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We investigate Stochastic Mirror Descent (SMD) with matrix parameters and vector-valued predictions, a framework relevant to multi-class classification and matrix completion problems. Focusing on the overparameterized regime, where the…
This paper studies the policy mirror descent (PMD) method, which is a general policy optimization framework in reinforcement learning and can cover a wide range of policy gradient methods by specifying difference mirror maps. Existing…
Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…
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…
In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning. Our algorithmic framework updates the primal variable…
Improving sample efficiency has been a longstanding goal in reinforcement learning. This paper proposes $\mathtt{VRMPO}$ algorithm: a sample efficient policy gradient method with stochastic mirror descent. In $\mathtt{VRMPO}$, a novel…
For solving pseudo-convex global optimization problems, we present a novel fully adaptive steepest descent method (or ASDM) without any hard-to-estimate parameters. For the step-size regulation in an $\varepsilon$-normalized direction, we…
Sharpness-aware minimization (SAM) is a recently proposed training method that seeks to find flat minima in deep learning, resulting in state-of-the-art performance across various domains. Instead of minimizing the loss of the current…
Given a nonsmooth, nonconvex minimization problem, we consider algorithms that iteratively sample and minimize stochastic convex models of the objective function. Assuming that the one-sided approximation quality and the variation of the…
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 develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting…
In this paper, we design an inertial accelerated primal-dual algorithm to address the convex-concave saddle point problem, which is formulated as $\min_{x}\max_{y} f(x) + \langle Kx, y \rangle - g(y)$. Remarkably, both functions $f$ and $g$…
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…
We present new policy mirror descent (PMD) methods for solving reinforcement learning (RL) problems with either strongly convex or general convex regularizers. By exploring the structural properties of these overall highly nonconvex…
Stochastic nonconvex-concave min-max saddle point problems appear in many machine learning and control problems including distributionally robust optimization, generative adversarial networks, and adversarial learning. In this paper, we…
SGD with momentum (SGDM) has been widely applied in many machine learning tasks, and it is often applied with dynamic stepsizes and momentum weights tuned in a stagewise manner. Despite of its empirical advantage over SGD, the role of…
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 consider solving saddle point problems using two variants of Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent (OGDA) methods. We show that both of these algorithms admit a…
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 studies first order methods for solving smooth minimax optimization problems $\min_x \max_y g(x,y)$ where $g(\cdot,\cdot)$ is smooth and $g(x,\cdot)$ is concave for each $x$. In terms of $g(\cdot,y)$, we consider two settings --…