Related papers: ALSO-X and ALSO-X+: Better Convex Approximations f…
We propose a new iteration scheme, the Cauchy-Simplex, to optimize convex problems over the probability simplex $\{w\in\mathbb{R}^n\ |\ \sum_i w_i=1\ \textrm{and}\ w_i\geq0\}$. Specifically, we map the simplex to the positive quadrant of a…
We investigate a class of chance-constrained combinatorial optimization problems. Given a pre-specified risk level $\epsilon \in [0,1]$, the chance-constrained program aims to find the minimum cost selection of a vector of binary decisions…
The problem of constrained reinforcement learning (CRL) holds significant importance as it provides a framework for addressing critical safety satisfaction concerns in the field of reinforcement learning (RL). However, with the introduction…
We consider stochastic optimization problems with non-convex functional constraints, such as those arising in trajectory generation, sparse approximation, and robust classification. To this end, we put forth a recursive momentum-based…
We consider the question of estimating a solution to a system of equations that involve convex nonlinearities, a problem that is common in machine learning and signal processing. Because of these nonlinearities, conventional estimators…
We study risk-sensitive Reinforcement Learning (RL), where we aim to maximize the Conditional Value at Risk (CVaR) with a fixed risk tolerance $\tau$. Prior theoretical work studying risk-sensitive RL focuses on the tabular Markov Decision…
This paper addresses risk averse constrained optimization problems where the objective and constraint functions can only be computed by a blackbox subject to unknown uncertainties. To handle mixed aleatory/epistemic uncertainties, the…
We present the conditional value-at-risk (CVaR) in the context of Markov chains and Markov decision processes with reachability and mean-payoff objectives. CVaR quantifies risk by means of the expectation of the worst p-quantile. As such it…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
Conditional value-at-risk (CVaR) is a prominent risk measure in financial engineering, energy systems, and supply chain management. In these domains, Markov decision processes (MDPs) with a long-run CVaR criterion effectively mitigate cost…
We developed a corporative stochastic approximation (CSA) type algorithm for semi-infinite programming (SIP), where the cut generation problem is solved inexactly. First, we provide general error bounds for inexact CSA. Then, we propose two…
Chance constrained optimization problems allow to model problems where constraints involving stochastic components should only be violated with a small probability. Evolutionary algorithms have been applied to this scenario and shown to…
In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…
We propose a new first-order augmented Lagrangian algorithm ALCC for solving convex conic programs of the form min{rho(x)+gamma(x): Ax-b in K, x in chi}, where rho and gamma are closed convex functions, and gamma has a Lipschitz continuous…
In this paper, Kernel PCA is reinterpreted as the solution to a convex optimization problem. Actually, there is a constrained convex problem for each principal component, so that the constraints guarantee that the principal component is…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
The Stochastic Shortest Path (SSP) problem models probabilistic sequential-decision problems where an agent must pursue a goal while minimizing a cost function. Because of the probabilistic dynamics, it is desired to have a cost function…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even…