arXiv:2608. 12134v1 Announce Type: cross Abstract: We study nonnegative submodular maximization subject to a general matroid when the offline algorithm is given an arbitrary controlled value oracle.
The paper presents an online algorithm that achieves the same $0.401$ approximation factor for maximizing nonnegative, non-monotone DR-submodular functions over compact convex down-closed subsets of the $d$-dimensional unit cube as the best known offline construction. In the full-information value-oracle model, the algorithm attains this factor with sublinear regret, using $O(dT^{1/4})$ oracle calls per round and $O(T^{3/4})$ regret, and offers flexible batching trade-offs. Under a positive-anchor condition, a randomized blocking strategy preserves the $0.401$ factor while achieving $O(T^{5/6})$ one-point bandit regret.
arXiv:2608.24627v1 Announce Type: new Abstract: We study adversarial bandit maximization of monotone submodular functions under a matroid constraint. For a rank-$k$ matroid on $n$ elements, we give a...
In bandit problems, standard regret-minimizing algorithms treat exploration as an amortized cost, which can expose early participants to unfair ex-ante losses in settings such as clinical trials. Recent work addresses this by evaluating the sequence of per-round expected rewards through the generalized $p$-mean, interpolating between utilitarian welfare ($p=1$), Nash welfare ($p\to0$), and Rawlsian fairness ($p\to-\infty$).
arXiv:2607. 13402v1 Announce Type: cross Abstract: In bandit problems, standard regret-minimizing algorithms treat exploration as an amortized cost, which can expose early participants to unfair ex-ante losses in settings such as clinical trials.
arXiv:2607. 19854v1 Announce Type: new Abstract: We study horizon-free regret minimization for finite-horizon time-homogeneous tabular Markov decision processes with $S$ states, $A$ actions, horizon $H$, and per-trajectory total reward bounded by $1$.
The paper presents the first adversarial linear bandit algorithm based on Follow-the-Perturbed-Leader (FTPL) that achieves √T regret over general convex action sets. It achieves a regret of ≥O(d^{5/4}√T) using only linear optimization oracles, and a near‑optimal ≥O(d√T) regret when an optimal‑design exploration distribution is available. The work improves on previous FTPL algorithms and generalizes earlier results for special action sets, offering a simpler and more computationally efficient approach that relies on adaptive perturbation distributions and a new analysis framework based on Fisher information.
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 presents the first adversarial linear bandit algorithm based on Follow-the-Perturbed-Leader (FTPL) that achieves √T regret over general action sets. It attains a ≥O(d^{5/4}√T) regret using only linear optimization oracles, and a near‑optimal ≥O(d√T) regret when an optimal‑design exploration distribution is available. The authors introduce adaptive perturbation distributions—including Gaussian, random‑weighting, and elliptical perturbations—and develop a systematic analysis of the FTPL stability term via Fisher information, extending the FTPL framework beyond previous approaches.
arXiv:2609.24569v1 Announce Type: cross Abstract: Over the past decade, a growing body of research has shown that $\gamma$-weak submodularity broadly arises in numerous subset selection tasks, includ...
arXiv:2607. 29460v1 Announce Type: new Abstract: Heavy-tailed distributions arise naturally in sequential decision-making problems such as financial investment, online advertising, and network management, where rare but extreme outcomes can dominate performance.
arXiv:2606. 01159v1 Announce Type: new Abstract: We study two-player zero-sum games (TPZSGs) with bandit feedback under fairness constraints requiring every action to be played with probability at least $\alpha/m$.