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).
arXiv:2607. 11684v1 Announce Type: cross Abstract: Existing contextual multinomial logit (MNL) bandits model relevance-driven choice but ignore the potential benefits of within-assortment diversity, while submodular/combinatorial bandits encode diversity in rewards but lack structured choice probabilities.
arXiv:2603. 10346v2 Announce Type: replace Abstract: We study the fixed-budget best-arm identification (BAI) problem in non-stationary linear bandits.
arXiv:2607. 08979v1 Announce Type: new Abstract: We study the active learning problem of fixed-confidence top-$k$ identification from noisy pairwise comparisons.
arXiv:2606. 00984v1 Announce Type: cross Abstract: We study linear contextual bandits under rare parameter updates: the learner may incorporate reward feedback into its parameter estimate only at a small number of update times, while still observing contexts online and selecting actions sequentially.
arXiv:2608. 12231v2 Announce Type: replace Abstract: We study adversarial combinatorial bandits with $m$-set actions, where at each round the learner selects $m$ out of $d$ items and observes only the aggregate loss of the selected items.
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.
arXiv:2502. 13467v2 Announce Type: replace Abstract: The $K$-Max combinatorial multi-armed bandit problem arises in applications such as recommendation and distributed decision making, where the reward is determined by the maximum outcome among $K$ selected arms.
arXiv:2509. 04194v3 Announce Type: replace-cross Abstract: We introduce a bandit framework for stochastic matching under the multinomial logit (MNL) choice model.
arXiv:2602. 09456v2 Announce Type: replace Abstract: We propose an algorithmic framework, Offline Estimation to Decisions (OE2D), that efficiently reduces contextual bandit learning with general reward function approximation to offline regression.
arXiv:2608. 04333v1 Announce Type: new Abstract: Large language model (LLM) configuration evaluation is challenging due to limited evaluation budgets, varying costs, and multiple competing objectives.
arXiv:2610.01951v1 Announce Type: cross Abstract: Top-two algorithms are simple and effective for fixed-confidence best-arm identification, but their sharp non-asymptotic behavior is still not well u...
arXiv:2608.12134v2 Announce Type: replace-cross Abstract: We study nonnegative submodular maximization on $n$ elements subject to a general matroid of rank $k$, when the offline algorithm is given an...