arXiv:2607. 18866v1 Announce Type: cross Abstract: Building on the identity that expected regret equals the covariance between costs and decisions, this paper develops the complete derivative theory of the covariance regret functional.
Building on the identity that expected regret equals the covariance between costs and decisions, this paper develops the complete derivative theory of the covariance regret functional. We derive the Gâteaux derivative, showing that the universal steepest-descent direction is the contrarian policy $-(c-\bar{c})$, while ascent yields momentum.
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.
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...
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.
arXiv:2603. 09276v2 Announce Type: replace-cross Abstract: We study a widely used Bayesian optimization method, Gaussian process Thompson sampling (GP-TS), under the assumption that the objective function is a sample path from a GP.
arXiv:2606. 01655v1 Announce Type: cross Abstract: The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints.
arXiv:2606. 27462v1 Announce Type: cross Abstract: The global minimum-variance portfolio (GMVP) is the canonical decision built from an estimated covariance matrix, yet covariance estimators are universally evaluated by matrix-norm loss, which is not the object the decision depends on.
arXiv:2512. 09850v2 Announce Type: replace Abstract: We introduce Conformal Bandits, a novel framework integrating Conformal Prediction (CP) into bandit problems, a classic paradigm for sequential decision-making under uncertainty.
The paper analyzes Bayesian linear bandits with isotropic Gaussian parameters, independent Gaussian arms, and Gaussian reward noise when the time horizon scales with the dimension. It derives explicit limits for the normalized posterior uncertainty and parameter overlaps, yielding exact regret curves for several policies—including Thompson sampling, posterior‑mean greedy selection, and scaled‑covariance variants. The results show that posterior‑mean greedy selection achieves the optimal Bayes regret, while Thompson sampling incurs a strictly larger leading regret whose ratio to greedy lies between one and two, approaching two for long horizons.
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.
arXiv:2610.01980v1 Announce Type: cross Abstract: Decision-focused learning for linear optimization is complicated by the discontinuity of the optimizer, where small cost errors may leave the decisio...
arXiv:2609. 22690v1 Announce Type: new Abstract: We develop an index policy for finite-horizon Bernoulli multi-armed bandits from minimax solutions to single-arm bandit (SAB) problems.