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.
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…
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.
Paper develops a robust Bayesian optimization method for noisy zeroth-order settings.
problem Achieving robustness to distributional shift in machine learning.
method Distributionally robust Bayesian optimization (DRBO) algorithm for noisy zeroth-order optimization.
result DRBO algorithm provably obtains sub-linear robust regret in various settings.
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.
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.
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.
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.
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.
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.
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.
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.
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)…
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.
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.
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.
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.
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.
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.
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.
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…
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.
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.
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 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.
A new gradient flow framework for distributionally robust optimization.
problem Optimizing under uncertainty with worst-case distributional constraints.
method Gradient flow theory applied to distributionally robust optimization.
result Practical algorithms for sampling from worst-case distributions.
A new method uses GANs for robust optimization under uncertain data.
problem Optimizing supply chains under demand uncertainty with ambiguous distributions.
method Generative adversarial networks (GANs) for data-driven distributionally robust chance constrained programming.
result The approach effectively handles uncertain data distributions and improves supply chain optimization.
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.
CreDRO learns credal ensembles via distributionally robust optimization, improving EU quantification.
problem Quantifying predictive epistemic uncertainty in credal models.
method Distributionally robust optimization to capture EU from training randomness and potential distribution shifts.
result Empirically, CreDRO outperforms existing credal methods on various tasks.
Integrates side information for robust portfolio optimization.
problem Portfolio optimization under uncertainty and side information.
method Distributionally robust optimization with optimal transport ambiguity set.
result The problem can be reformulated as a finite-dimensional optimization problem.
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…
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.
Drago optimizes DRO problems with faster convergence.
problem Distributionally robust optimization with closed, convex uncertainty sets.
method Primal-dual coupled variance reduction algorithm with cyclic and randomized updates.
result Achieves state-of-the-art linear convergence rate on strongly convex-strongly concave problems.
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.
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.
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…
CADRO optimizes DRO by reducing conservatism through cost-aware ambiguity sets.
problem Optimizing solutions under uncertainty with reduced conservatism.
method CADRO uses a cost-aware ambiguity set to reduce DRO's conservatism.
result CADRO provides high-confidence upper bounds and consistent estimators of out-of-sample expected cost.
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.
Unified framework for DRO using OT with constraints.
problem Handling ambiguity in likelihood ratios and outcomes.
method Unified framework leveraging optimal transport with conditional moment constraints.
result Unified approach enables adversarial perturbation of likelihood ratios and outcomes.
Paper develops robust OPF method using contextual information.
problem Optimal Power Flow problem under incomplete uncertainty knowledge.
method Distributionally robust chance-constrained formulation with probability trimmings and optimal transport.
result Distributional robustness improves expected cost and system reliability.
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a generalized empirical likelihood framework---based on distributional uncertainty se…
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.
Kernel DRO uses RKHS to optimize under distributional uncertainty.
problem Optimizing under distributional uncertainty with limited knowledge.
method Kernel DRO using RKHS ambiguity sets and duality theory.
result Unified approach to robust and stochastic optimization.
Proposes a method to learn adaptive ambiguity sets for robust optimization.
problem Misspecification in distributionally robust optimization (DRO).
method Learned predictive ambiguity sets (LPAS) using deep contextual models.
result Significantly improves portfolio optimization performance compared to baselines.
Flexible framework integrates machine learning and DRO for uncertain parameter prediction.
problem Limited joint observations of uncertain parameters and covariates.
method Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets.
result Validation of theoretical and practical benefits in limited data scenarios.
Efficiently addresses federated learning challenges with reduced communication and sample complexity.
problem Heterogeneity in data volumes and distributions at different clients compromises model generalization ability.
method Introduces algorithms for communication-efficient Federated Group Distributionally Robust Optimization (FGDRO).
result Communication complexity reduced to O(1/ε4) for FGDRO-CVaR and O(1/ε3) for FGDRO-KL. Develops ODRPO to improve RL algorithms with better performance and stability.
problem RL algorithms converge to sub-optimal solutions due to limited policy representation.
method Integrates DRO approach to solve trust region constrained optimization problem without parameterizing policies.
result Achieves globally optimal policy update and higher sample efficiency.
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 …