Related papers: Single-Timescale Stochastic Nonconvex-Concave Opti…
Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…
Recently, the centroidal momentum dynamics has received substantial attention to plan dynamically consistent motions for robots with arms and legs in multi-contact scenarios. However, it is also non convex which renders any optimization…
We propose a new stochastic proximal quasi-Newton method for minimizing the sum of two convex functions in the particular context that one of the functions is the average of a large number of smooth functions and the other one is nonsmooth.…
In this paper, we propose two novel non-stationary first-order primal-dual algorithms to solve nonsmooth composite convex optimization problems. Unlike existing primal-dual schemes where the parameters are often fixed, our methods use…
We establish an optimal sample complexity of $O(\epsilon^{-2})$ for obtaining an $\epsilon$-optimal global policy using a single-timescale actor-critic (AC) algorithm in infinite-horizon discounted Markov decision processes (MDPs) with…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal…
We propose an adaptive proximal gradient method for minimizing the sum of two functions, where one is a simple convex function, and the other belongs to one of the three classes: nonconvex smooth, convex nonsmooth, or convex smooth. The key…
Stochastic gradient descent (SGD) with stochastic momentum is popular in nonconvex stochastic optimization and particularly for the training of deep neural networks. In standard SGD, parameters are updated by improving along the path of the…
In this paper, we study a class of stochastic bilevel optimization problems, also known as stochastic simple bilevel optimization, where we minimize a smooth stochastic objective function over the optimal solution set of another stochastic…
This work provides the first finite-time convergence guarantees for linearly constrained stochastic bilevel optimization using only first-order methods, requiring solely gradient information without any Hessian computations or second-order…
This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…
We study a class of non-convex and non-smooth problems with \textit{rank} regularization to promote sparsity in optimal solution. We propose to apply the proximal gradient descent method to solve the problem and accelerate the process with…
Stochastic momentum methods have been widely adopted in training deep neural networks. However, their theoretical analysis of convergence of the training objective and the generalization error for prediction is still under-explored. This…
We study stochastic algorithms for solving nonconvex optimization problems with a convex yet possibly nonsmooth regularizer, which find wide applications in many practical machine learning applications. However, compared to asynchronous…
Stochastic non-smooth convex optimization constitutes a class of problems in machine learning and operations research. This paper considers minimization of a non-smooth function based on stochastic subgradients. When the function has a…
We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the…
Multi-time-scale stochastic approximation is an iterative algorithm for finding the fixed point of a set of $N$ coupled operators given their noisy samples. It has been observed that due to the coupling between the decision variables and…
This paper considers time-average stochastic optimization, where a time average decision vector, an average of decision vectors chosen in every time step from a time-varying (possibly non-convex) set, minimizes a convex objective function…
This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a…