The paper introduces a new approach to safety in contextual bandits with continuous actions, focusing on high‑probability constraints on the realized cost rather than expected cost. It presents the High‑Probability Constrained UCB algorithm, which balances reward exploration with conservative safety estimation, and provides theoretical regret guarantees for linear models and extensions to general function classes. Experiments demonstrate that this realized‑cost safety framework significantly reduces safety violations compared to expected‑cost constrained methods.
By Spyros Dragazis, Aldo Pacchiano
The paper introduces a new approach to safety in contextual bandits with continuous actions by enforcing high‑probability constraints on the realized cost rather than on its expectation. It proposes the High‑Probability Constrained UCB algorithm, which balances optimistic reward exploration with pessimistic safety estimation. The authors provide theoretical regret guarantees for linear models and extend the analysis to general function classes, demonstrating experimentally that realized‑cost constraints significantly reduce safety violations compared to expected‑cost baselines.
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.
By Hao Qin, Chicheng Zhang
The paper presents the first high‑probability regret bounds for both cumulative and current‑step variants of Feel‑Good Thompson Sampling (FGTS) in contextual bandits with general realizable function approximation. The bounds rely on decoupling coefficients and prior mass near the true reward function, and in the linear setting they achieve ≠d√T log(2T)+√T log(1/δ) regret with probability at least 1‑δ. This matches the dimension and horizon dependence of upper‑confidence‑bound algorithms up to logarithmic factors, while the high‑probability cost adds only linear dependence on log(1/δ).
By Xuheng Li, Qingyue Zhao, Quanquan Gu
We study the contextual combinatorial semi-bandit (CCSB) problem with general reward function approximation. At each round, the learner observes a context, selects a combinatorial action consisting of a subset of basic arms, and receives the reward of each selected arm; the goal is to maximize the cumulative reward over time.
The paper investigates stochastic contextual bandits in an agnostic setting, aiming to compete with the best policy in a given class without assuming realizability or specific loss/reward models. It introduces an algorithm that updates the policy each round by minimizing a pessimistic objective— a clipped inverse‑propensity estimate of the policy value plus a variance penalty— and proves the first fast regret rates relative to the best‑in‑class policy. By exploiting entropy assumptions on the policy class and a H"olderian error‑bound condition, the authors achieve fast best‑in‑class regret rates, including polylogarithmic rates in the parametric case, using a sequential self‑normalized maximal inequality for bounded martingale empirical processes to derive uniform variance‑adaptive confidence bounds and ensure pessimism under adaptive data collection.
By Samuel Girard, Aurelien Bibaut, Arthur Gretton, Nathan Kallus, Houssam Zenati