Related papers: Mirror descent for constrained stochastic control …
This paper deals with a new Tikhonov regularized primal-dual dynamical system with variable mass and Hessian-driven damping for solving a convex optimization problem with linear equality constraints. The system features several…
We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics.…
In this paper, we propose a class of general second-order primal-dual dynamical systems with Tikhonov regularization and Hessian-driven damping for solving convex-concave bilinear saddle point problems. The proposed dynamical system…
The training of modern machine learning models often consists in solving high-dimensional non-convex optimisation problems that are subject to large-scale data. In this context, momentum-based stochastic optimisation algorithms have become…
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…
We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds…
In this paper, we propose a second-order extension of the continuous-time game-theoretic mirror descent (MD) dynamics, referred to as MD2, which provably converges to mere (but not necessarily strict) variationally stable states (VSS)…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
In a real Hilbert space setting, we reconsider the classical Arrow-Hurwicz differential system in view of solving linearly constrained convex minimization problems. We investigate the asymptotic properties of the differential system and…
In this paper, we propose Distributed Mirror Descent (DMD) algorithm for constrained convex optimization problems on a (strongly-)connected multi-agent network. We assume that each agent has a private objective function and a constraint…
Despite its popularity in the reinforcement learning community, a provably convergent policy gradient method for continuous space-time control problems with nonlinear state dynamics has been elusive. This paper proposes proximal gradient…
We consider infinite-horizon discounted Markov decision problems with finite state and action spaces and study the convergence rates of the projected policy gradient method and a general class of policy mirror descent methods, all with…
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 problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
The present article studies the minimization of convex, L-smooth functions defined on a separable real Hilbert space. We analyze regularized stochastic gradient descent (reg-SGD), a variant of stochastic gradient descent that uses a…
Dual-based proportional-integral-derivative (PID) controllers are often employed in practice to solve online allocation problems with global constraints, such as budget pacing in online advertising. However, controllers are used in a…
In this work, we investigate the idea of variance reduction by studying its properties with general adaptive mirror descent algorithms in nonsmooth nonconvex finite-sum optimization problems. We propose a simple yet generalized framework…
We study a continuous-time dynamical system which arises as the limit of a broad class of nonlinearly preconditioned gradient methods. Under mild assumptions, we establish existence of global solutions and derive Lyapunov-based convergence…