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This work studies linear bandits under a new notion of gap-adjusted misspecification and is an extension of Liu et al. (2023). When the underlying reward function is not linear, existing linear bandits work usually relies on a uniform…

We study stochastic linear optimization problem with bandit feedback. The set of arms take values in an $N$-dimensional space and belong to a bounded polyhedron described by finitely many linear inequalities. We provide a lower bound for…

We revisit the challenge of designing online algorithms for the bandit convex optimization problem (BCO) which are also scalable to high dimensional problems. Hence, we consider algorithms that are \textit{projection-free}, i.e., based on…

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…

We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret…

We study the adaptive control of an unknown linear system with a quadratic cost function subject to safety constraints on both the states and actions. The challenges of this problem arise from the tension among safety, exploration,…

In the contextual pricing problem a seller repeatedly obtains products described by an adversarially chosen feature vector in $\mathbb{R}^d$ and only observes the purchasing decisions of a buyer with a fixed but unknown linear valuation…

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…

We study a constrained contextual linear bandit setting, where the goal of the agent is to produce a sequence of policies, whose expected cumulative reward over the course of $T$ rounds is maximum, and each has an expected cost below a…

We study the K-armed dueling bandit problem which is a variation of the classical Multi-Armed Bandit (MAB) problem in which the learner receives only relative feedback about the selected pairs of arms. We propose a new algorithm called…

Hoffman's classical result gives a bound on the distance of a point from a convex and compact polytope in terms of the magnitude of violation of the constraints. Recently, several results showed that Hoffman's bound can be used to derive…

Follow-the-Regularized-Leader (FTRL) algorithms are a popular class of learning algorithms for online linear optimization (OLO) that guarantee sub-linear regret, but the choice of regularizer can significantly impact dimension-dependent…

Online linear programming plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of…

This paper studies the problem of controlling linear dynamical systems subject to point-wise-in-time constraints. We present an algorithm similar to online gradient descent, that can handle time-varying and a priori unknown convex cost…

We revisit the standard perturbation-based approach of Abernethy et al. (2008) in the context of unconstrained Bandit Linear Optimization (uBLO). We show the surprising result that in the unconstrained setting, this approach effectively…

We study time-inhomogeneous episodic reinforcement learning (RL) under general function approximation and sparse rewards. We design a new algorithm, Variance-weighted Optimistic $Q$-Learning (VO$Q$L), based on $Q$-learning and bound its…

In digital health and EdTech, recommendation systems face a significant challenge: users often choose impulsively, in ways that conflict with the platform's long-term payoffs. This misalignment makes it difficult to effectively learn to…

Bandit convex optimization (BCO) is a general framework for online decision making under uncertainty. While tight regret bounds for general convex losses have been established, existing algorithms achieving these bounds have prohibitive…

We study how to adapt to smoothly-varying ('easy') environments in well-known online learning problems where acquiring information is expensive. For the problem of label efficient prediction, which is a budgeted version of prediction with…

Machine learning algorithms are often repeatedly applied to problems with similar structure over and over again. We focus on solving a sequence of bandit optimization tasks and develop LIBO, an algorithm which adapts to the environment by…