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We present an adaptive online gradient descent algorithm to solve online convex optimization problems with long-term constraints , which are constraints that need to be satisfied when accumulated over a finite number of rounds T , but can…
This paper considers the distributed online convex optimization problem with time-varying constraints over a network of agents. This is a sequential decision making problem with two sequences of arbitrarily varying convex loss and…
The performance of online convex optimization algorithms in a dynamic environment is often expressed in terms of the dynamic regret, which measures the decision maker's performance against a sequence of time-varying comparators. In the…
This paper proposes a modular approach that combines the online convex optimization framework and reference governors to solve a constrained control problem featuring time-varying and a priori unknown cost functions. Compared to existing…
The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence ($V_T$) and/or the path-length of the minimizer sequence after $T$ rounds. For strongly convex and smooth…
In online convex optimization, the player aims to minimize regret, or the difference between her loss and that of the best fixed decision in hindsight over the entire repeated game. Algorithms that minimize (standard) regret may converge to…
Universal online learning aims to achieve optimal regret guarantees without requiring prior knowledge of the curvature of online functions. Existing methods have established minimax-optimal regret bounds for universal online learning, where…
Regret has been widely adopted as the metric of choice for evaluating the performance of online optimization algorithms for distributed, multi-agent systems. However, data/model variations associated with agents can significantly impact…
We consider online forecasting problems for non-convex machine learning models. Forecasting introduces several challenges such as (i) frequent updates are necessary to deal with concept drift issues since the dynamics of the environment…
Non-stationary online learning has drawn much attention in recent years. Despite considerable progress, dynamic regret minimization has primarily focused on convex functions, leaving the functions with stronger curvature (e.g., squared or…
This paper describes a new online convex optimization method which incorporates a family of candidate dynamical models and establishes novel tracking regret bounds that scale with the comparator's deviation from the best dynamical model in…
In this paper, we consider the problem of distributed online convex optimization, where a network of local agents aim to jointly optimize a convex function over a period of multiple time steps. The agents do not have any information about…
Projection-free online learning has drawn increasing interest due to its efficiency in solving high-dimensional problems with complicated constraints. However, most existing projection-free online methods focus on minimizing the static…
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…
This paper addresses an online convex optimization problem where the cost function at each step depends on a history of past decisions (i.e., memory), and the decision maker has access to limited predictions of future cost values within a…
In repeated interaction problems with adaptive agents, our objective often requires anticipating and optimizing over the space of possible agent responses. We show that many problems of this form can be cast as instances of online…
We consider a generalization of the celebrated Online Convex Optimization (OCO) framework with adversarial online constraints. In this problem, an online learner interacts with an adversary sequentially over multiple rounds. At the…
A new algorithm for regret minimization in online convex optimization is described. The regret of the algorithm after $T$ time periods is $O(\sqrt{T \log T})$ - which is the minimum possible up to a logarithmic term. In addition, the new…
In this paper, the problem of distributed optimization is studied via a network of agents. Each agent only has access to a stochastic gradient of its own objective function in the previous time, and can communicate with its neighbors via a…
To deal with non-stationary online problems with complex constraints, we investigate the dynamic regret of online Frank-Wolfe (OFW), which is an efficient projection-free algorithm for online convex optimization. It is well-known that in…