相关论文: Continuous-time Discounted Mirror-Descent Dynamics…

In this paper, we provide exponential rates of convergence to the interior Nash equilibrium for continuous-time dual-space game dynamics such as mirror descent (MD) and actor-critic (AC). We perform our analysis in $N$-player continuous…

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)…

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…

Mirror descent is a well established tool for solving convex optimization problems with convex constraints. This article introduces continuous-time mirror descent dynamics for approximating optimal Markov controls for stochastic control…

In this paper we study two-player bilinear zero-sum games with constrained strategy spaces. An instance of natural occurrences of such constraints is when mixed strategies are used, which correspond to a probability simplex constraint. We…

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…

We study the problem of no-regret learning algorithms for general monotone and smooth games and their last-iterate convergence properties. Specifically, we investigate the problem under bandit feedback and strongly uncoupled dynamics, which…

Different types of dynamics have been studied in repeated game play, and one of them which has received much attention recently consists of those based on "no-regret" algorithms from the area of machine learning. It is known that dynamics…

Given a convex optimization problem and its dual, there are many possible first-order algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is…

Gradient-based methods for two-player games produce rich dynamics that can solve challenging problems, yet can be difficult to stabilize and understand. Part of this complexity originates from the discrete update steps given by simultaneous…

Low-complexity non-smooth convex regularizers are routinely used to impose some structure (such as sparsity or low-rank) on the coefficients for linear predictors in supervised learning. Model consistency consists then in selecting the…

Most existing results about \emph{last-iterate convergence} of learning dynamics are limited to two-player zero-sum games, and only apply under rigid assumptions about what dynamics the players follow. In this paper we provide new results…

Learning in multi-player games can model a large variety of practical scenarios, where each player seeks to optimize its own local objective function, which at the same time relies on the actions taken by others. Motivated by the frequent…

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…

Owing to their connection with generative adversarial networks (GANs), saddle-point problems have recently attracted considerable interest in machine learning and beyond. By necessity, most theoretical guarantees revolve around…

As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on $\mathbb{R}^d$ have received their counterpart analog on the Wasserstein space. We…

Many recent AI architectures are inspired by zero-sum games, however, the behavior of their dynamics is still not well understood. Inspired by this, we study standard gradient descent ascent (GDA) dynamics in a specific class of non-convex…

In this paper we describe how imitative logit dynamic (rather popular in population games theory) can be interpreted in terms of mirror descent method (well known in convex optimization). We demonstrate the connection of this two type…

In this paper, we examine the convergence of mirror descent in a class of stochastic optimization problems that are not necessarily convex (or even quasi-convex), and which we call variationally coherent. Since the standard technique of…

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…