We solve robust optimization problems using Wasserstein balls and apply it to mean-CVaR optimization.
problem Distributionally robust optimization with Wasserstein ambiguity sets.
method Transformed robust optimization into non-robust with penalty term, selecting ambiguity set size.
result Impressive results in robust mean-CVaR optimization compared to other strategies.
Robust portfolio optimization considers uncertainty in market probabilities.
problem Uncertainty in market probabilities in multiperiod portfolio selection.
method Robust mean-variance optimization using Wasserstein ball centered at empirical data.
result Numerical simulations show improved performance compared to other strategies.
This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ball is chosen judiciously, we can guarantee that it contains t…
Proposes a fair classification model using robust optimization.
problem Preventing discrimination in classification models.
method Distributionally robust logistic regression with Wasserstein ball and convex unfairness measure.
result Improves fairness with minimal loss in predictive accuracy.
A new portfolio model improves on Kelly's by accounting for estimation error.
problem Estimation error in Kelly portfolio optimization.
method Wasserstein distributionally robust optimization (DRO) to define a robust log-optimal portfolio.
result The Wasserstein-Kelly portfolio outperforms the Kelly portfolio in out-of-sample testing.
FDR-SVM improves classification robustness in federated learning with uncertain data.
problem Federated learning with uncertain and private client data.
method Develops FDR-SVM, a robust SVM approach using a mixture of Wasserstein balls ambiguity set.
result Establishes theoretical guarantees and derives algorithms with performance bounds.
Investors optimize their portfolios within a Wasserstein ball to match a benchmark's risk profile.
problem Optimizing portfolio performance while maintaining risk proximity to a benchmark.
method Optimal dynamic strategy selection based on minimizing distortion risk measures within a Wasserstein ball.
result An optimal dynamic strategy exists and can be calculated through isotonic projections.
Optimal financial strategies minimize risk under uncertain models.
problem Maximizing utility in financial markets with model uncertainty.
method Optimized strategies converge to those with minimal norm as uncertainty increases.
result Optimal strategies with minimal norm emerge as uncertainty grows.
Paper introduces robust market making using Wasserstein distance and entropy regularization.
problem Market making robustness under uncertainty.
method Wasserstein distance, entropy regularization, convex optimization, optimal radius selection.
result The robust market making problem can be reformulated as a convex optimization problem.
A risk-aware RL approach using RDEU and Wasserstein ball for robust performance.
problem Optimizing risk-aware performance criteria in uncertain environments.
method Rank dependent expected utility (RDEU) for risk assessment, Wasserstein ball for robustness, actor/agent framework.
result Explicit policy gradient formulae for robust optimization.
New framework robustly handles outliers in Wasserstein DRO for better decision-making.
problem Non-geometric perturbations like adversarial outliers distort Wasserstein distance.
method Proposes an outlier-robust WDRO framework using a robust Wasserstein ball.
result Derives minimax optimal excess risk bounds for robust WDRO.
We improve image perturbation defenses using a better-defined Wasserstein threat model.
problem Real-world image perturbations are not pixel-independent, unlike ℓ p \ell_p ℓ p threat models. method We rectify flaws in the Wasserstein threat model and explore stronger attacks and defenses.
result Current Wasserstein-robust models are ineffective against real-world perturbations.
Nonparametric adaptive robust control tackles model uncertainty in stochastic processes.
problem Model uncertainty in stochastic processes.
method Adaptive robust control methodology using online learning and uncertainty reduction, empirical distribution, and Lagrangian duality.
result Nonparametric adaptive robust control approach is preferable to traditional robust frameworks.
A rapidly growing area of work has studied the existence of adversarial examples, datapoints which have been perturbed to fool a classifier, but the vast majority of these works have focused primarily on threat models defined by ℓ p \ell_p ℓ p norm-bounded perturbations. In this paper, we propose a new threat model for adver…
We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zero-sum game between a statistician choosing an estimator -- that is, a measurable function of the observation…
This work presents a reformulation of the recently proposed Wasserstein autoencoder framework on a non-Euclidean manifold, the Poincaré ball model of the hyperbolic space. By assuming the latent space to be hyperbolic, we can use its intrinsic hierarchy to impose structure on the learned latent space representations. W…
New algorithm solves uncertain Markov decision processes using Wasserstein uncertainty.
problem Solving Markov decision processes with uncertain transition probabilities.
method Distributionally robust Q Q Q -learning algorithm for Wasserstein uncertainty. result Convergence of the algorithm proved and demonstrated with real data.
Paper proposes a robust method for inferring parameters in multiobjective optimization.
problem Uncertainty in hypothetical decision-making problem, data quality, and parameter space.
method Wasserstein distributionally robust approach for inverse multiobjective optimization.
result WRO-IMOP minimizes worst-case expected loss over a Wasserstein ball of distributions.
As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this work, we describe a minimax framework for statistical learning with ambiguity sets …
Paper proposes robust estimators for GANs under Wasserstein contamination.
problem Robust estimation of distributions under contamination.
method Wasserstein GAN-based estimators for location, covariance, and regression.
result Proposed estimators are minimax optimal in many scenarios.
Framework for robust control under model uncertainty, improving financial derivatives hedging.
problem Model uncertainty in financial derivatives hedging.
method Dynamic programming principle for solving one-step optimization problems.
result Robust hedging strategy outperforms model-based strategies during adverse scenarios.
A new portfolio model considers investor aversion to loss and risk.
problem Constructing a robust portfolio under uncertain asset returns and investor aversion.
method Distributional robust optimization (DRP) with a Wasserstein ball centered on empirical distribution, mixed-integer quadratic programming, and hybrid algorithm.
result Empirical testing shows superior performance in asset allocation compared to common strategies.
K-means clustering improved for robustness to outliers and distribution shifts.
problem K-means is brittle to outliers, distribution shifts, and limited samples.
method Developed a distributionally robust variant using Wasserstein-2 ball around the empirical distribution.
result Substantial gains in outlier detection and robustness to noise demonstrated.
New metric derived for robust optimization in stochastic control problems.
problem Non-parametric uncertainty in multiperiod stochastic control problems.
method Derived a new metric, adapted ( p , ∞ ) (p, \infty) ( p , ∞ ) --Wasserstein distance, and used dynamic programming principle. result Dynamic programming principle for DRO problems with semi-separable cost functions.
Our attacks are stronger and faster under Wasserstein metric.
problem Vulnerability of deep models to adversarial attacks.
method Developed an exact yet efficient projection operator and used the Frank-Wolfe method.
result Generated much stronger attacks and improved model robustness.
Bayesian optimization tackles uncertainty in context variables.
problem Sequential decision-making under context distributional uncertainty.
method Wasserstein Distributionally Robust Bayesian Optimization.
result Sublinear regret bounds matching state-of-the-art results.
Improved robustness in multivariate regression and classification with DRO under Wasserstein metric.
problem Outliers in covariates and responses.
method Distributionally Robust Optimization (DRO) with Wasserstein metric ambiguity set and regularization.
result Significant improvement in predictive error and robustness.
We analyze how uncertainty in models affects optimization outcomes using Wasserstein distances.
problem Sensitivity of optimization problems to model uncertainty.
method Non-parametric approach using Wasserstein balls to capture uncertainty, providing explicit corrections for value function and optimizer.
result Explicit formulae for first-order corrections to value function and optimizer.
Researchers quantify risk exposure and sensitivities in financial markets under model uncertainty.
problem Optimizing investment and pricing under model uncertainty in financial markets.
method Distributionally robust optimization, Wasserstein ball, first-order sensitivity analysis.
result Sensitivities of value function, investment policy, and marginal prices to model uncertainty can be non-monotonic.
Study shows k k k -NN classifier is not universally consistent on ( 0 , 1 ) (0,1) ( 0 , 1 ) but consistent on discrete and specific measure spaces.
problem Consistency of k k k -NN classifier under Wasserstein distance on measure spaces. method Analysis of k k k -NN classifier properties under Wasserstein distance, use of σ σ σ -finite metric dimension, geodesic structures of Wasserstein spaces. result Consistency of k k k -NN classifier on specific measure spaces (discrete, Gaussian, wavelet series) but not on ( 0 , 1 ) (0,1) ( 0 , 1 ) . The paper analyzes insurance contracts under distributional uncertainty using Bregman-Wasserstein divergence.
problem Optimal insurance contracts under distributional ambiguity.
method Utilizes Bregman-Wasserstein ball to characterize ambiguity sets, employs robust optimization.
result Derives optimal indemnity functions in closed form and studies their properties.
Framework for optimizing portfolios under model uncertainty.
problem Optimizing portfolios in volatile markets considering model uncertainty.
method Dynamic programming and robust optimization for Markov decision processes.
result Robust optimization leads to better portfolio strategies in uncertain market conditions.
Efficient algorithms solve large-scale DRSVM problems.
problem Optimizing support vector machines under worst-case distribution uncertainty.
method Epigraphical projection-based incremental algorithms.
result Incremental algorithms solve DRSVM problems up to 1000x faster than state-of-the-art methods.
Paper proposes a new method for WDRO with local perturbations, achieving better accuracy.
problem Wasserstein distributionally robust optimization's theoretical understanding needs improvement.
method Develops a new approximation theorem and risk consistency results for WDRO.
result The proposed method achieves significantly higher accuracy on noisy datasets.
Batch normalization makes deep neural networks' representations increasingly orthogonal.
problem Orthogonality of deep neural network representations.
method Random linear transformations in successive batch-normalizations.
result Orthogonality of representations improves SGD performance.
This paper tackles cost-sensitive portfolio optimization under ambiguous return distributions.
problem Tackles cost-sensitive distributionally robust log-optimal portfolio problem with ambiguous return distributions.
method Uses Wasserstein metric for distributional ambiguity, incorporates convex transaction costs, and approximates infinite-dimensional problem with finite convex program.
result Establishes conditions for robustly survivable trades and validates theoretical framework with empirical studies.
This paper studies geodesics between covariance matrices of different ranks using the Bures-Wasserstein metric.
problem Geodesics between covariance matrices of varying ranks.
method Analyzes the Bures-Wasserstein distance on covariance matrices, completing previous work on geodesics and providing explicit formulas.
result The set of all minimizing geodesics between two covariance matrices is parametrized by a closed unit ball in R ( k − r ) i m e s ( l − r ) \mathbb{R}^{(k-r) imes(l-r)} R ( k − r ) im es ( l − r ) . The paper uses EVT to improve tail risk measures under ambiguity sets.
problem Misspecification of tail risk measures leads to inflated risk estimates.
method Applies Extreme Value Theory to derive worst-case tail risk under ambiguity sets.
result Proposes a tail-calibrated ambiguity design that preserves nominal tail asymptotic scaling.
AdaRL improves robust RL by adaptively adjusting policy complexity.
problem Handling epistemic uncertainty in environment dynamics.
method Bi-level optimization framework with adaptive rank adjustment.
result AdaRL outperforms existing methods on MuJoCo benchmarks.
This study improves estimation of locally stationary functional time series using NW method.
problem Accurately capturing time-dependence in locally stationary functional time series with time-varying covariates.
method Nadaraya-Watson (NW) estimation procedure for the conditional distribution of LSFTS.
result Established convergence rates of NW estimator for LSFTS with respect to Wasserstein distance.
Paper shows how noisy data can improve robust decision-making.
problem The challenge of noisy data in decision-making.
method Distributionally robust optimization (DRO) with a novel ambiguity set construction.
result Noisy data can lead to more robust and equitable decisions.
Improves GANs' generalization by promoting local robustness.
problem Stability and generalization issues in GANs.
method Designs a robust optimization framework where generator and discriminator compete in worst-case setting within a small Wasserstein ball.
result Proves tighter generalization upper bound for RGAN than traditional GANs under mild assumptions.
EDRBO optimizes Bayesian optimization with continuous contexts using ensemble models and robust methods.
problem Bayesian optimization with unknown and continuous contextual distributions leads to suboptimal results.
method EDRBO uses ensemble surrogate models and Wasserstein ball ambiguity sets to handle uncertainty and maintain computational tractability.
result EDRBO achieves sublinear cumulative regret guarantees of order O ( γ T T ) \mathcal{O}(γ_T \sqrt{T}) O ( γ T T ) . Momentum methods such as Polyak's heavy ball (HB) method, Nesterov's accelerated gradient (AG) as well as accelerated projected gradient (APG) method have been commonly used in machine learning practice, but their performance is quite sensitive to noise in the gradients. We study these methods under a first-order stoch…
Paper proposes an algorithm for sampling from complex mixture distributions without requiring smoothness.
problem Sampling from a mixture of weakly smooth potentials.
method Unadjusted Langevin algorithm with Euler discretization for a mixture of weakly smooth distributions.
result Convergence in Kullback-Leibler divergence and L β L_β L β -Wasserstein metric with polynomial dependence on dimension. Develops a robust multiclass classification method for deep image classifiers.
problem Tackles data contamination and robustness to outliers in deep image classifiers.
method Uses Distributionally Robust Optimization (DRO) with Wasserstein metric ambiguity sets and regularized learning.
result Reduces test error rate by up to 83.5% and loss by up to 91.3% in image classification tasks.
We study the problem of sampling from a distribution p ∗ ( x ) ∝ exp ( − U ( x ) ) p^*(x) \propto \exp\left(-U(x)\right) p ∗ ( x ) ∝ exp ( − U ( x ) ) , where the function U U U is L L L -smooth everywhere and m m m -strongly convex outside a ball of radius R R R , but potentially nonconvex inside this ball. We study both overdamped and underdamped Langevin MCMC and establish upper bound…
The paper refines and generalizes worst-case law invariant convex risk measures.
problem Developing robust convex risk measures under uncertainty sets.
method Generalizing closed forms for worst-case law invariant convex risk measures with uncertainty sets based on norms and moment constraints.
result Explicit closed forms for convex risk measures are developed and assessed through numerical simulations.