The paper presents an improved analysis of non‑consecutive gradient variation in Bandit Convex Optimization (BCO) with two‑point feedback, leading to better dimension dependence for both convex and strongly convex functions compared to prior work. It also derives new problem‑dependent guarantees such as gradient‑variance and small‑loss regret bounds, extends the technique to one‑point bandit linear optimization over hyper‑rectangular domains, and establishes the first gradient‑variation dynamic and universal regret bounds for two‑point BCO.
In many online learning and bandit problems, the actions we consider possess inherent similarities--for instance because they share latent traits, tags, or hierarchical structure. We study online learning with a similarity-structured action set, encoded by a rooted tree whose leaves are the actions and whose levels quantify how closely two actions are related.
arXiv:2606. 19891v1 Announce Type: new Abstract: We study adversarial bandit optimization in which the loss functions may be non-convex and non-smooth.
arXiv:2603. 28201v3 Announce Type: replace Abstract: We revisit the standard perturbation-based approach of Abernethy et al.
arXiv:2601.13519v4 Announce Type: replace-cross Abstract: This paper introduces a new problem-dependent regret measure for online convex optimization with smooth losses. The notion, which we call the...
arXiv:2502. 08870v2 Announce Type: replace Abstract: We provide an approach for the analysis of randomised exploration algorithms like Thompson sampling that does not rely on forced optimism or posterior inflation.
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.
arXiv:2608. 15050v1 Announce Type: new Abstract: We study online convex optimization with dueling (pairwise comparison) feedback, where the learner observes only a binary preference between two queried points.
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:2609.37209v1 Announce Type: new Abstract: Pairwise losses are increasingly used for reward learning even when pointwise rewards are observed, with mixed empirical results. When and why do pairw...
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:2605. 09454v2 Announce Type: replace-cross Abstract: We study the $\textit{single-index bandit}$ problem, where rewards depend on an unknown one-dimensional projection of high-dimensional contexts through an unknown reward function.
arXiv:2609.13564v1 Announce Type: new Abstract: We study KL-regularized contextual bandits under both reward and preference feedback. We show that greedy sampling can achieve logarithmic regret witho...