Related papers: Regret Analysis: a control perspective
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…
We study online decision making problems under resource constraints, where both reward and cost functions are drawn from distributions that may change adversarially over time. We focus on two canonical settings: $(i)$ online resource…
A natural goal when designing online learning algorithms for non-stationary environments is to bound the regret of the algorithm in terms of the temporal variation of the input sequence. Intuitively, when the variation is small, it should…
A constrained version of the online convex optimization (OCO) problem is considered. With slotted time, for each slot, first an action is chosen. Subsequently the loss function and the constraint violation penalty evaluated at the chosen…
Inspired by online learning, data-dependent regret has recently been proposed as a criterion for controller design. In the regret-optimal control paradigm, causal controllers are designed to minimize regret against a hypothetical optimal…
The regret bound of an optimization algorithms is one of the basic criteria for evaluating the performance of the given algorithm. By inspecting the differences between the regret bounds of traditional algorithms and adaptive one, we…
To cope with changing environments, recent developments in online learning have introduced the concepts of adaptive regret and dynamic regret independently. In this paper, we illustrate an intrinsic connection between these two concepts by…
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…
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 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…
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop…
This paper considers online convex optimization with long term constraints, where constraints can be violated in intermediate rounds, but need to be satisfied in the long run. The cumulative constraint violation is used as the metric to…
Many techniques for online optimization problems involve making decisions based solely on presently available information: fewer works take advantage of potential predictions. In this paper, we discuss the problem of online convex…
In the setting of online learning, Implicit algorithms turn out to be highly successful from a practical standpoint. However, the tightest regret analyses only show marginal improvements over Online Mirror Descent. In this work, we shed…
We consider the problem of online learning in Linear Quadratic Control systems whose state transition and state-action transition matrices $A$ and $B$ may be initially unknown. We devise an online learning algorithm and provide guarantees…
Online learning algorithms for dynamical systems provide finite time guarantees for control in the presence of sequentially revealed cost functions. We pose the classical linear quadratic tracking problem in the framework of online…
We investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
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…
This paper addresses the distributed online control problem over a network of linear time-invariant (LTI) systems (with possibly unknown dynamics) in the presence of adversarial perturbations. There exists a global network cost that is…
We study the problem of adaptively controlling a known discrete-time nonlinear system subject to unmodeled disturbances. We prove the first finite-time regret bounds for adaptive nonlinear control with matched uncertainty in the stochastic…