Related papers: SMOP: Stochastic trust region method for multi-obj…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential…
We propose a globally convergent trust-region bundle method for minimizing lower-$C^2$ functions using higher-order cutting-plane models. Under certain growth assumptions on the objective around its minimum, the method is able to compute…
We study the canonical problem of maximizing a stochastic submodular function subject to a cardinality constraint, where the goal is to select a subset from a ground set of items with uncertain individual performances to maximize their…
We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior…
In this paper, we propose a general class of algorithms for optimizing an extensive variety of nonsmoothly penalized objective functions that satisfy certain regularity conditions. The proposed framework utilizes the…
We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…
This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…
In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path…
A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD). Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under…
We consider the stochastic variational inequality problem in which the map is expectation-valued in a component-wise sense. Much of the available convergence theory and rate statements for stochastic approximation schemes are limited to…
In this article, we propose a Newton-based method for solving multiobjective interval optimization problems (MIOPs). We first provide a connection between weakly Pareto optimal points and Pareto critical points in the context of MIOPs.…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
Gradient-based methods have been highly successful for solving a variety of both unconstrained and constrained nonlinear optimization problems. In real-world applications, such as optimal control or machine learning, the necessary function…
Multi-objective optimization aims to solve problems with competing objectives. Evaluating such problems is often slow or expensive, limiting the budget of evaluations. In many applications, historical data from related optimization tasks is…
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…
This paper studies constrained Markov decision processes (CMDPs) with constraints against stochastic thresholds, aiming at safety of reinforcement learning in unknown and uncertain environments. We leverage a Growing-Window estimator…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
We present a unified probabilistic framework for simultaneous trajectory estimation and planning (STEAP). Estimation and planning problems are usually considered separately, however, within our framework we show that solving them…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…