相关论文: Convergence Rate Analysis of LION

This paper studies a class of adaptive gradient based momentum algorithms that update the search directions and learning rates simultaneously using past gradients. This class, which we refer to as the "Adam-type", includes the popular…

A novel Follow-the-Perturbed-Leader type algorithm is proposed and analyzed for solving general long-term constrained optimization problems in an online manner, where the target and constraint functions are oblivious adversarially generated…

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness…

The analysis in Part I revealed interesting properties for subgradient learning algorithms in the context of stochastic optimization when gradient noise is present. These algorithms are used when the risk functions are non-smooth and…

We initiate the study of algorithms for constraint satisfaction problems with ML oracle advice. We introduce two models of advice and then design approximation algorithms for Max Cut, Max $2$-Lin, and Max $3$-Lin in these models. In…

We study the convergence dynamics of Gradient Descent (GD) in a minimal binary classification setting, consisting of a two-neuron ReLU network and two training instances. We prove that even under these strong simplifying assumptions, while…

Gradient Temporal Difference (GTD) algorithms (Sutton et al., 2008, 2009) are the first $O(d)$ ($d$ is the number features) algorithms that have convergence guarantees for off-policy learning with linear function approximation. Liu et al.…

We study the problem of safe online convex optimization, where the action at each time step must satisfy a set of linear safety constraints. The goal is to select a sequence of actions to minimize the regret without violating the safety…

$Q$-learning is one of the most fundamental reinforcement learning algorithms. It is widely believed that $Q$-learning with linear function approximation (i.e., linear $Q$-learning) suffers from possible divergence until the recent work…

Communication efficiency is a major bottleneck in the applications of distributed networks. To address the problem, the problem of quantized distributed optimization has attracted a lot of attention. However, most of the existing quantized…

We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…

We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth…

Optimal algorithm design for federated learning (FL) remains an open problem. This paper explores the full potential of FL in practical edge computing systems where workers may have different computation and communication capabilities, and…

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 proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…

The Lion optimizer has been a promising competitor with the AdamW for training large AI models, with advantages on memory, computation, and sample efficiency. In this paper, we introduce Distributed Lion, an innovative adaptation of Lion…

We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…

For quasi-linear interface problems with discontinuous diffusion coefficients, the nonconvex objective functional often leads to optimization stagnation in randomized neural network approximations. This paper Proposes a…

We study a robust online convex optimization framework, where an adversary can introduce outliers by corrupting loss functions in an arbitrary number of rounds k, unknown to the learner. Our focus is on a novel setting allowing unbounded…

We consider convex and nonconvex constrained optimization with a partially separable objective function: agents minimize the sum of local objective functions, each of which is known only by the associated agent and depends on the variables…