Related papers: Convergence of Policy Mirror Descent Beyond Compat…
A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…
Theoretical estimates of the convergence rate of many well-known gradient-type optimization methods are based on quadratic interpolation, provided that the Lipschitz condition for the gradient is satisfied. In this article we obtain a…
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…
We propose and study a general framework for regularized Markov decision processes (MDPs) where the goal is to find an optimal policy that maximizes the expected discounted total reward plus a policy regularization term. The extant…
First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias, plays a critical role in…
Masked diffusion models (MDMs) have recently emerged as a novel framework for language modeling. MDMs generate sentences by iteratively denoising masked sequences, filling in [MASK] tokens step by step. Although MDMs support any-order…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
The convergence of deterministic policy gradient under the Hadamard parameterization is studied in the tabular setting and the linear convergence of the algorithm is established. To this end, we first show that the error decreases at an…
Matrix completion has attracted much interest in the past decade in machine learning and computer vision. For low-rank promotion in matrix completion, the nuclear norm penalty is convenient due to its convexity but has a bias problem.…
Learning-to-optimize is an emerging framework that leverages training data to speed up the solution of certain optimization problems. One such approach is based on the classical mirror descent algorithm, where the mirror map is modelled…
This paper is concerned with multi-agent optimization problem. A distributed randomized gradient-free mirror descent (DRGFMD) method is developed by introducing a randomized gradient-free oracle in the mirror descent scheme where the…
Constrained decision-making is essential for designing safe policies in real-world control systems, yet simulated environments often fail to capture real-world adversities. We consider the problem of learning a policy that will maximize the…
We consider the problem of minimizing the sum of an average function of a large number of smooth convex components and a general, possibly non-differentiable, convex function. Although many methods have been proposed to solve this problem…
We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…
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…
Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are generally considered to be intractable for large models. The intractability of these algorithms is to a large extent a…
We make three contributions toward better understanding policy gradient methods in the tabular setting. First, we show that with the true gradient, policy gradient with a softmax parametrization converges at a $O(1/t)$ rate, with constants…
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 paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…
We propose a new family of subgradient- and gradient-based methods which converges with optimal complexity for convex optimization problems whose feasible region is simple enough. This includes cases where the objective function is…