From Moderate Deviations Theory To Distributionally Robust Optimization Correlated Data

(PDF) Distributionally Robust Optimization With Correlated Data From Vector Autoregressive Processes

(PDF) Distributionally Robust Optimization With Correlated Data From Vector Autoregressive Processes We aim to learn a performance function of the invariant state distribution of an unknown linear dynamical system based on a single trajectory of correlated state observations. the function to be learned may represent, for example, an identification objective or a value function. Full title: from moderate deviations theory to distributionally robust optimization: learning from correlated dataabstract: we aim to learn a performance fun.

Distributionally Robust Optimization With Probabilistic Group | DeepAI

Distributionally Robust Optimization With Probabilistic Group | DeepAI By leveraging sanov's theorem from large deviations theory, we prove that the meta optimization problem admits a unique optimal solution for any given stochastic program. We study stochastic programs where the decision maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. Using the empirical distribution f n as a surrogate for f would overfit the data, especially when we have very few samples. one way to overcome the uncertainty attached to the probability density f itself is to investigate distributionally robust stochastic optimization (drso). To our best knowledge, we are the first to recognize the optimality of distributionally robust optimization in its ability to transform data to predictors and prescriptors.

(PDF) Wasserstein Distributionally Robust Optimization: Theory And Applications In Machine Learning

(PDF) Wasserstein Distributionally Robust Optimization: Theory And Applications In Machine Learning Using the empirical distribution f n as a surrogate for f would overfit the data, especially when we have very few samples. one way to overcome the uncertainty attached to the probability density f itself is to investigate distributionally robust stochastic optimization (drso). To our best knowledge, we are the first to recognize the optimality of distributionally robust optimization in its ability to transform data to predictors and prescriptors. We apply the general framework by sutter et al. (2020), which uses ideas from large deviations theory to construct statistically optimal data driven dro models, to decision problems where the training data is generated by a time homogeneous, ergodic finite state markov chain. We propose a data driven distributionally robust optimization model to estimate the problem's objective function and optimal solution. by leveraging results from large deviations theory, we derive statistical guarantees on the quality of these estimators. From moderate deviations theory to distributionally robust optimization: learning from correlated data we aim to learn a performance function of the invariant state distribution of an unknown linear dynamical system based on a single trajectory of correlated state observations. We study stochastic programs where the decision maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution.

From Moderate Deviations Theory to Distributionally Robust Optimization: Correlated Data