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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…
We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and…
An abundance of recent impossibility results establish that regret minimization in Markov games with adversarial opponents is both statistically and computationally intractable. Nevertheless, none of these results preclude the possibility…
We study the problem of system identification and adaptive control in partially observable linear dynamical systems. Adaptive and closed-loop system identification is a challenging problem due to correlations introduced in data collection.…
In this paper, we study adaptive online convex optimization, and aim to design a universal algorithm that achieves optimal regret bounds for multiple common types of loss functions. Existing universal methods are limited in the sense that…
We show how to take any two parameter-free online learning algorithms with different regret guarantees and obtain a single algorithm whose regret is the minimum of the two base algorithms. Our method is embarrassingly simple: just add the…
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…
This paper studies online nonstochastic control problems with adversarial and static constraints. We propose online nonstochastic control algorithms that achieve both sublinear regret and sublinear adversarial constraint violation while…
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…
In learning theory, the performance of an online policy is commonly measured in terms of the static regret metric, which compares the cumulative loss of an online policy to that of an optimal benchmark in hindsight. In the definition of…
This paper introduces \textit{online bilevel optimization} in which a sequence of time-varying bilevel problems is revealed one after the other. We extend the known regret bounds for online single-level algorithms to the bilevel setting.…
This paper considers the distributed online bandit optimization problem with nonconvex loss functions over a time-varying digraph. This problem can be viewed as a repeated game between a group of online players and an adversary. At each…
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…
Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding of…
Some of the most compelling applications of online convex optimization, including online prediction and classification, are unconstrained: the natural feasible set is R^n. Existing algorithms fail to achieve sub-linear regret in this…
We study the problem of online learning and online regret minimization when samples are drawn from a general unknown non-stationary process. We introduce the concept of a dynamic changing process with cost $K$, where the conditional…
The growing prevalence of drift and shocks in modern decision environments exposes a gap between classical optimization theory and real-world practice. Standard models assume fixed objectives, yet organizations from hospitals to power grids…
Most methods for decision-theoretic online learning are based on the Hedge algorithm, which takes a parameter called the learning rate. In most previous analyses the learning rate was carefully tuned to obtain optimal worst-case…
We consider the problem of minimizing different notions of swap regret in online optimization. These forms of regret are tightly connected to correlated equilibrium concepts in games, and have been more recently shown to guarantee…
In the online non-stochastic control problem, an agent sequentially selects control inputs for a linear dynamical system when facing unknown and adversarially selected convex costs and disturbances. A common metric for evaluating control…