Related papers: On Convergence of Binary Trust-Region Steepest Des…
We consider stochastic optimization problems with the dual tasks of (i) effectively finding the optimizer and (ii) reliably conducting statistical inference for the optimal objective function value. We find that classical simulation…
Behavior trees (BTs) are an optimally modular framework to assemble hierarchical hybrid control policies from a set of low-level control policies using a tree structure. Many robotic tasks are naturally decomposed into a hierarchy of…
Thresholding based iterative algorithms have the trade-off between effectiveness and optimality. Some are effective but involving sub-matrix inversions in every step of iterations. For systems of large sizes, such algorithms can be…
In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on…
A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…
We propose a stochastic nonconvex optimization algorithm that achieves almost sure $\tilde{\mathcal{O}}(\epsilon^{-1.5})$ iteration complexity for problems with smooth objective functions and gradients only observable with noise. The…
The decoding of Low-Density Parity-Check codes by the Belief Propagation (BP) algorithm is revisited. We check the iterative algorithm for its convergence to a codeword (termination), we run Monte Carlo simulations to find the probability…
Distributionally robust optimization (DRO) can improve the robustness and fairness of learning methods. In this paper, we devise stochastic algorithms for a class of DRO problems including group DRO, subpopulation fairness, and empirical…
The presence of uncertainty in material properties and geometry of a structure is ubiquitous. The design of robust engineering structures, therefore, needs to incorporate uncertainty in the optimization process. Stochastic gradient descent…
In this work, we analyze two of the most fundamental algorithms in geodesically convex optimization: Riemannian gradient descent and (possibly inexact) Riemannian proximal point. We quantify their rates of convergence and produce different…
We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…
We consider the minimization of a cost function $f$ on a manifold $M$ using Riemannian gradient descent and Riemannian trust regions (RTR). We focus on satisfying necessary optimality conditions within a tolerance $\varepsilon$.…
We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates…
Branch and bound algorithms have been developed for reliability analysis of coherent systems. They exhibit a set of advantages; in particular, they can find a computationally efficient representation of a system failure or survival event,…
We study three families of online convex optimization algorithms: follow-the-proximally-regularized-leader (FTRL-Proximal), regularized dual averaging (RDA), and composite-objective mirror descent. We first prove equivalence theorems that…
We introduce a game of trusted computation in which a sensor equipped with limited computing power leverages a central node to evaluate a specified function over a large dataset, collected over time. We assume that the central computer can…
This article extends the optimal covariance steering (CS) problem for discrete time linear stochastic systems modeled using moment-based ambiguity sets. To hedge against the uncertainty in the state distributions while performing covariance…
The Steiner Tree problem asks for the cheapest way of connecting a given subset of the vertices in an undirected graph. One of the most prominent linear programming relaxations for Steiner Tree is the Bidirected Cut Relaxation (BCR).…
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…
We consider descent methods for solving non-finite valued nonsmooth convex-composite optimization problems that employ Gauss-Newton subproblems to determine the iteration update. Specifically, we establish the global convergence properties…