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This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
Recently, literature on dynamic coherent risk measures has broadened the choices for risk-sensitive performance evaluation. A running example includes Cumulative prospect theory and Conditional variance at risk. Most of them can be can be…
A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…
Non-prehensile manipulation such as pushing is typically subject to uncertain, non-smooth dynamics. However, modeling the uncertainty of the dynamics typically results in intractable belief dynamics, making data-efficient planning under…
Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This…
We study robust stochastic optimization problems in the quasi-sure setting in discrete-time. The strategies in the multi-period-case are restricted to those taking values in a discrete set. The optimization problems under consideration are…
Many engineering problems have multiple objectives, and the overall aim is to optimize a non-linear function of these objectives. In this paper, we formulate the problem of maximizing a non-linear concave function of multiple long-term…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
The problem of computing near-optimal contracts in combinatorial settings has recently attracted significant interest in the computer science community. Previous work has provided a rich body of structural and algorithmic insights into this…
Real-world engineering systems are typically compared and contrasted using multiple metrics. For practical machine learning systems, performance tuning is often more nuanced than minimizing a single expected loss objective, and it may be…
This paper proposes an algorithm to calculate the maximal probability of unsafety with respect to trajectories of a stochastic process and a hazard set. The unsafe probability estimation problem is cast as a primal-dual pair of…
This article introduces a framework for evaluating statistical decisions under both prior ambiguity and likelihood misspecification. We begin with an ambiguity set - a frequentist model that pairs a possibly misspecified likelihood with…
We show that a wide class of risk-constrained nonconvex functional optimization problems exhibit strong duality, regardless of nonconvexity. We develop two novel results under distinct sets of assumptions, establishing strong duality over…
Uncertainty is a pervasive challenge in decision and risk management and it is usually studied by quantification and modeling. Interestingly, engineers and other decision makers usually manage uncertainty with strategies such as…
Selective classification (or classification with a reject option) pairs a classifier with a selection function to determine whether or not a prediction should be accepted. This framework trades off coverage (probability of accepting a…
This paper describes a novel approach to planning which takes advantage of decision theory to greatly improve robustness in an uncertain environment. We present an algorithm which computes conditional plans of maximum expected utility. This…
Nonlinear control systems with partial information to the decision maker are prevalent in a variety of applications. As a step toward studying such nonlinear systems, this work explores reinforcement learning methods for finding the optimal…
We investigate the problem of finding upper and lower bounds for a Choquet risk measure of a nonlinear function of two risk factors, when the marginal distributions of the risk factors are ambiguous and represented by nonadditive measures…
We investigate a continuous-time investment-consumption problem with model uncertainty in a general diffusion-based market with random model coefficients. We assume that a power utility investor is ambiguity-averse, with the preference to…
Consider the seller's problem of finding optimal prices for her $n$ (divisible) goods when faced with a set of $m$ consumers, given that she can only observe their purchased bundles at posted prices, i.e., revealed preferences. We study…