The paper presents a computationally efficient optimal design framework for multinomial logit (MNL) bandits, addressing the combinatorial action space that makes traditional methods infeasible. It introduces two approaches: an exact or certified-approximate mixed-integer linear program with solver‑certified early stopping, and a fully polynomial‑time lifted design using a tractable surrogate objective. Leveraging the Kiefer‑Wolfowitz equivalence theorem, the authors provide near G‑optimality guarantees and apply the framework to develop a best assortment identification algorithm with an instance‑dependent sample complexity of τO((d log N)/Δ²).
By Joongkyu Lee, Min-hwan Oh
The paper studies high‑dimensional linear contextual bandits with knapsack constraints (CBwK), aiming to exploit sparsity for tighter regret bounds. It introduces an online hard‑thresholding estimator integrated into a primal‑dual framework, achieving sub‑linear regret that grows only logarithmically with the feature dimension. Under either a diverse‑covariate or margin condition, the regret improves to τ‑dependent rates, and when both hold simultaneously, a dual resolving scheme yields an even tighter bound. The approach also recovers optimal rates for high‑dimensional contextual bandits without knapsacks, and experiments demonstrate its practical effectiveness.
By Wanteng Ma, Dong Xia, Jiashuo Jiang
The paper investigates preference-based bandits where a learner selects pairs of arms and receives binary preference feedback modeled by Bradley–Terry. It introduces the locally sensitive eluder dimension, a new complexity measure for logistic preference feedback, and proposes the GINOP algorithm that uses log-loss confidence sets to balance optimism and exploration. The authors prove a first-order regret bound showing that learning with preference feedback can be as statistically efficient as learning from direct rewards, and they validate their theory with empirical experiments.
By Ahmed Ben Yahmed (CREST, ENSAE Paris, FAIRPLAY), Marc Abeille (FAIRPLAY), Cl\'ement Calauz\`enes (FAIRPLAY)
arXiv:2603.21716v2 Announce Type: replace-cross
Abstract: Efficient selection among multiple generative models is increasingly important in modern generative AI, where sampling from suboptimal models...
By Bahar Dibaei Nia, Farzan Farnia
arXiv:2608. 11383v1 Announce Type: new Abstract: We study new algorithms for Contextual Bandits with Knapsack.
By Zhen Xu
arXiv:2606. 09802v1 Announce Type: cross Abstract: We consider a variant of the linear contextual stochastic multi-armed bandits, where the learner must provide recommendations to a group of users, each having its personalized preference vector, and in the presence of context distributions that are drifting over time.
By Udvas Das, Waris Radji, Debabrota Basu, Odalric-Ambrym Maillard