Related papers: Gradient-Based Multiobjective Optimization with Un…
We present a systematic derivation of the algorithms required for computing the gradient and the action of the Hessian of an arbitrary misfit function for large-scale parameter estimation problems involving linear time-dependent PDEs with…
In monocular depth estimation, disturbances in the image context, like moving objects or reflecting materials, can easily lead to erroneous predictions. For that reason, uncertainty estimates for each pixel are necessary, in particular for…
In this paper we provide oracle complexity lower bounds for finding a point in a given set using a memory-constrained algorithm that has access to a separation oracle. We assume that the set is contained within the unit $d$-dimensional ball…
We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic…
Meta learning with multiple objectives can be formulated as a Multi-Objective Bi-Level optimization Problem (MOBLP) where the upper-level subproblem is to solve several possible conflicting targets for the meta learner. However, existing…
This paper investigates the point convergence of accelerated gradient methods for multiobjective optimization, in both continuous and discrete settings. We address the open problems of whether the solution trajectory of the multiobjective…
The recently introduced Gradient Methods with Memory use a subset of the past oracle information to create an accurate model of the objective function that enables them to surpass the Gradient Method in practical performance. The model…
Selecting an effective step-size is a fundamental challenge in first-order optimization, especially for problems with non-Euclidean geometries. This paper presents a novel adaptive step-size strategy for optimization algorithms that rely on…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
In this article, we develop an efficient algorithm based on three special variants of the nonlinear conjugate gradient method, namely, the Polak--Ribiere--Polyak, Hestenes--Stiefel, and Liu--Story schemes for computing Pareto critical…
In the recent years, various gradient descent algorithms including the methods of gradient descent, gradient descent with momentum, adaptive gradient (AdaGrad), root-mean-square propagation (RMSProp) and adaptive moment estimation (Adam)…
We develop a gradient-like algorithm to minimize a sum of peer objective functions based on coordination through a peer interconnection network. The coordination admits two stages: the first is to constitute a gradient, possibly with…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
Real-world problems are often multi-objective with decision-makers unable to specify a priori which trade-off between the conflicting objectives is preferable. Intuitively, building machine learning solutions in such cases would entail…
This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…
For the composite multi-objective optimization problem composed of two nonsmooth terms, a smoothing method is used to overcome the nonsmoothness of the objective function, making the objective function contain at most one nonsmooth term.…
Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
In this work, we revisit a classical distributed gradient-descent algorithm, introducing an interesting class of perturbed multi-agent systems. The state of each subsystem represents a local estimate of a solution to the global optimization…