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Recently, there has been a growing research interest in the analysis of dynamic regret, which measures the performance of an online learner against a sequence of local minimizers. By exploiting the strong convexity, previous studies have…
In this paper, we consider the sequential decision problem where the goal is to minimize the general dynamic regret on a complete Riemannian manifold. The task of offline optimization on such a domain, also known as a geodesic metric space,…
The Quickest Transshipment Problem is to route flow as quickly as possible from sources with supplies to sinks with demands in a network with capacities and transit times on the arcs. It is of fundamental importance for numerous…
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 an optimisation-based method for synthesising a dynamic regret optimal controller for linear systems with potentially adversarial disturbances and known or adversarial initial conditions. The dynamic regret is defined as the…
We consider the problem of sequentially maximizing an unknown function $f$ over a set of actions of the form $(s,\mathbf{x})$, where the selected actions must satisfy a safety constraint with respect to an unknown safety function $g$. We…
In this paper, we consider the problem of scheduling jobs on parallel identical machines, where the processing times of jobs are uncertain: only interval bounds of processing times are known. The optimality criterion of a schedule is the…
In online learning, the dynamic regret metric chooses the reference (optimal) solution that may change over time, while the typical (static) regret metric assumes the reference solution to be constant over the whole time horizon. The…
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 a system consisting of a single transmitter/receiver pair and $N$ channels over which they may communicate. Packets randomly arrive to the transmitter's queue and wait to be successfully sent to the receiver. The transmitter may…
We consider the problem of distributed online optimization, with a group of learners connected via a dynamic communication graph. The goal of the learners is to track the global minimizer of a sum of time-varying loss functions in a…
We consider the problem of joint routing and scheduling in queueing networks, where the edge transmission costs are unknown. At each time-slot, the network controller receives noisy observations of transmission costs only for those edges it…
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…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
We investigate the problem of online learning, which has gained significant attention in recent years due to its applicability in a wide range of fields from machine learning to game theory. Specifically, we study the online optimization of…
We study dynamic clustering problems from the perspective of online learning. We consider an online learning problem, called \textit{Dynamic $k$-Clustering}, in which $k$ centers are maintained in a metric space over time (centers may…
The minmax multiple traveling salesman problem involves minimizing the longest tour among a set of tours. The problem is of great practical interest because it can be used to formulate several real-life applications. To solve this…
Partial monitoring is a general model for sequential learning with limited feedback formalized as a game between two players. In this game, the learner chooses an action and at the same time the opponent chooses an outcome, then the learner…
This article focuses on a biobjective extension of the maximum flow network interdiction problem, where each arc in the network is associated with two capacity values. Two maximum flows from a source to a sink are to be computed…
We study the Stochastic Shortest Path (SSP) problem in which an agent has to reach a goal state in minimum total expected cost. In the learning formulation of the problem, the agent has no prior knowledge about the costs and dynamics of the…