Related papers: Mathematical Foundations of Distributionally Robus…
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
This paper addresses risk awareness of stochastic optimization problems. Nested risk measures appear naturally in this context, as they allow beneficial reformulations for algorithmic treatments. The reformulations presented extend usual…
Real-world applications require RL algorithms to act safely. During learning process, it is likely that the agent executes sub-optimal actions that may lead to unsafe/poor states of the system. Exploration is particularly brittle in…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
We introduce the concept of a risk form, which is a real functional of two arguments: a measurable function on a Polish space and a measure on that space. We generalize the duality theory and the Kusuoka representation to this setting. For…
We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the…
The distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust policy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we…
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of…
Nested simulation is a natural approach to tackle nested estimation problems in operations research and financial engineering. The outer-level simulation generates outer scenarios and the inner-level simulations are run in each outer…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
We consider nonlinear multistage stochastic optimization problems in the spaces of integrable functions. We allow for nonlinear dynamics and general objective functionals, including dynamic risk measures. We study causal operators…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
In performative prediction, the choice of a model influences the distribution of future data, typically through actions taken based on the model's predictions. We initiate the study of stochastic optimization for performative prediction.…
Performative prediction aims to model scenarios where predictive outcomes subsequently influence the very systems they target. The pursuit of a performative optimum (PO) -- minimizing performative risk -- is generally reliant on modeling of…
We study multistage distributionally robust optimization (DRO) to hedge against ambiguity in quantifying the underlying uncertainty of a problem. Recognizing that not all the realizations and scenario paths might have an "effect" on the…
An integration of distributionally robust risk allocation into sampling-based motion planning algorithms for robots operating in uncertain environments is proposed. We perform non-uniform risk allocation by decomposing the distributionally…
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes…
We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…
In this work we propose deep learning-based algorithms for the computation of systemic shortfall risk measures defined via multivariate utility functions. We discuss the key related theoretical aspects, with a particular focus on the…