Related papers: A Continuous-Time Nesterov Accelerated Gradient Me…
Recent literature has made much progress in understanding \emph{online LQR}: a modern learning-theoretic take on the classical control problem in which a learner attempts to optimally control an unknown linear dynamical system with fully…
In this paper, we focus on a theory-practice gap for Adam and its variants (AMSgrad, AdamNC, etc.). In practice, these algorithms are used with a constant first-order moment parameter $\beta_{1}$ (typically between $0.9$ and $0.99$). In…
We consider a family of learning strategies for online optimization problems that evolve in continuous time and we show that they lead to no regret. From a more traditional, discrete-time viewpoint, this continuous-time approach allows us…
In this paper, we consider an online distributed composite optimization problem over a time-varying multi-agent network that consists of multiple interacting nodes, where the objective function of each node consists of two parts: a loss…
This paper presents a new framework for analyzing and designing no-regret algorithms for dynamic (possibly adversarial) systems. The proposed framework generalizes the popular online convex optimization framework and extends it to its…
We consider the problem of the Zinkevich (2003)-style dynamic regret minimization in online learning with exp-concave losses. We show that whenever improper learning is allowed, a Strongly Adaptive online learner achieves the dynamic regret…
This paper addresses the design and analysis of feedback-based online algorithms to control systems or networked systems based on performance objectives and engineering constraints that may evolve over time. The emerging time-varying convex…
Nowadays, online learning is an appealing learning paradigm, which is of great interest in practice due to the recent emergence of large scale applications such as online advertising placement and online web ranking. Standard online…
This paper considers distributed online convex optimization with adversarial constraints. In this setting, a network of agents makes decisions at each round, and then only a portion of the loss function and a coordinate block of the…
We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is desirable,…
We investigate distributed online convex optimization with compressed communication, where $n$ learners connected by a network collaboratively minimize a sequence of global loss functions using only local information and compressed data…
We propose computationally tractable accelerated first-order methods for Riemannian optimization, extending the Nesterov accelerated gradient (NAG) method. For both geodesically convex and geodesically strongly convex objective functions,…
We investigate constrained online convex optimization, in which decisions must belong to a fixed and typically complicated domain, and are required to approximately satisfy additional time-varying constraints over the long term. In this…
This paper considers the problem of online trajectory design under time-varying environments. We formulate the general trajectory optimization problem within the framework of time-varying constrained convex optimization and proposed a novel…
This paper studies online convex optimization with stochastic constraints. We propose a variant of the drift-plus-penalty algorithm that guarantees $O(\sqrt{T})$ expected regret and zero constraint violation, after a fixed number of…
This paper addresses the distributed online control problem over a network of linear time-invariant (LTI) systems (with possibly unknown dynamics) in the presence of adversarial perturbations. There exists a global network cost that is…
Recursive least-squares algorithms often use forgetting factors as a heuristic to adapt to non-stationary data streams. The first contribution of this paper rigorously characterizes the effect of forgetting factors for a class of online…
We consider an online learning problem on a continuum. A decision maker is given a compact feasible set $S$, and is faced with the following sequential problem: at iteration~$t$, the decision maker chooses a distribution $x^{(t)} \in…
Nesterov's accelerated gradient method (NAG) is widely used in problems with machine learning background including deep learning, and is corresponding to a continuous-time differential equation. From this connection, the property of the…
Various distributed gradient descent algorithms for multi-agent optimization have incorporated the Nesterov accelerated gradient method, where the use of momentum enhances convergence rates. These algorithms have found broad applications in…