Related papers: Mirror descent for constrained stochastic control …
In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to…
We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and…
Attention mechanisms have revolutionized several domains of artificial intelligence, such as natural language processing and computer vision, by enabling models to selectively focus on relevant parts of the input data. While recent work has…
This paper deals with a Tikhonov regularized second-order inertial dynamical system that incorporates time scaling, asymptotically vanishing damping and Hessian-driven damping for solving convex optimization problems. Under appropriate…
We propose a novel continuous-time algorithm for inequality-constrained convex optimization inspired by proportional-integral control. Unlike the popular primal-dual gradient dynamics, our method includes a proportional term to control the…
Stochastic mirror descent (SMD) is a fairly new family of algorithms that has recently found a wide range of applications in optimization, machine learning, and control. It can be considered a generalization of the classical stochastic…
Recently there has been renewed interests in derivative free approaches to stochastic optimization. In this paper, we examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various…
Adaptive control achieves concurrent parameter learning and stable control under uncertainties that are linearly parameterized with known nonlinear features. Nonetheless, it is often difficult to obtain such nonlinear features. To address…
In recent years, attention has been focused on the relationship between black-box optimiza- tion problem and reinforcement learning problem. In this research, we propose the Mirror Descent Search (MDS) algorithm which is applicable both for…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
In view of solving convex optimization problems with noisy gradient input, we analyze the asymptotic behavior of gradient-like flows under stochastic disturbances. Specifically, we focus on the widely studied class of mirror descent schemes…
We address the problem of finding the optimal policy of a constrained Markov decision process (CMDP) using a gradient descent-based algorithm. Previous results have shown that a primal-dual approach can achieve an $\mathcal{O}(1/\sqrt{T})$…
We study the unconstrained and the minimax saddle point variants of the convex multi-stage stochastic programming problem, where consecutive decisions are coupled through the objective functions, rather than through the constraints. We…
This paper studies early-stopped mirror descent applied to noisy sparse phase retrieval, which is the problem of recovering a $k$-sparse signal $\mathbf{x}^\star\in\mathbb{R}^n$ from a set of quadratic Gaussian measurements corrupted by…
In this paper, the optimal convergence rate $O\left(N^{-1/2}\right)$ (where $N$ is the total number of iterations performed by the algorithm), without the presence of a logarithmic factor, is proved for mirror descent algorithms with…
We propose a new policy gradient method, named homotopic policy mirror descent (HPMD), for solving discounted, infinite horizon MDPs with finite state and action spaces. HPMD performs a mirror descent type policy update with an additional…
We propose a new method called the Metropolis-adjusted Mirror Langevin algorithm for approximate sampling from distributions whose support is a compact and convex set. This algorithm adds an accept-reject filter to the Markov chain induced…
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…
Inspired by the remarkable success of large neural networks, there has been significant interest in understanding the generalization performance of over-parameterized models. Substantial efforts have been invested in characterizing how…
We propose some adaptive mirror descent dethods for convex programming problems with delta-subgradients and prove some theoretical results.