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Optimization of decision problems in stochastic environments is usually concerned with maximizing the probability of achieving the goal and minimizing the expected episode length. For interacting agents in time-critical applications,…
One of the most fundamental problems in Markov decision processes is analysis and control synthesis for safety and reachability specifications. We consider the stochastic reach-avoid problem, in which the objective is to synthesize a…
The performance of standard stochastic approximation implementations can vary significantly based on the choice of the steplength sequence, and in general, little guidance is provided about good choices. Motivated by this gap, in the first…
It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…
Many stochastic optimization problems include chance constraints that enforce constraint satisfaction with a specific probability; however, solving an optimization problem with chance constraints assumes that the solver has access to the…
In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center…
We propose a robust optimization approach for constructing confidence bands for stochastic processes using a finite number of simulated sample paths. Our approach can be used to quantify uncertainty in realizations of stochastic processes…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…
Stochastic process discovery is concerned with deriving a model capable of reproducing the stochastic character of observed executions of a given process, stored in a log. This leads to an optimisation problem in which the model's parameter…
Given data generated by an observable stochastic process, we study how to construct statistically optimal decisions for general stochastic optimization problems. Our setting encompasses non-standard data structures, including data…
This paper is a study on solutions of the Sample Average Approximation Method to solve compound stochastic programs. We derive nonasymptotic upper estimates for probabilities of the approximation errors. The results depend on the sample…
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…
While Robust Model Predictive Control considers the worst-case system uncertainty, Stochastic Model Predictive Control, using chance constraints, provides less conservative solutions by allowing a certain constraint violation probability…
This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of…
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…
Scenario reduction algorithms can be an effective means to provide a tractable description of the uncertainty in optimal control problems. However, they might significantly compromise the performance of the controlled system. In this paper,…
The analysis of computer models can be aided by the construction of surrogate models, or emulators, that statistically model the numerical computer model. Increasingly, computer models are becoming stochastic, yielding different outputs…