Multi-kernel learning (MKL) exhibits well-documented performance in online non-linear function approximation. Federated learning enables a group of learners (called clients) to train an MKL model on the data distributed among clients to perform online non-linear function approximation. There are some challenges in online federated MKL that need to be addressed: i) Communication efficiency especially when a large number of kernels are considered ii) Heterogeneous data distribution among clients. The present paper develops an algorithmic framework to enable clients to communicate with the server to send their updates with affordable communication cost while clients employ a large dictionary of kernels. Utilizing random feature (RF) approximation, the present paper proposes scalable online federated MKL algorithm. We prove that using the proposed online federated MKL algorithm, each client enjoys sub-linear regret with respect to the RF approximation of its best kernel in hindsight, which indicates that the proposed algorithm can effectively deal with heterogeneity of the data distributed among clients. Experimental results on real datasets showcase the advantages of the proposed algorithm compared with other online federated kernel learning ones.

Optimal transport with quadratic cost provides a geometric framework for steering an ensemble, modeled by a probability law, with minimal effort. Yet ambient-space formulations become unwieldy in high dimensions, and sensing or actuation in practice often reveals only linear views of the state -- camera silhouettes, LiDAR beams, tomographic slices. We develop a sliced feedback controller for distribution steering: the evolving law is projected onto one-dimensional directions on the sphere, the optimal one-dimensional velocity is synthesized in each projection, and these velocities are averaged to produce a feedback control in the ambient space. The construction reduces to the Benamou--Brenier problem in one dimension. In addition, it is invariant under orthogonal transforms, nonexpansive under projections, and well posed on $\mathcal{P}_2(\mathbb{R}^n)$. Computation proceeds by sampling directions on the sphere and solving independent one-dimensional subproblems, yielding a scalable method aligned with partial observations. In the Gaussian setting, we show that the developed sliced controller steers the law to the prescribed target. Furthermore, we derive an identity relating the energy consumption incurred by the controller to the sliced Wasserstein distance.

Trust Region Bayesian Optimization (TuRBO) is an effective strategy for alleviating the curse of dimensionality in high-dimensional black-box optimization. However, inappropriate lengthscale design can cause the local Gaussian process (GP) model within the trust region to degenerate, leading to suboptimal performance in high dimensions. In this work, we show that TuRBO's local GP may remain either excessively complex or overly simple as the dimension $D$ and trust region side length $L$ vary. To address this issue, we propose a straightforward variant, AdaScale-TuRBO, which scales the GP lengthscale with both the problem dimension and trust region size, thereby preserving kernel geometry and maintaining consistent prior complexity. Empirically, we show that AdaScale-TuRBO can robustly outperform standard TuRBO and other popular high-dimensional BO methods on synthetic benchmarks and real-world trajectory planning tasks.

Two-stage recommender systems first choose a candidate generator and then rank items within the generated set. Because the generator decides which items are available to the ranker, changing the generator changes both the policy value and the data support used to estimate that value. This creates an offline selection problem that standard single-stage objectives do not capture: a policy may look good under a retrieval score or a raw off-policy value estimate, but still be unreliable if it depends on weakly supported generator-item pairs. We propose CASP (Coupled Action-Set Pessimism), a support-aware offline selector for finite libraries of two-stage recommender policies. CASP combines doubly robust value estimation with a support-burden penalty. We show that stagewise rules that ignore downstream continuation value can be arbitrarily suboptimal, and we derive population, finite-class, and reconstructed-propensity guarantees for conservative selection. In simulations and a reconstructed MovieLens 1M application, CASP selects lower-burden policies when estimated value and support credibility are in tension.

We argue that current definitions of machine unlearning are underspecified for second-order optimizers. We compare first-order and second-order learners for their ability to handle the data deletion task with varying degrees of eigendecomposition to mimic the loss model memory. While both first and second-order methods realign with the ideal counterfactul in terms of performance and gradient, the second-order optimizer shows significant volatility in the optimizer state. This indicates residual information, supposedly deleted, that isn't detectable by first-order analysis. Various eigendecay treatments show that stability and information loss is regained only under controlled state pertubation where geometric information (or memory) is erased.

Generative approaches to clustering provide information on geometric properties of clusters, whereas discriminative approaches provide boundaries between clusters. Ideas from both approaches are incorporated to present a fully unsupervised, probabilistic, and discriminative clustering method via a regularized mutual information objective function, wherein a mixture of mixtures of Gaussian and uniform distributions is used for formulation of the conditional model. Automatic selection of the number of components is established with the introduction of the regularizing term and a merge step, similar to those applied in reversible jump Markov chain Monte Carlo methods used in Bayesian clustering. Consequently, the turtle shell method -- a fully unsupervised clustering method capable of estimating non-linear boundary lines, automatically selecting the number of components, and capturing intuitive clusters in the presence of data abnormalities such as noise and/or irregular cluster shapes -- is introduced. We test this method on various simulated and real datasets commonly explored in clustering research, and extend the analysis to datasets arising from flow cytometry experiments.

Evaluating generative AI models is increasingly resource-intensive due to slow inference, expensive raters, and a rapidly growing landscape of models and benchmarks. We propose ProEval, a proactive evaluation framework that leverages transfer learning to efficiently estimate performance and identify failure cases. ProEval employs pre-trained Gaussian Processes (GPs) as surrogates for the performance score function, mapping model inputs to metrics such as the severity of errors or safety violations. By framing performance estimation as Bayesian quadrature (BQ) and failure discovery as superlevel set sampling, we develop uncertainty-aware decision strategies that actively select or synthesize highly informative inputs for testing. Theoretically, we prove that our pre-trained GP-based BQ estimator is unbiased and bounded. Empirically, extensive experiments on reasoning, safety alignment, and classification benchmarks demonstrate that ProEval is significantly more efficient than competitive baselines. It requires 8-65x fewer samples to achieve estimates within 1% of the ground truth, while simultaneously revealing more diverse failure cases under a stricter evaluation budget.