Related papers: A Note on Piecewise Affine Decision Rules for Robu…
This paper addresses the question of whether it can be beneficial for an optimization algorithm to follow directions of negative curvature. Although prior work has established convergence results for algorithms that integrate both descent…
To integrate strategic, tactical and operational decisions, the two-stage optimization has been widely used to guide dynamic decision making. In this paper, we study the two-stage stochastic programming for complex systems with unknown…
This research considers the ranking and selection with input uncertainty. The objective is to maximize the posterior probability of correctly selecting the best alternative under a fixed simulation budget, where each alternative is measured…
We consider the problem of analyzing the probabilistic performance of first-order methods when solving convex optimization problems drawn from an unknown distribution only accessible through samples. By combining performance estimation…
A data-driven MPC scheme is proposed to safely control constrained stochastic linear systems using distributionally robust optimization. Distributionally robust constraints based on the Wasserstein metric are imposed to bound the state…
We consider a two-stage distributionally robust optimization (DRO) model with multimodal uncertainty, where both the mode probabilities and uncertainty distributions could be affected by the first-stage decisions. To address this setting,…
This paper presents a novel distributed robust optimization scheme for steering distributions of multi-agent systems under stochastic and deterministic uncertainty. Robust optimization is a subfield of optimization which aims to discover an…
Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein…
We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local,…
This paper studies a data-driven predictive control for a class of control-affine systems which is subject to uncertainty. With the accessibility to finite sample measurements of the uncertain variables, we aim to find controls which are…
In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…
It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…
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…
We study the problem of minimizing a strongly convex, smooth function when we have noisy estimates of its gradient. We propose a novel multistage accelerated algorithm that is universally optimal in the sense that it achieves the optimal…
Complex systems display variability over a broad range of spatial and temporal scales. Some scales are unresolved due to computational limitations. The impact of these unresolved scales on the resolved scales needs to be parameterized or…
We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…
We consider a general online stochastic optimization problem with multiple budget constraints over a horizon of finite time periods. In each time period, a reward function and multiple cost functions are revealed, and the decision maker…
In this paper, we show the optimality of a certain class of disturbance-affine control policies in the context of one-dimensional, constrained, multi-stage robust optimization. Our results cover the finite horizon case, with minimax…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…
Policy optimization methods have shown great promise in solving complex reinforcement and imitation learning tasks. While model-free methods are broadly applicable, they often require many samples to optimize complex policies. Model-based…