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We study distributionally robust online learning, where a risk-averse learner updates decisions sequentially to guard against worst-case distributions drawn from a Wasserstein ambiguity set centered at past observations. While this paradigm…
Despite superior performance in many situations, deep neural networks are often vulnerable to adversarial examples and distribution shifts, limiting model generalization ability in real-world applications. To alleviate these problems,…
Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein…
Distributionally Robust Optimization (DRO) has enabled to prove the equivalence between robustness and regularization in classification and regression, thus providing an analytical reason why regularization generalizes well in statistical…
In this paper, we consider a network capacity expansion problem in the context of telecommunication networks, where there is uncertainty associated with the expected traffic demand. We employ a distributionally robust stochastic…
Decision making under uncertainty is challenging since the data-generating process (DGP) is often unknown. Bayesian inference proceeds by estimating the DGP through posterior beliefs about the model's parameters. However, minimising the…
We develop a semi-static framework for the variance-optimal hedging of multi-asset derivatives exposed to correlation and covariance risk. The approach combines continuous-time dynamic trading in the underlying assets with a static…
Duality is a foundational tool in robust and distributionally robust optimization (RO and DRO), underpinning both analytical insights and tractable reformulations. The prevailing approaches in the literature primarily rely on saddle-point…
We investigate the use of distributionally robust optimization (DRO) as a tractable tool to recover the asymptotic statistical guarantees provided by the Central Limit Theorem, for maintaining the feasibility of an expected value constraint…
This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk…
We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We…
This paper concerns the central issues of model robustness and sample efficiency in offline reinforcement learning (RL), which aims to learn to perform decision making from history data without active exploration. Due to uncertainties and…
We consider hedging of a contingent claim by a 'semi-static' strategy composed of a dynamic position in one asset and static (buy-and-hold) positions in other assets. We give general representations of the optimal strategy and the hedging…
Reliability-based design optimization (RBDO) is traditionally formulated as a nested optimization and reliability problem. Although surrogate models are generally employed to improve efficiency, the approach remains computationally…
To ensure a successful bid while maximizing of profits, generation companies (GENCOs) need a self-scheduling strategy that can cope with a variety of scenarios. So distributionally robust opti-mization (DRO) is a good choice because that it…
Model-free reinforcement learning (RL) methods are succeeding in a growing number of tasks, aided by recent advances in deep learning. However, they tend to suffer from high sample complexity, which hinders their use in real-world domains.…
We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the…
Distributionally Robust Optimization (DRO), which aims to find an optimal decision that minimizes the worst case cost over the ambiguity set of probability distribution, has been widely applied in diverse applications, e.g., network…
The availability of deep hedging has opened new horizons for solving hedging problems under a large variety of realistic market conditions. At the same time, any model - be it a traditional stochastic model or a market generator - is at…
We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when…