相关论文: Nash Regret Guarantees for Linear Bandits

Nash regret has recently emerged as a principled fairness-aware performance metric for stochastic multi-armed bandits, motivated by the Nash Social Welfare objective. Although this notion has been extended to linear bandits, existing…

We extend the notion of regret with a welfarist perspective. Focussing on the classic multi-armed bandit (MAB) framework, the current work quantifies the performance of bandit algorithms by applying a fundamental welfare function, namely…

Regret in stochastic multi-armed bandits traditionally measures the difference between the highest reward and either the arithmetic mean of accumulated rewards or the final reward. These conventional metrics often fail to address fairness…

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 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 consider the problem of online multi-agent Nash social welfare (NSW) maximization. While previous works of Hossain et al. [2021], Jones et al. [2023] study similar problems in stochastic multi-agent multi-armed bandits and show that…

We study finite-armed semiparametric bandits, where each arm's reward combines a linear component with an unknown, potentially adversarial shift. This model strictly generalizes classical linear bandits and reflects complexities common in…

Motivated by economic applications such as recommender systems, we study the behavior of stochastic bandits algorithms under \emph{strategic behavior} conducted by rational actors, i.e., the arms. Each arm is a \emph{self-interested}…

Stochastic linear bandits are a fundamental model for sequential decision making, where an agent selects a vector-valued action and receives a noisy reward with expected value given by an unknown linear function. Although well studied in…

We propose a simple model selection approach for algorithms in stochastic bandit and reinforcement learning problems. As opposed to prior work that (implicitly) assumes knowledge of the optimal regret, we only require that each base…

In this paper, we study the problem of stochastic linear bandits with finite action sets. Most of existing work assume the payoffs are bounded or sub-Gaussian, which may be violated in some scenarios such as financial markets. To settle…

We present simple and efficient algorithms for the batched stochastic multi-armed bandit and batched stochastic linear bandit problems. We prove bounds for their expected regrets that improve over the best-known regret bounds for any number…

We present improved algorithms with worst-case regret guarantees for the stochastic linear bandit problem. The widely used "optimism in the face of uncertainty" principle reduces a stochastic bandit problem to the construction of a…

In this work, we study potential games and Markov potential games under stochastic cost and bandit feedback. We propose a variant of the Frank-Wolfe algorithm with sufficient exploration and recursive gradient estimation, which provably…

We study stochastic linear bandits where, in each round, the learner receives a set of actions (i.e., feature vectors), from which it chooses an element and obtains a stochastic reward. The expected reward is a fixed but unknown linear…

We study the tail behavior of regret in stochastic multi-armed bandits for algorithms that are asymptotically optimal in expectation. While minimizing expected regret is the classical objective, recent work shows that even such algorithms…

In this paper, we consider the multi-armed bandit problem with high-dimensional features. First, we prove a minimax lower bound, $\mathcal{O}\big((\log d)^{\frac{\alpha+1}{2}}T^{\frac{1-\alpha}{2}}+\log T\big)$, for the cumulative regret,…

We study stochastic linear bandits with heavy-tailed rewards, where the rewards have a finite $(1+\epsilon)$-absolute central moment bounded by $\upsilon$ for some $\epsilon \in (0,1]$. We improve both upper and lower bounds on the minimax…

Classic no-regret multi-armed bandit algorithms, including the Upper Confidence Bound (UCB), Hedge, and EXP3, are inherently unfair by design. Their unfairness stems from their objective of playing the most rewarding arm as frequently as…

We consider minimisation of dynamic regret in non-stationary bandits with a slowly varying property. Namely, we assume that arms' rewards are stochastic and independent over time, but that the absolute difference between the expected…