Related papers: Strategy-Driven Limit Theorems Associated Bandit P…

This paper investigates the problem of generalized linear bandits with heavy-tailed rewards, whose $(1+\epsilon)$-th moment is bounded for some $\epsilon\in (0,1]$. Although there exist methods for generalized linear bandits, most of them…

We consider multi-armed bandit problems in social groups wherein each individual has bounded memory and shares the common goal of learning the best arm/option. We say an individual learns the best option if eventually (as $t \to \infty$) it…

We study a grouped bandit setting where each arm comprises multiple independent sub-arms referred to as attributes. Each attribute of each arm has an independent stochastic reward. We impose the constraint that for an arm to be deemed…

In this paper, we develop a general law of large numbers and central limit theorem for cumulative reward processes associated with finite state Markov jump processes with non-stationary transition rates. Such models commonly arise in…

We study a generalization of the multi-armed bandit problem with multiple plays where there is a cost associated with pulling each arm and the agent has a budget at each time that dictates how much she can expect to spend. We derive an…

Bandit algorithms solve diverse sequential decision-making problems, but are often too sample-inefficient for from-scratch personalization. To substantially reduce exploration times, latent bandit algorithms exploit cross-instance structure…

This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…

The stochastic generalised linear bandit is a well-understood model for sequential decision-making problems, with many algorithms achieving near-optimal regret guarantees under immediate feedback. However, the stringent requirement for…

An extension of the traditional two-armed bandit problem is considered, in which the decision maker has access to some side information before deciding which arm to pull. At each time t, before making a selection, the decision maker is able…

Bandit problems model the trade-off between exploration and exploitation in various decision problems. We study two-armed bandit problems in continuous time, where the risky arm can have two types: High or Low; both types yield stochastic…

Information and free-energy maximization are physics principles that provide general rules for an agent to optimize actions in line with specific goals and policies. These principles are the building blocks for designing decision-making…

Traditional multi-armed bandit (MAB) formulations usually make certain assumptions about the underlying arms' distributions, such as bounds on the support or their tail behaviour. Moreover, such parametric information is usually 'baked'…

In a sequential decision-making problem, having a structural dependency amongst the reward distributions associated with the arms makes it challenging to identify a subset of alternatives that guarantees the optimal collective outcome.…

The multi-armed bandit problems have been studied mainly under the measure of expected total reward accrued over a horizon of length $T$. In this paper, we address the issue of risk in multi-armed bandit problems and develop parallel…

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

We study adaptive regret bounds in terms of the variation of the losses (the so-called path-length bounds) for both multi-armed bandit and more generally linear bandit. We first show that the seemingly suboptimal path-length bound of (Wei…

We obtain the upper bound of the loss function for a strategy in the multi-armed bandit problem with Gaussian distributions of incomes. Considered strategy is an asymptotic generalization of the strategy proposed by J. Bather for the…

The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

We study a sequential resource allocation problem between a fixed number of arms. On each iteration the algorithm distributes a resource among the arms in order to maximize the expected success rate. Allocating more of the resource to a…

Multi-arm bandits are gaining popularity as they enable real-world sequential decision-making across application areas, including clinical trials, recommender systems, and online decision-making. Consequently, there is an increased desire…