a patch, and experiments have tested for conditions where animals do or do not follow an optimal strategy. Nevertheless, models of patch-leaving decisions do not consider the imperfect and noisy sampling process through which an animal gathers information, and how this process is constrained by neurobiological mechanisms. In this theoretical study, we formulate an evidence accumulation model of patch-leaving decisions where the animal averages over noisy measurements to estimate the state of the current patch and the overall environment. Evidence accumulation models belong to the class of drift diffusion processes and have been used to model decision making in different contexts. We solve the model for conditions where foraging decisions are optimal and equivalent to the marginal value theorem, and perform simulations to analyze deviations from optimal when these conditions are not met. By adjusting the drift rate and decision threshold, the model can represent different strategies, for example an increment-decrement or counting strategy. These strategies yield identical decisions in the limiting case but differ in how patch residence times adapt when the foraging environment is uncertain. To account for sub-optimal decisions, we introduce an energy-dependent utility function that predicts longer than optimal patch residence times when food is plentiful. Our model provides a quantitative connection between ecological models of foraging behavior and evidence accumulation models of decision making. Moreover, it provides a theoretical framework for potential experiments which seek to identify neural circuits underlying patch leaving decisions

Environmental public good provision under robust decision making

We study public good provision in a two-country dynamic setup with environmental externalities. In this framework, we examine robust decision making under potential misspecification of the process that describes the evolution of the environmental public good. Robust policies, arising from fear of model misspecification, help to correct for the inefficiencies associated with free riding and thus increase the provision of the public good. As a result, there can be welfare gains from robust policies even when the fear of model misspecification proves to be unfounded

Structuring Decisions Under Deep Uncertainty

Innovative research on decision making under ‘deep uncertainty’ is underway in applied fields such as engineering and operational research, largely outside the view of normative theorists grounded in decision theory. Applied methods and tools for decision support under deep uncertainty go beyond standard decision theory in the attention that they give to the structuring of decisions. Decision structuring is an important part of a broader philosophy of managing uncertainty in decision making, and normative decision theorists can both learn from, and contribute to, the growing deep uncertainty decision support literature