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In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
As application demands for online convex optimization accelerate, the need for designing new methods that simultaneously cover a large class of convex functions and impose the lowest possible regret is highly rising. Known online…
We study the control of finite-state systems driven by exogenous disturbances, and design causal policies that track the performance of a lookahead benchmark controller. This objective is formalized through dynamic regret, so that favorable…
We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected,…
We investigate online convex optimization in changing environments, and choose the adaptive regret as the performance measure. The goal is to achieve a small regret over every interval so that the comparator is allowed to change over time.…
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…
We derive a novel asymptotic problem-dependent lower-bound for regret minimization in finite-horizon tabular Markov Decision Processes (MDPs). While, similar to prior work (e.g., for ergodic MDPs), the lower-bound is the solution to an…
In this paper, we develop a unified framework for analyzing the tracking error and dynamic regret of inexact online optimization methods under a variety of settings. Specifically, we leverage the quadratic constraint approach from control…
The study of first-order optimization is sensitive to the assumptions made on the objective functions. These assumptions induce complexity classes which play a key role in worst-case analysis, including the fundamental concept of algorithm…
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding of…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
Algorithmic reproducibility measures the deviation in outputs of machine learning algorithms upon minor changes in the training process. Previous work suggests that first-order methods would need to trade-off convergence rate (gradient…
Gradient descent optimization algorithms, while increasingly popular, are often used as black-box optimizers, as practical explanations of their strengths and weaknesses are hard to come by. This article aims to provide the reader with…
We revisit the classic regret-minimization problem in the stochastic multi-armed bandit setting when the arm-distributions are allowed to be heavy-tailed. Regret minimization has been well studied in simpler settings of either bounded…
Non-stationary online learning has drawn much attention in recent years. In particular, dynamic regret and adaptive regret are proposed as two principled performance measures for online convex optimization in non-stationary environments. To…
We present new algorithms for online convex optimization over unbounded domains that obtain parameter-free regret in high-probability given access only to potentially heavy-tailed subgradient estimates. Previous work in unbounded domains…
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop…
First-order methods with momentum such as Nesterov's fast gradient method are very useful for convex optimization problems, but can exhibit undesirable oscillations yielding slow convergence rates for some applications. An adaptive…
We study online learning in constrained Markov decision processes (CMDPs) in which rewards and constraints may be either stochastic or adversarial. In such settings, Stradi et al.(2024) proposed the first best-of-both-worlds algorithm able…