English
Related papers

Related papers: Mirror descent for constrained stochastic control …

200 papers

We investigated a cost-constrained static ergodic control problem of the variance of measure-valued affine processes and its application in streamflow management. The controlled system is a jump-driven mixed moving average process that…

Optimization and Control · Mathematics 2025-11-24 Hidekazu Yoshioka , Tomohiro Tanaka , Yumi Yoshioka , Ayumi Hashiguchi

We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…

Optimization and Control · Mathematics 2021-07-09 Laurent Pfeiffer , Xiaolu Tan , Yulong Zhou

In the paper we consider an application of mirror descent (dual averaging) to the stochastic online convex optimization problems. We compare classical mirror descent (Nemirovski-Yudin, 1979) with dual averaging (Nesterov, 2005) and…

Optimization and Control · Mathematics 2016-12-12 Alexander Gasnikov , Yurii Nesterov , Vladimir Spokoiny

In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…

Optimization and Control · Mathematics 2022-11-22 Weijia Shao , Fikret Sivrikaya , Sahin Albayrak

As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow…

Optimization and Control · Mathematics 2007-05-23 Markus Fischer , Markus Reiss

Mirror descent is an elegant optimization technique that leverages a dual space of parametric models to perform gradient descent. While originally developed for convex optimization, it has increasingly been applied in the field of machine…

Machine Learning · Computer Science 2023-05-10 Hyungjoon Soh , Dongyeob Kim , Juno Hwang , Junghyo Jo

In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involves the errors in the gradient and proximal operator. We…

Optimization and Control · Mathematics 2023-04-11 Woocheol Choi , Myeong-Su Lee , Seok-Bae Yun

We study discrete-time mirror descent applied to the unregularized empirical risk in matrix sensing. In both the general case of rectangular matrices and the particular case of positive semidefinite matrices, a simple potential-based…

Machine Learning · Statistics 2021-10-28 Fan Wu , Patrick Rebeschini

We consider the following class of online optimization problems with functional constraints. Assume, that a finite set of convex Lipschitz-continuous non-smooth functionals are given on a closed set of $n$-dimensional vector space. The…

Optimization and Control · Mathematics 2021-12-30 Alexander Titov , Fedor Stonyakin , Alexander Gasnikov , Mohammad Alkousa

In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the…

Optimization and Control · Mathematics 2013-09-10 Cong D. Dang , Guanghui Lan

To control humanoid robots, the reference pose of end effector(s) is planned in task space, then mapped into the reference joints by IK. By viewing that problem as approximate quadratic programming (QP), recent QP solvers can be applied to…

Robotics · Computer Science 2023-12-06 Taisuke Kobayashi , Takanori Jin

This paper is devoted to the study of acceleration methods for an inequality constrained convex optimization problem by using Lyapunov functions. We first approximate such a problem as an unconstrained optimization problem by employing the…

Optimization and Control · Mathematics 2024-11-25 Juan Liu , Nan-Jing Huang , Xian-Jun Long , Xue-song Li

We study the problem of differentially-private (DP) stochastic (convex-concave) saddle-points in the $\ell_1$ setting. We propose $(\varepsilon, \delta)$-DP algorithms based on stochastic mirror descent that attain nearly…

Optimization and Control · Mathematics 2025-11-17 Tomás González , Cristóbal Guzmán , Courtney Paquette

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation…

Optimization and Control · Mathematics 2016-09-06 Vincent Guigues

In the paper, we propose a class of efficient adaptive bilevel methods based on mirror descent for nonconvex bilevel optimization, where its upper-level problem is nonconvex possibly with nonsmooth regularization, and its lower-level…

Optimization and Control · Mathematics 2023-11-21 Feihu Huang

We study the max-margin solutions reached by mirror flow in deep neural networks with homogeneous activation functions. Extending classical results on gradient flow, we derive a novel balance equation for mirror flow from convex duality,…

Machine Learning · Computer Science 2026-05-20 Tom Jacobs , Guido Montufar

We analyze continuous-time mirror descent applied to sparse phase retrieval, which is the problem of recovering sparse signals from a set of magnitude-only measurements. We apply mirror descent to the unconstrained empirical risk…

Machine Learning · Statistics 2020-10-21 Fan Wu , Patrick Rebeschini

We propose a new discretization of the mirror-Langevin diffusion and give a crisp proof of its convergence. Our analysis uses relative convexity/smoothness and self-concordance, ideas which originated in convex optimization, together with a…

Statistics Theory · Mathematics 2021-10-26 Kwangjun Ahn , Sinho Chewi

We generalize stochastic subgradient descent methods to situations in which we do not receive independent samples from the distribution over which we optimize, but instead receive samples that are coupled over time. We show that as long as…

Optimization and Control · Mathematics 2012-08-02 John C. Duchi , Alekh Agarwal , Mikael Johansson , Michael I. Jordan

The part of the analysis of the convergence rate of the mirror descent method that is connected with the adaptive time-varying step size rules due to Alkousa et al. (MOTOR 2024, pp. 3-18) is corrected. Moreover, a Lipschitz-free mirror…

Optimization and Control · Mathematics 2025-06-03 Bowen Yuan , Mohammad S. Alkousa