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This work addresses the fundamental problem of unbounded metric movement costs in bandit online convex optimization, by considering high-dimensional dynamic quadratic hitting costs and $\ell_2$-norm switching costs in a noisy bandit…
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…
Sequential prediction problems such as imitation learning, where future observations depend on previous predictions (actions), violate the common i.i.d. assumptions made in statistical learning. This leads to poor performance in theory and…
Towards bridging classical optimal control and online learning, regret minimization has recently been proposed as a control design criterion. This competitive paradigm penalizes the loss relative to the optimal control actions chosen by a…
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…
This paper revisits the online learning approach to inverse linear optimization studied by B\"armann et al. (2017), where the goal is to infer an unknown linear objective function of an agent from sequential observations of the agent's…
In this paper, the online variants of the classical Frank-Wolfe algorithm are considered. We consider minimizing the regret with a stochastic cost. The online algorithms only require simple iterative updates and a non-adaptive step size…
We study the problems of offline and online contextual optimization with feedback information, where instead of observing the loss, we observe, after-the-fact, the optimal action an oracle with full knowledge of the objective function would…
A well-studied generalization of the standard online convex optimization (OCO) framework is constrained online convex optimization (COCO). In COCO, on every round, a convex cost function and a convex constraint function are revealed to the…
An online policy learning problem of linear control systems is studied. In this problem, the control system is known and linear, and a sequence of quadratic cost functions is revealed to the controller in hindsight, and the controller…
We propose a novel change point detection approach for online learning control with full information feedback (state, disturbance, and cost feedback) for unknown time-varying dynamical systems. We show that our algorithm can achieve a…
We study online prediction where regret of the algorithm is measured against a benchmark defined via evolving constraints. This framework captures online prediction on graphs, as well as other prediction problems with combinatorial…
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…
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…
In this paper we study the mincut problem in the online setting. We consider two distinct models: A) competitive analysis and B) regret analysis. In the competitive setting we consider the vertex arrival model; whenever a new vertex arrives…
To deal with changing environments, a new performance measure -- adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms…
We investigate online Markov Decision Processes (MDPs) with adversarially changing loss functions and known transitions. We choose dynamic regret as the performance measure, defined as the performance difference between the learner and any…
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…
Understanding how to efficiently learn while adhering to safety constraints is essential for using online reinforcement learning in practical applications. However, proving rigorous regret bounds for safety-constrained reinforcement…
We study the problem of online convex optimization (OCO) under unknown linear constraints that are either static, or stochastically time-varying. For this problem, we introduce an algorithm that we term Optimistically Safe OCO (OSOCO) and…