Related papers: Nash Regret Guarantees for Linear Bandits

We study the stochastic linear bandit problem with multiple arms over $T$ rounds, where the covariate dimension $d$ may exceed $T$, but each arm-specific parameter vector is $s$-sparse. We begin by analyzing the sequential estimation…

We consider a linear stochastic bandit problem involving $M$ agents that can collaborate via a central server to minimize regret. A fraction $\alpha$ of these agents are adversarial and can act arbitrarily, leading to the following tension:…

In this paper we propose a general methodology to derive regret bounds for randomized multi-armed bandit algorithms. It consists in checking a set of sufficient conditions on the sampling probability of each arm and on the family of…

Symmetry arises in many optimization and decision-making problems, and has attracted considerable attention from the optimization community: By utilizing the existence of such symmetries, the process of searching for optimal solutions can…

This work addresses the problem of regret minimization in non-stochastic multi-armed bandit problems, focusing on performance guarantees that hold with high probability. Such results are rather scarce in the literature since proving them…

Much of the literature on optimal design of bandit algorithms is based on minimization of expected regret. It is well known that designs that are optimal over certain exponential families can achieve expected regret that grows…

We consider bandit optimization of a smooth reward function, where the goal is cumulative regret minimization. This problem has been studied for $\alpha$-H\"older continuous (including Lipschitz) functions with $0<\alpha\leq 1$. Our main…

We consider a linear stochastic bandit problem where the dimension $K$ of the unknown parameter $\theta$ is larger than the sampling budget $n$. In such cases, it is in general impossible to derive sub-linear regret bounds since usual…

Under the uncoupled learning setup, the last-iterate convergence guarantee towards Nash equilibrium is shown to be impossible in many games. This work studies the last-iterate convergence guarantee in general games toward rationalizability,…

Many works have developed no-regret algorithms for contextual bandits with function approximation, where the mean reward function over context-action pairs belongs to a function class. Although there are many approaches to this problem, one…

We study the Gaussian process (GP) bandit problem, whose goal is to minimize regret under an unknown reward function lying in some reproducing kernel Hilbert space (RKHS). The maximum posterior variance analysis is vital in analyzing…

We develop a general theory to optimize the frequentist regret for sequential learning problems, where efficient bandit and reinforcement learning algorithms can be derived from unified Bayesian principles. We propose a novel optimization…

Cascading bandits is a natural and popular model that frames the task of learning to rank from Bernoulli click feedback in a bandit setting. For the case of unstructured rewards, we prove matching upper and lower bounds for the…

Bayesian bandit algorithms with approximate Bayesian inference have been widely used in real-world applications. Despite the superior practical performance, their theoretical justification is less investigated in the literature, especially…

This paper studies batched bandit learning problems for nondegenerate functions. We introduce an algorithm that solves the batched bandit problem for nondegenerate functions near-optimally. More specifically, we introduce an algorithm,…

Bayesian optimization is a framework for global search via maximum a posteriori updates rather than simulated annealing, and has gained prominence for decision-making under uncertainty. In this work, we cast Bayesian optimization as a…

This paper proposes a linear bandit algorithm that is adaptive to environments at two different levels of hierarchy. At the higher level, the proposed algorithm adapts to a variety of types of environments. More precisely, it achieves…

We consider a situation where an agent has $T$ ressources to be allocated to a larger number $N$ of actions. Each action can be completed at most once and results in a stochastic reward with unknown mean. The goal of the agent is to…

We introduce and study a new class of stochastic bandit problems, referred to as predictive bandits. In each round, the decision maker first decides whether to gather information about the rewards of particular arms (so that their rewards…

We study the stochastic multi-armed bandit problem and design new policies that enjoy both worst-case optimality for expected regret and light-tailed risk for regret distribution. Specifically, our policy design (i) enjoys the worst-case…