Related papers: Mirror descent method for stochastic multi-objecti…
This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…
Over the past two decades, descent methods have received substantial attention within the multiobjective optimization field. Nonetheless, both theoretical analyses and empirical evidence reveal that existing first-order methods for…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm's iterates under the…
In this work we propose MirrorCBO, a consensus-based optimization (CBO) method which generalizes standard CBO in the same way that mirror descent generalizes gradient descent. For this we apply the CBO methodology to a swarm of dual…
Machine learning problems with multiple objective functions appear either in learning with multiple criteria where learning has to make a trade-off between multiple performance metrics such as fairness, safety and accuracy; or, in…
We investigate Stochastic Mirror Descent (SMD) with matrix parameters and vector-valued predictions, a framework relevant to multi-class classification and matrix completion problems. Focusing on the overparameterized regime, where the…
In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the…
We investigate the convergence of stochastic mirror descent (SMD) under interpolation in relatively smooth and smooth convex optimization. In relatively smooth convex optimization we provide new convergence guarantees for SMD with a…
Mirror Descent (MD) is a scalable first-order method widely used in large-scale optimization, with applications in image processing, policy optimization, and neural network training. This paper generalizes MD to optimization on Riemannian…
Value iteration-type methods have been extensively studied for computing a nearly optimal value function in reinforcement learning (RL). Under a generative sampling model, these methods can achieve sharper sample complexity than policy…
To solve distributed optimization efficiently with various constraints and nonsmooth functions, we propose a distributed mirror descent algorithm with embedded Bregman damping, as a generalization of conventional distributed…
Sampling from an unnormalized target distribution is an essential problem with many applications in probabilistic inference. Stein Variational Gradient Descent (SVGD) has been shown to be a powerful method that iteratively updates a set of…
In machine learning and statistical data analysis, we often run into objective function that is a summation: the number of terms in the summation possibly is equal to the sample size, which can be enormous. In such a setting, the stochastic…
This paper explores a new framework for reinforcement learning based on online convex optimization, in particular mirror descent and related algorithms. Mirror descent can be viewed as an enhanced gradient method, particularly suited to…
Constrained competitive optimization involves multiple agents trying to minimize conflicting objectives, subject to constraints. This is a highly expressive modeling language that subsumes most of modern machine learning. In this work we…
This paper revisits the convergence of Stochastic Mirror Descent (SMD) in the contemporary nonconvex optimization setting. Existing results for batch-free nonconvex SMD restrict the choice of the distance generating function (DGF) to be…
The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…
We propose a descent subgradient algorithm for unconstrained nonsmooth nonconvex multiobjective optimization problems. To find a descent direction, we present an iterative process that efficiently approximates the Goldstein subdifferential…
This paper studies the convergence of the mirror descent algorithm for finite horizon stochastic control problems with measure-valued control processes. The control objective involves a convex regularisation function, denoted as $h$, with…