Related papers: Target Mirror Descent: A Unifying Framework for So…
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…
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
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…
Recent work by Woodworth et al. (2020) shows that the optimization dynamics of gradient descent for overparameterized problems can be viewed as low-dimensional dual dynamics induced by a mirror map, explaining the implicit regularization…
Learning-to-optimize (L2O) is an emerging research area in large-scale optimization with applications in data science. Recently, researchers have proposed a novel L2O framework called learned mirror descent (LMD), based on the classical…
Policy mirror descent (PMD) is a general policy optimization framework in reinforcement learning, which can cover a wide range of typical policy optimization methods by specifying different mirror maps. Existing analysis of PMD requires…
Online mirror descent (OMD) and dual averaging (DA) -- two fundamental algorithms for online convex optimization -- are known to have very similar (and sometimes identical) performance guarantees when used with a fixed learning rate. Under…
Policy Mirror Descent (PMD) has emerged as a unifying framework in reinforcement learning (RL) by linking policy gradient methods with a first-order optimization method known as mirror descent. At its core, PMD incorporates two key…
This paper proposes a payoff perturbation technique for the Mirror Descent (MD) algorithm in games where the gradient of the payoff functions is monotone in the strategy profile space, potentially containing additive noise. The optimistic…
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…
We provide theoretical guarantees for convergence of discrete-time policy mirror descent with inexact advantage functions updated using temporal difference (TD) learning for entropy regularised MDPs in Polish state and action spaces. We…
We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective…
This paper seeks to address how to solve non-smooth convex and strongly convex optimization problems with functional constraints. The introduced Mirror Descent (MD) method with adaptive stepsizes is shown to have a better convergence rate…
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…
Despite perfectly interpolating the training data, deep neural networks (DNNs) can often generalize fairly well, in part due to the "implicit regularization" induced by the learning algorithm. Nonetheless, various forms of regularization,…
We study two variants of the mirror descent-ascent (MDA) algorithm for solving min-max problems on the space of measures: simultaneous and alternating. We work under assumptions of convexity-concavity and relative smoothness of the payoff…
Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational…
Optimisers are an essential component for training machine learning models, and their design influences learning speed and generalisation. Several studies have attempted to learn more effective gradient-descent optimisers via solving a…
We introduce and analyze a new family of first-order optimization algorithms which generalizes and unifies both mirror descent and dual averaging. Within the framework of this family, we define new algorithms for constrained optimization…
Policy optimization, which finds the desired policy by maximizing value functions via optimization techniques, lies at the heart of reinforcement learning (RL). In addition to value maximization, other practical considerations arise as…