Related papers: Stochastic Saddle Point Problems with Decision-Dep…
In the paper, we generalize the approach Gasnikov et. al, 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle, to the convex-concave saddle-point problem. The proposed approach works,…
We study stochastic programs where the decision-maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a…
The primal-dual distributed optimization methods have broad large-scale machine learning applications. Previous primal-dual distributed methods are not applicable when the dual formulation is not available, e.g. the sum-of-non-convex…
We propose a novel framework for analyzing the dynamics of distribution shift in real-world systems that captures the feedback loop between learning algorithms and the distributions on which they are deployed. Prior work largely models…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
This paper considers stochastic-constrained stochastic optimization where the stochastic constraint is to satisfy that the expectation of a random function is below a certain threshold. In particular, we study the setting where data samples…
Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…
We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with $d$ states. We…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
We consider the distributionally robust optimization (DRO) problem with spectral risk-based uncertainty set and $f$-divergence penalty. This formulation includes common risk-sensitive learning objectives such as regularized condition…
We study decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. The developed…
As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine…
We provide a unifying approximate dynamic programming framework that applies to a broad variety of problems involving sequential estimation. We consider first the construction of surrogate cost functions for the purposes of optimization,…
We consider the problem of computing optimal policies in average-reward Markov decision processes. This classical problem can be formulated as a linear program directly amenable to saddle-point optimization methods, albeit with a number of…
Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…
This paper considers a class of distributed resource allocation problems where each agent privately holds a smooth, potentially non-convex local objective, subject to a globally coupled equality constraint. Built upon the existing method,…
We study data-driven learning of robust stochastic control for infinite-horizon systems with potentially continuous state and action spaces. In many managerial settings--supply chains, finance, manufacturing, services, and dynamic…