A general duality proof for Wasserstein distributionally robust optimization.
problem Optimizing under uncertainty with Wasserstein distance.
method One-dimensional convex analysis and interchangeability principle.
result General duality result holds for various distributions and costs.
Develops robust learning framework under distributional perturbations.
problem Learning robust to data distributional changes.
method Distributionally Robust Optimization (DRO) under Wasserstein metric.
result Establishes performance guarantees and tractable formulations.
Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance (in a Wasserstein sense) from the underlying empirical measure. While motivated by…
New scalable methods for robust model learning from large datasets.
problem Training robust models resistant to data distribution shifts.
method Composite optimization for distributionally robust optimization (DRO).
result Scalable methods for learning robust models from large datasets.
Tikhonov regularization is robust under specific martingale constraints in distributionally robust optimization.
problem Distributionally robust optimization and regularization of learning models.
method Optimal transport approach with martingale constraints.
result Tikhonov regularization is optimal transport robust under specified martingale constraints.
A new framework for performative prediction robust to distributional misspecification.
problem Performative prediction models can be influenced by their own predictions, leading to suboptimal outcomes.
method Introduces distributionally robust performative prediction (DRPO) to approximate the true performative optimum (PO) robustly.
result DRPO provides provable guarantees as a robust approximation to the true PO when the nominal distribution map is misspecified.
Paper proves robust estimators' generalization guarantees without dimensionality issues.
problem Generalization guarantees for Wasserstein distributionally robust models.
method Analyzes and extends existing guarantees to broader classes of models and regularized versions.
result Generalization guarantees hold without dimensionality issues and cover distribution shifts.
New approach improves model generalization through distributionally robust learning.
problem Improving model generalization in machine learning.
method Stochastic gradient descent applied to the outer minimization problem, with gradient estimation through multi-level Monte Carlo randomization.
result Our approach yields significant benefits over previous work in numerical experiments.
New algorithm improves RL performance across different environments.
problem Improving reinforcement learning performance across various environments.
method Designing a fully model-free DRRL algorithm that learns from a single trajectory.
result Demonstrates superior robustness and sample efficiency compared to existing methods.
New regularizer for machine learning using private data.
problem Machine learning with private data.
method Distributionally-robust optimization with locally-differentially-private datasets.
result New regularizer for training linear regression models.
The paper connects three machine learning methods to reduce generalization errors.
problem Reducing generalization errors in machine learning models.
method Distributionally robust optimization, Bayesian methods, and regularization.
result Machine learning models can be characterized using distributional uncertainty and robustness measures.
Proposes using Wasserstein barycenters for robust optimization with multiple data sources.
problem Distributionally robust optimization with multiple heterogeneous data sources.
method Construct nominal distribution through Wasserstein barycenter of multiple data samples, reformulates as a finite convex program.
result Proposed scheme outperforms other estimators in sparse inverse covariance matrix estimation.
Robustness to distributional shift is one of the key challenges of contemporary machine learning. Attaining such robustness is the goal of distributionally robust optimization, which seeks a solution to an optimization problem that is worst-case robust under a specified distributional shift of an uncontrolled covariate…
Improved estimator reduces bias in statistical learning models.
problem Asymptotic bias in classic WDRO estimator.
method Adjusted Wasserstein distributionally robust estimator.
result Asymptotic unbiased estimator with smaller MSE.
Extends ML fairness to handle minority groups over time.
problem Limitations of existing fairness criteria.
method Performative Distributionally Robust Optimization.
result Improves fairness for minority groups over time.
A method for robust reinforcement learning in large state spaces.
problem Challenges in RL with large state spaces, costly data, and real-world dynamics deviation.
method Distributionally robust Markov decision processes with Gaussian Processes and maximum variance reduction.
result Efficient learning of multi-output nominal transition dynamics with statistical sample complexity bounds.
This work evaluates risks over time using robust measures and neural networks.
problem Distributionally robust risk evaluation over temporal data.
method Characterizes alternative measures using causal optimal transport, approximates test functions by neural networks, and proves sample complexity.
result Framework outperforms classic counterparts in portfolio selection problems.
Optimizes distributions robustly with Sinkhorn distance.
problem Distributionally robust optimization with Wasserstein distance.
method Convex programming dual reformulation, stochastic mirror descent algorithm.
result Demonstrates superior performance in synthetic and real data.
End-to-end portfolio system accounts for model risk.
problem Model risk in portfolio selection.
method Distributionally robust optimization with convex duality.
result Explicitly accounts for model risk in portfolio selection.
Study improves adversarial classification using distributionally robust models.
problem Improving robustness against adversarial attacks in classification models.
method Distributionally robust chance constraints with Wasserstein ambiguity, reformulated as a regularized ramp loss minimization problem.
result Standard descent methods can converge to the global minimizer for the distributionally robust adversarial classification model.
Proposes a risk parity portfolio optimization method that accounts for uncertainty in asset returns.
problem Risk parity portfolio optimization under uncertainty.
method Distributionally robust optimization with ambiguity set for worst-case scenario analysis.
result Distributionally robust risk parity portfolios can yield higher risk-adjusted returns.
We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash equilibrium. Despite the non-convex nature of the ambiguity set, we prove that the …
Scaff-PD improves fairness and robustness in federated learning with reduced communication.
problem Improving fairness and robustness in federated learning with limited communication.
method Scaff-PD uses a family of distributionally robust objectives and an accelerated primal dual algorithm with bias-corrected steps.
result Scaff-PD achieves significant gains in communication efficiency and convergence speed while maintaining fairness and robustness.
Paper introduces DOO models to outperform SAA out-of-sample.
problem Outperforming SAA in out-of-sample performance.
method Introduces DOO models that consider both worst-case and best-case scenarios.
result DOO models can always outperform SAA out-of-sample.
Data-driven Distributionally Robust Optimization (DD-DRO) via optimal transport has been shown to encompass a wide range of popular machine learning algorithms. The distributional uncertainty size is often shown to correspond to the regularization parameter. The type of regularization (e.g. the norm used to regularize)…
A new algorithm reduces bias and variance in distributionally robust optimization.
problem Distributionally robust optimization with bias and variance issues.
method Prospect, a stochastic gradient-based algorithm that reduces hyperparameter tuning.
result Prospect achieves linear convergence and 2-3x faster convergence on various benchmarks.
Exact generalization guarantees for robust models using Wasserstein distance are established.
problem Capturing data uncertainty and distribution shifts in machine learning models.
method Establishes exact generalization guarantees for robust models based on the Wasserstein distance, covering various cases and transport costs.
result Exact generalization guarantees are provided for a wide range of cases, including deep learning objectives with nonsmooth activations.
New method reduces over-pessimism in Bayesian control under parameter uncertainty.
problem Over-pessimism in Bayesian control due to misspecified priors.
method Distributionally robust Bayesian control (DRBC) with strong duality and optimization.
result Validated algorithm on synthetic and real data, reducing over-pessimism.
Algorithm solves robust linear regression with block Lewis weights.
problem Group distributionally robust least squares problem.
method Algorithm based on geometric construction and block Lewis weights, using accelerated proximal methods.
result Improves over known methods for moderate accuracy regimes and matches state-of-the-art guarantees.
Adaptive optimal transport priors improve few-shot learning robustness.
problem Limited supervision and distribution shifts in few-shot learning.
method Prototype-Guided Distributionally Robust Optimization (PG-DRO) framework.
result PG-DRO achieves stronger robust generalization in few-shot scenarios.
DRDA robustly adapts models across domains with mismatched distributions.
problem Vulnerability of DA methods to noise and inability to generalize to unseen samples.
method DRDA uses distributionally robust optimization (DRO) with MMD metric to learn robust decision functions.
result DRDA outperforms existing robust learning approaches in experiments.
Robust risk minimisation has several advantages: it has been studied with regards to improving the generalisation properties of models and robustness to adversarial perturbation. We bound the distributionally robust risk for a model class rich enough to include deep neural networks by a regularised empirical risk invol…
Study shows convergence of stochastic gradient method for unregularized Wasserstein optimization.
problem Wasserstein distributionally robust optimization under potential distribution shifts.
method Regularized approximation with stochastic gradient methods, convergence analysis.
result Stochastic gradient method converges to subgradients of unregularized objective as regularization vanishes.
Study optimal transport for robust optimization, showing how adversary's strategy relates to regularization.
problem Optimizing under uncertain parameters with a fictitious adversary reshaping a reference distribution.
method Introduces optimal transport and regularization to relate robustification to variation and Lipschitz norms.
result Conditions for existence and computability of Nash equilibrium between decision-maker and adversary.
New algorithm reduces communication in federated learning.
problem Communication inefficiency in distributed federated learning.
method Distributionally Robust Federated Averaging (DRFA) with snapshotting scheme.
result DRFA achieves efficient convergence in various settings.
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 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…
Expands newsvendor model with moment constraints using Wasserstein distance.
problem Optimizing order quantity under distributional ambiguity.
method Formulates infinite dimensional primal problem, derives finite dimensional dual problem using problem of moments duality.
result Distributional ambiguity affects optimal order quantity and profits/costs.
Discuss new policy learning objectives and methods.
problem Improving policy learning efficiency and robustness.
method Introducing curvature considerations and calibration data methods.
result Efficient retargeting and distributionally robust policies.
Abstract: Nonlinear random walk with distributionally robust transition probabilities.
problem Modeling nonlinear random walks with robust transition probabilities.
method Scaling limit and nonlinear semigroup approach.
result Explicit computation of the generator and corresponding PDE.
We present a distributionally robust formulation of a stochastic optimization problem for non-i.i.d vector autoregressive data. We use the Wasserstein distance to define robustness in the space of distributions and we show, using duality theory, that the problem is equivalent to a finite convex-concave saddle point pro…
Investigates model risk and semi-static hedging for martingale constrained models.
problem Model risk distributionally robust sensitivities for functionals on the Wasserstein space.
method Introduces distributionally robust problem with semi-static hedging strategies.
result Explicit characterizations of model risk optimal semi-static hedging strategies.
Enhances survival analysis predictions with a robust learning approach.
problem Improving robustness and accuracy in survival analysis predictions.
method Integrates Distributionally Robust Learning (DRL) into Cox regression using Wasserstein distance-based ambiguity set.
result Demonstrates superior performance in prediction accuracy and robustness compared to traditional methods.
The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimizat…
We propose a novel data-driven method to learn a mixture of multiple kernels with random features that is certifiabaly robust against adverserial inputs. Specifically, we consider a distributionally robust optimization of the kernel-target alignment with respect to the distribution of training samples over a distributi…
New method clusters variables using robust nodewise regression.
problem Variable clustering in multi-factor models.
method Distributionally robust nodewise regression with convex relaxation and ADMM.
result Superior performance in numerical studies.
Paper tackles robust optimization under uncertainty using nested distance.
problem Optimizing under distributionally robust uncertainty with nested distance.
method Equivalent recursive and dynamic programming reformulations for tractable optimization.
result Optimal robust policies can be found efficiently using convex optimization.
New method optimises worst-case risk under model uncertainty.
problem Minimizing expected risk under posterior beliefs leads to sub-optimal decisions due to model uncertainty.
method Distributionally Robust Optimisation with Bayesian Ambiguity Sets (DRO-BAS)
result Improved out-of-sample robustness in the Newsvendor problem.