We study distributed online submodular maximization under partition matroid constraints, in which multiple agents select a limited number of actions from their own subsets sequentially to maximize the cumulative value of a sequence of objective functions. We develop a unified algorithmic framework that accommodates full-information and bandit feedback models. For both feedback models, we prove that the proposed algorithms achieve sublinear $(1-1/e)$-regret guarantees, which are comparable to those achieved by existing centralized counterparts. Furthermore, to tackle the sampling violation issue caused by continuous relaxation and rounding, we develop a bounded stochastic pipage rounding scheme and show that the probability of sampling violation vanishes asymptotically. As a result, the cumulative sampling violation remains sublinear in $T$, which is further shown to be not improvable under certain conditions. Numerical results validate the theoretical findings in this paper.
Motivated by the challenge of testing distributions over high-dimensional or continuous domains, we study distribution testing with respect to bounded classes of distinguishers. A representative task is to use samples from an unknown distribution $P$ over a very large domain to d…
Estimating entropy from samples is fundamental in information theory and property testing. Shannon entropy measures average uncertainty and can be estimated to constant additive accuracy over a $k$-symbol alphabet using $Θ(k/\log k)$ samples. Min-entropy depends only on the most…
We establish a $\widetildeΩ(d^{5/4}\sqrt T)$ lower bound on the minimax expected regret of stochastic bandit convex optimization of $1$-Lipschitz functions on the Euclidean ball. This presents the first nontrivial regret lower bound that grows faster than $d\sqrt{T}$ for this pro…
In many scientific and engineering domains, maximizing discovery within a limited sampling budget demands strategic, observation-guided exploration. While generative models have enabled training-free reward alignment, current methods typically excel in local searches within narro…
Causal bandits exploit structural relationships among variables to share information across interventions and accelerate the identification of high-reward decisions. In many applications, however, some variables cannot be directly manipulated, even though they influence the rewar…
We establish approximation and learning guarantees for Fourier neural operators (FNOs) applied to time-$T$ solution operators of dissipative evolution equations. The analysis builds on the premise that FNOs can efficiently approximate and learn solution operators whenever these o…