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We analyze and evaluate an online gradient descent algorithm with adaptive per-coordinate adjustment of learning rates. Our algorithm can be thought of as an online version of batch gradient descent with a diagonal preconditioner. This…
The theory of deep learning focuses almost exclusively on supervised learning, non-convex optimization using stochastic gradient descent, and overparametrized neural networks. It is common belief that the optimizer dynamics, network…
This paper considers the distributed online convex-concave optimization with constraint sets over a multiagent network, in which each agent autonomously generates a series of decision pairs through a designable mechanism to cooperatively…
In this paper, we consider the problem of prediction with expert advice in dynamic environments. We choose tracking regret as the performance metric and develop two adaptive and efficient algorithms with data-dependent tracking regret…
We study online inverse linear optimization, also known as contextual recommendation, where a learner sequentially infers an agent's hidden objective vector from observed optimal actions over feasible sets that change over time. The learner…
We present safe control of partially-observed linear time-varying systems in the presence of unknown and unpredictable process and measurement noise. We introduce a control algorithm that minimizes dynamic regret, i.e., that minimizes the…
Recently, much work has been done on extending the scope of online learning and incremental stochastic optimization algorithms. In this paper we contribute to this effort in two ways: First, based on a new regret decomposition and a…
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…
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…
We develop a reduction-based framework for online learning with delayed feedback that recovers and improves upon existing results for both first-order and bandit convex optimization. Our approach introduces a continuous-time model under…
This paper investigates the problem of regret minimization in linear time-varying (LTV) dynamical systems. Due to the simultaneous presence of uncertainty and non-stationarity, designing online control algorithms for unknown LTV systems…
We introduce a new online convex optimization algorithm that adaptively chooses its regularization function based on the loss functions observed so far. This is in contrast to previous algorithms that use a fixed regularization function…
Online multi-agent control problems, where many agents pursue competing and time-varying objectives, are widespread in domains such as autonomous robotics, economics, and energy systems. In these settings, robustness to adversarial…
Performance of adaptive control policies is assessed through the regret with respect to the optimal regulator, which reflects the increase in the operating cost due to uncertainty about the dynamics parameters. However, available results in…
Time-varying systems are a challenge in many scientific and engineering areas. Usually, estimation of time-varying parameters or signals must be performed online, which calls for the development of responsive online algorithms. In this…
We study the problem of adaptive control of the linear quadratic regulator for systems in very high, or even infinite dimension. We demonstrate that while sublinear regret requires finite dimensional inputs, the ambient state dimension of…
Recently, several universal methods have been proposed for online convex optimization which can handle convex, strongly convex and exponentially concave cost functions simultaneously. However, most of these algorithms have been designed…
We address the problem of learning to control an unknown nonlinear dynamical system through sequential interactions. Motivated by high-stakes applications in which mistakes can be catastrophic, such as robotics and healthcare, we study…
We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller…
We consider the problem of controlling an unknown linear dynamical system in the presence of (nonstochastic) adversarial perturbations and adversarial convex loss functions. In contrast to classical control, the a priori determination of an…