Related papers: Simple Combinatorial Algorithms for Combinatorial …
We consider the framework of stochastic multi-armed bandit problems and study the possibilities and limitations of forecasters that perform an on-line exploration of the arms. These forecasters are assessed in terms of their simple regret,…
We consider the stochastic bandit problem in the sublinear space setting, where one cannot record the win-loss record for all $K$ arms. We give an algorithm using $O(1)$ words of space with regret \[ \sum_{i=1}^{K}\frac{1}{\Delta_i}\log…
We consider stochastic multi-armed bandit problems where the expected reward is a Lipschitz function of the arm, and where the set of arms is either discrete or continuous. For discrete Lipschitz bandits, we derive asymptotic problem…
We address the problem of stochastic combinatorial semi-bandits, where a player selects among P actions from the power set of a set containing d base items. Adaptivity to the problem's structure is essential in order to obtain optimal…
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…
Linear bandit algorithms yield $\tilde{\mathcal{O}}(n\sqrt{T})$ pseudo-regret bounds on compact convex action sets $\mathcal{K}\subset\mathbb{R}^n$ and two types of structural assumptions lead to better pseudo-regret bounds. When…
In the classic multi-armed bandits problem, the goal is to have a policy for dynamically operating arms that each yield stochastic rewards with unknown means. The key metric of interest is regret, defined as the gap between the expected…
This paper introduces and addresses a wide class of stochastic bandit problems where the function mapping the arm to the corresponding reward exhibits some known structural properties. Most existing structures (e.g. linear, Lipschitz,…
We study a regret minimization problem with the existence of multiple best/near-optimal arms in the multi-armed bandit setting. We consider the case when the number of arms/actions is comparable or much larger than the time horizon, and…
Combinatorial Multi-Armed Bandit with fairness constraints is a framework where multiple arms form a super arm and can be pulled in each round under uncertainty to maximize cumulative rewards while ensuring the minimum average reward…
We study agents communicating over an underlying network by exchanging messages, in order to optimize their individual regret in a common nonstochastic multi-armed bandit problem. We derive regret minimization algorithms that guarantee for…
Motivated by models of human decision making proposed to explain commonly observed deviations from conventional expected value preferences, we formulate two stochastic multi-armed bandit problems with distorted probabilities on the reward…
We consider a novel multi-armed bandit framework where the rewards obtained by pulling the arms are functions of a common latent random variable. The correlation between arms due to the common random source can be used to design a…
The Colonel Blotto game is a renowned resource allocation problem with a long-standing literature in game theory (almost 100 years). However, its scope of application is still restricted by the lack of studies on the incomplete-information…
I present the first algorithm for stochastic finite-armed bandits that simultaneously enjoys order-optimal problem-dependent regret and worst-case regret. Besides the theoretical results, the new algorithm is simple, efficient and…
We study finite-armed stochastic bandits where the rewards of each arm might be correlated to those of other arms. We introduce a novel phased algorithm that exploits the given structure to build confidence sets over the parameters of the…
In this work, we extend the concept of the $p$-mean welfare objective from social choice theory (Moulin 2004) to study $p$-mean regret in stochastic multi-armed bandit problems. The $p$-mean regret, defined as the difference between the…
We consider a novel stochastic multi-armed bandit setting, where playing an arm makes it unavailable for a fixed number of time slots thereafter. This models situations where reusing an arm too often is undesirable (e.g. making the same…
Influence maximization, adaptive routing, and dynamic spectrum allocation all require choosing the right action from a large set of alternatives. Thanks to the advances in combinatorial optimization, these and many similar problems can be…
This paper considers stochastic linear bandits with general nonlinear constraints. The objective is to maximize the expected cumulative reward over horizon $T$ subject to a set of constraints in each round $\tau\leq T$. We propose a…