We present an efficient algorithm for linear contextual bandits with adversarial losses and stochastic action sets. Our approach reduces this setting to misspecification-robust adversarial linear bandits with fixed action sets. Without knowledge of the context distribution or access to a context simulator, the algorithm achieves eO(min{d2 T, p d3T logK})regret and runs in poly(d,C,T) time, where d is the feature dimension, C is an upper bound on the number of linear constraints defining the action set in each round, K is an upper bound on the number of actions in each round, and T is number of rounds. This resolves the open question by Liu et al. (2023) on whether one can obtain poly(d) T regret in polynomial time independent of the number of actions. For the important class of combinatorial bandits with adversarial losses and stochastic action sets where the action sets can be described by a polynomial number of linear constraints, our algorithm is the first to achieve poly(d) T regret in polynomial time, while no prior algorithm achieves even o(T) regret in polynomial time to our knowledge. When a simulator is available, the regret bound can be improved to eO(d L), where L is the cumulative loss of the best policy.

As trained intelligent systems become increasingly pervasive, multi-agent learning has emerged as a popular framework for studying complex interactions between autonomous agents. Yet, a formal understanding of how and when learners in heterogeneous environments benefit from sharing their respective experiences is still in its infancy. In this paper, we seek answers to these questions in the context of linear contextual bandits. We present a novel distributed learning algorithm based on the upper confidence bound (UCB) algorithm, which we refer to as H-LINUCB, wherein agents cooperatively minimize the group regret under the coordination of a central server. In the setting where the level of heterogeneity or dissimilarity across the environments is known to the agents, we show that H-LINUCB is provably optimal in regimes where the tasks are highly similar or highly dissimilar.

Linear contextual bandits represent a fundamental class of models with numerous real-world applications, and it is critical to developing algorithms that can effectively manage noise with unknown variance, ensuring provable guarantees for both worst-case constant-variance noise and deterministic reward scenarios.

How can we make use of information parallelism in online decision making problems while efficiently balancing the exploration-exploitation trade-off? In this paper, we introduce a batch Thompson Sampling framework for two canonical online decision making problems, namely, stochastic multi-arm bandit and linear contextual bandit with finitely many arms. Over a time horizon T, our batch Thompson Sampling policy achieves the same (asymptotic) regret bound of a fully sequential one while carrying out only O(log T) batch queries. To achieve this exponential reduction, i.e., reducing the number of interactions from T to O(log T), our batch policy dynamically determines the duration of each batch in order to balance the exploration-exploitation trade-off. We also demonstrate experimentally that dynamic batch allocation dramatically outperforms natural baselines such as static batch allocations.

Linear contextual bandits represent a fundamental class of models with numerous real-world applications, and it is critical to developing algorithms that can effectively manage noise with unknown variance, ensuring provable guarantees for both worst-case constant-variance noise and deterministic reward scenarios.

Recommendation algorithms that select the most relevant item for sequentially arriving users or queries have become vital for navigating the internet and its many online platforms.

UCB, wherein agents cooperatively minimize the group regret under the coordination of a central server.