Related papers: Black-Box Min--Max Continuous Optimization Using C…
Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective…
In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…
The low-rank matrix optimization with affine manifold (rank-MOA) aims to minimize a continuously differentiable function over a low-rank set intersecting with an affine manifold. This paper is devoted to the optimality analysis for…
We propose a new majorization-minimization (MM) method for non-smooth and non-convex programs, which is general enough to include the existing MM methods. Besides the local majorization condition, we only require that the difference between…
We study binary optimization problems of the form \( \min_{x\in\{-1,1\}^n} f(Ax-b) \) with possibly nonsmooth loss \(f\). Following the lifted rank-one semidefinite programming (SDP) approach\cite{qian2023matrix}, we develop a…
Consider approximating a "black box" function $f$ by an emulator $\hat{f}$ based on $n$ noiseless observations of $f$. Let $w$ be a point in the domain of $f$. How big might the error $|\hat{f}(w) - f(w)|$ be? If $f$ could be arbitrarily…
Quantum computing and machine learning are state-of-the-art technologies that have been investigated intensively in both academia and industry. The hybrid technology of these two ingredients is expected to be a powerful tool to solve…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
State-of-the-art methods for solving smooth optimization problems are nonlinear conjugate gradient, low memory BFGS, and Majorize-Minimize (MM) subspace algorithms. The MM subspace algorithm which has been introduced more recently has shown…
We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \in [0,1]^{m \times n}$, a vector $b \in [1,\infty)^m$, and a monotone…
We propose a multi-objective optimization algorithm aimed at achieving good anytime performance over a wide range of problems. Performance is assessed in terms of the hypervolume metric. The algorithm called HMO-CMA-ES represents a hybrid…
In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…
This paper presents a piecewise convexification method to approximate the whole approximate optimal solution set of non-convex optimization problems with box constraints. In the process of box division, we first classify the sub-boxes and…
Study about theory and algorithms for constrained optimization usually assumes that the feasible region of the optimization problem is nonempty. However, there are many important practical optimization problems whose feasible regions are…
We study the optimal lower and upper complexity bounds for finding approximate solutions to the composite problem $\min_x\ f(x)+h(Ax-b)$, where $f$ is smooth and $h$ is convex. Given access to the proximal operator of $h$, for strongly…
In many real-world problems, we want to infer some property of an expensive black-box function $f$, given a budget of $T$ function evaluations. One example is budget constrained global optimization of $f$, for which Bayesian optimization is…
Many optimization problems arising in high-dimensional statistics decompose naturally into a sum of several terms, where the individual terms are relatively simple but the composite objective function can only be optimized with iterative…
In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuous DR-submodular…
In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent…
Contextual policy search (CPS) is a class of multi-task reinforcement learning algorithms that is particularly useful for robotic applications. A recent state-of-the-art method is Contextual Covariance Matrix Adaptation Evolution Strategies…