Adversarial attacks pose a major challenge to distributed learning systems, prompting the development of numerous robust learning methods. However, most existing approaches suffer from the curse of dimensionality, i.e. the error increases with the number of model parameters. In this paper, we make a progress towards high dimensional problems, under arbitrary number of Byzantine attackers. The cornerstone of our design is a direct high dimensional semi-verified mean estimation method. The idea is to identify a subspace with large variance. The components of the mean value perpendicular to this subspace are estimated using corrupted gradient vectors uploaded from worker machines, while the components within this subspace are estimated using auxiliary dataset. As a result, a combination of large corrupted dataset and small clean dataset yields significantly better performance than using them separately. We then apply this method as the aggregator for distributed learning problems. The theoretical analysis shows that compared with existing solutions, our method gets rid of sqrt{d} dependence on the dimensionality, and achieves minimax optimal statistical rates. Numerical results validate our theory as well as the effectiveness of the proposed method.

Evolutionary algorithms (EAs) are optimization algorithms that simulate natural selection and genetic mechanisms. Despite advancements, existing EAs have two main issues: (1) they rarely update next-generation individuals based on global correlations, thus limiting comprehensive learning; (2) it is challenging to balance exploration and exploitation, excessive exploitation leads to premature convergence to local optima, while excessive exploration results in an excessively slow search. Existing EAs heavily rely on manual parameter settings, inappropriate parameters might disrupt the exploration-exploitation balance, further impairing model performance. To address these challenges, we propose a novel evolutionary algorithm framework called Graph Neural Evolution (GNE). Unlike traditional EAs, GNE represents the population as a graph, where nodes correspond to individuals, and edges capture their relationships, thus effectively leveraging global information. Meanwhile, GNE utilizes spectral graph neural networks (GNNs) to decompose evolutionary signals into their frequency components and designs a filtering function to fuse these components. High-frequency components capture diverse global information, while low-frequency components capture more consistent information. This explicit frequency filtering strategy directly controls global-scale features through frequency components, overcoming the limitations of manual parameter settings and making the exploration-exploitation control more interpretable and effective. Extensive evaluations on nine benchmark functions (e.g., Sphere, Rastrigin, and Rosenbrock) demonstrate that GNE consistently outperforms both classical algorithms (GA, DE, CMA-ES) and advanced algorithms (SDAES, RL-SHADE) under various conditions, including original, noise-corrupted, and optimal solution deviation scenarios. GNE achieves solution quality several orders of magnitude better than other algorithms (e.g., 3.07e-20 mean on Sphere vs. 1.51e-07).

How should we quantify the value of each training example when datasets are large, heterogeneous, and geometrically structured? Classical Data-Shapley answers in principle, but its O(n!) complexity and point-wise perspective are ill-suited to modern scales. We propose Hierarchical Contrastive Data Valuation (HCDV), a three-stage framework that (i) learns a contrastive, geometry-preserving representation, (ii) organizes the data into a balanced coarse-to-fine hierarchy of clusters, and (iii) assigns Shapley-style pay-offs to coalitions via local Monte-Carlo games whose budgets are propagated downward. HCDV collapses the factorial burden to O(T∑ℓKℓ) = O(TKmax log n), rewards examples that sharpen decision boundaries, and regularizes outliers through curvature-based smoothness. We prove that HCDV approximately satisfies the four Shapley axioms with surplus loss O(η log n), enjoys sub-Gaussian coalition deviation Õ(1/√T), and incurs at most kε∞ regret for top-k selection. Experiments on four benchmarks — tabular, vision, streaming, and a 45 M-sample CTR task — plus the OpenDataVal suite show that HCDV lifts accuracy by up to +5 pp, slashes valuation time by up to 100×, and directly supports tasks such as augmentation filtering, low-latency streaming updates, and fair marketplace payouts.

Nonparametric contextual bandit is an important model of sequential decision making problems. Under $\alpha$-Tsybakov margin condition, existing research has established a regret bound of $\tilde{O}\left(T^{1-\frac{\alpha+1}{d+2}}\right)$ for bounded supports. However, the optimal regret with unbounded contexts has not been analyzed. The challenge of solving contextual bandit problems with unbounded support is to achieve both exploration-exploitation tradeoff and bias-variance tradeoff simultaneously. In this paper, we solve the nonparametric contextual bandit problem with unbounded contexts. We propose two nearest neighbor methods combined with UCB exploration. The first method uses a fixed $k$. Our analysis shows that this method achieves minimax optimal regret under a weak margin condition and relatively light-tailed context distributions. The second method uses adaptive $k$. By a proper data-driven selection of $k$, this method achieves an expected regret of $\tilde{O}\left(T^{1-\frac{(\alpha+1)\beta}{\alpha+(d+2)\beta}}+T^{1-\beta}\right)$, in which $\beta$ is a parameter describing the tail strength. This bound matches the minimax lower bound up to logarithm factors, indicating that the second method is approximately optimal.