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: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.
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: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...
arXiv:2405.00065v4 Announce Type: replace-cross Abstract: This paper introduces the notion of upper-linearizable/quadratizable functions, a class that extends concavity and DR-submodularity in variou...
arXiv:2606. 06043v1 Announce Type: cross Abstract: Follow-the-regularized-leader framework has shown effectiveness and flexibility in online learning problems, where the choice of learning rates are known to be crucial.
arXiv:2311. 07565v3 Announce Type: replace Abstract: We introduce exploration via linear loss perturbations (EVILL), a randomised exploration method for structured stochastic bandit problems that works by solving for the minimiser of a linearly perturbed regularised negative log-likelihood function.
arXiv:2512. 00517v3 Announce Type: replace-cross Abstract: Sequential optimization of black-box functions from noisy evaluations has been widely studied, with Gaussian Process bandit algorithms such as GP-UCB guaranteeing no-regret in stationary settings.