Related papers: On the Convergence Time of Dual Subgradient Method…
We study the iteration complexity of the optimistic gradient descent-ascent (OGDA) method and the extra-gradient (EG) method for finding a saddle point of a convex-concave unconstrained min-max problem. To do so, we first show that both…
Primal-dual algorithm (PDA) is a classic and popular scheme for convex-concave saddle point problems. It is universally acknowledged that the proximal terms in the subproblems about the primal and dual variables are crucial to the…
We show that accelerated gradient descent, averaged gradient descent and the heavy-ball method for non-strongly-convex problems may be reformulated as constant parameter second-order difference equation algorithms, where stability of the…
Stochastic gradient methods (SGMs) have been widely used for solving stochastic optimization problems. A majority of existing works assume no constraints or easy-to-project constraints. In this paper, we consider convex stochastic…
This work considers gradient descent for L-smooth convex optimization with stepsizes larger than the classic regime where descent can be ensured. The stepsize schedules considered are similar to but differ slightly from the recent silver…
Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…
In this work, we first consider distributed convex constrained optimization problems where the objective function is encoded by multiple local and possibly nonsmooth objectives privately held by a group of agents, and propose a distributed…
This paper considers time-average optimization, where a decision vector is chosen every time step within a (possibly non-convex) set, and the goal is to minimize a convex function of the time averages subject to convex constraints on these…
We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function…
In this paper, the optimal convergence rate $O\left(N^{-1/2}\right)$ (where $N$ is the total number of iterations performed by the algorithm), without the presence of a logarithmic factor, is proved for mirror descent algorithms with…
Temporal-difference learning with gradient correction (TDC) is a two time-scale algorithm for policy evaluation in reinforcement learning. This algorithm was initially proposed with linear function approximation, and was later extended to…
This paper considers the problem of minimizing the time average of a controlled stochastic process subject to multiple time average constraints on other related processes. The probability distribution of the random events in the system is…
The push-sum based subgradient is an important method for distributed convex optimization over unbalanced directed graphs, which is known to converge at a rate of $O(\ln t/\sqrt{t})$. This paper shows that the subgradient-push algorithm…
This paper considers the fundamental convergence time for opportunistic scheduling over time-varying channels. The channel state probabilities are unknown and algorithms must perform some type of estimation and learning while they make…
In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…
A popular approach to the MAP inference problem in graphical models is to minimize an upper bound obtained from a dual linear programming or Lagrangian relaxation by (block-)coordinate descent. This is also known as convex/convergent…
We study the worst-case convergence rates of the proximal gradient method for minimizing the sum of a smooth strongly convex function and a non-smooth convex function whose proximal operator is available. We establish the exact worst-case…
In this note we give a simple proof for the convergence of stochastic gradient (SGD) methods on $\mu$-convex functions under a (milder than standard) $L$-smoothness assumption. We show that for carefully chosen stepsizes SGD converges after…
In this paper, we consider conditional gradient methods. These are methods that use a linear minimization oracle, which, for a given vector $p \in \mathbb{R}^n$, computes the solution of the subproblem $$\arg \min_{x\in X}{\langle p,x…
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…