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Large data sets often require performing distributed statistical estimation, with a full data set split across multiple machines and limited communication between machines. To study such scenarios, we define and study some refinements of…

This paper features expectiles in dynamic and stochastic optimization. Expectiles are a family of risk functionals characterized as minimizers of optimization problems. For this reason, they enjoy various unique stability properties, which…

We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…

High penetration of renewable energy sources and the increasing share of stochastic loads require the explicit representation of uncertainty in tools such as the optimal power flow (OPF). Current approaches follow either a linearized…

Stochastic Model Predictive Control has proved to be an efficient method to plan trajectories in uncertain environments, e.g., for autonomous vehicles. Chance constraints ensure that the probability of collision is bounded by a predefined…

This paper studies the robust optimal gain selection problem for financial trading systems, formulated within a \emph{double linear policy} framework, which allocates capital across long and short positions. The key objective is to…

Policy learning using historical observational data is an important problem that has found widespread applications. Examples include selecting offers, prices, advertisements to send to customers, as well as selecting which medication to…

This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…

The performance of learning models often deteriorates when deployed in out-of-sample environments. To ensure reliable deployment, we propose a stability evaluation criterion based on distributional perturbations. Conceptually, our stability…

Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness,…

Distributionally robust optimization has been shown to offer a principled way to regularize learning models. In this paper, we find that Tikhonov regularization is distributionally robust in an optimal transport sense (i.e., if an adversary…

This article introduces a decentralized robust optimization framework for safe multi-agent control under uncertainty. Although stochastic noise has been the primary form of modeling uncertainty in such systems, these formulations might fall…

In this research, starting from a widely accepted definition of risk, we support the idea that risk reduction is a more realistic objective than risk minimization, which represents a theoretical utopia. Furthermore, significant risk…

Safe reinforcement learning (RL) aims to learn policies that satisfy certain constraints before deploying them to safety-critical applications. Previous primal-dual style approaches suffer from instability issues and lack optimality…

Any optimization algorithm based on the risk parity approach requires the formulation of portfolio total risk in terms of marginal contributions. In this paper we use the independence of the underlying factors in the market to derive the…

We propose a novel conditional diffusion model for contextual portfolio optimization that learns the cross-sectional distribution of next-day stock returns conditioned on high-dimensional asset-specific factors. Our model leverages a…

We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…

Single-level reformulations of (non-convex) distributionally robust optimization (DRO) problems are often intractable, as they contain semiinfinite dual constraints. Based on such a semiinfinite reformulation, we present a safe…

Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor's portfolio consists of a dynamically traded stock and a static…

In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we…