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We revisit the question of reducing online learning to approximate optimization of the offline problem. In this setting, we give two algorithms with near-optimal performance in the full information setting: they guarantee optimal regret and…

We study finite-time horizon continuous-time linear-quadratic reinforcement learning problems in an episodic setting, where both the state and control coefficients are unknown to the controller. We first propose a least-squares algorithm…

We consider the general problem of online convex optimization with time-varying additive constraints in the presence of predictions for the next cost and constraint functions. A novel primal-dual algorithm is designed by combining a…

In this paper, we propose a fast reinforcement learning (RL) control algorithm that enables online control of large-scale networked dynamic systems. RL is an effective way of designing model-free linear quadratic regulator (LQR) controllers…

Motivated by the EU's "Right To Be Forgotten" regulation, we initiate a study of statistical data deletion problems where users' data are accessible only for a limited period of time. This setting is formulated as an online supervised…

In online learning the performance of an algorithm is typically compared to the performance of a fixed function from some class, with a quantity called regret. Forster proposed a last-step min-max algorithm which was somewhat simpler than…

Quantile (and, more generally, KL) regret bounds, such as those achieved by NormalHedge (Chaudhuri, Freund, and Hsu 2009) and its variants, relax the goal of competing against the best individual expert to only competing against a majority…

Smoothness is known to be crucial for acceleration in offline optimization, and for gradient-variation regret minimization in online learning. Interestingly, these two problems are actually closely connected -- accelerated optimization can…

We consider online imitation learning (OIL), where the task is to find a policy that imitates the behavior of an expert via active interaction with the environment. We aim to bridge the gap between the theory and practice of policy…

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…

Optimization theory has been widely studied in academia and finds a large variety of applications in industry. The different optimization models in their discrete and/or continuous settings have catered to a rich source of research…

We study a general online linear optimization problem(OLO). At each round, a subset of objects from a fixed universe of $n$ objects is chosen, and a linear cost associated with the chosen subset is incurred. To measure the performance of…

We investigate the problem of online convex optimization with unknown delays, in which the feedback of a decision arrives with an arbitrary delay. Previous studies have presented a delayed variant of online gradient descent (OGD), and…

In this paper, we formalise order-robust optimisation as an instance of online learning minimising simple regret, and propose Vroom, a zero'th order optimisation algorithm capable of achieving vanishing regret in non-stationary…

Much of the work in online learning focuses on the study of sublinear upper bounds on the regret. In this work, we initiate the study of best-case lower bounds in online convex optimization, wherein we bound the largest improvement an…

In offline reinforcement learning (RL), a learner leverages prior logged data to learn a good policy without interacting with the environment. A major challenge in applying such methods in practice is the lack of both theoretically…

We consider the problem of controlling an unknown linear time-invariant dynamical system from a single chain of black-box interactions, with no access to resets or offline simulation. Under the assumption that the system is controllable, we…

Reinforcement Learning (RL) has achieved tremendous success in recent years. However, the classical foundations of RL do not account for the risk sensitivity of the objective function, which is critical in various fields, including…

Among recent insights into learning quantum states, online learning and shadow tomography procedures are notable for their ability to accurately predict expectation values even of adaptively chosen observables. In contrast to the state…

In this paper, we consider unregularized online learning algorithms in a Reproducing Kernel Hilbert Spaces (RKHS). Firstly, we derive explicit convergence rates of the unregularized online learning algorithms for classification associated…