Bayesian optimization routinely warm-starts a target experiment with data from related source tasks, and the multi-task Gaussian process is the textbook surrogate for the job, but it is found that it misestimates the cross-task correlation even in the simplest non-trivial case.
Abstract
Bayesian optimization routinely warm-starts a target experiment with data from related source tasks, and the multi-task Gaussian process is the textbook surrogate for the job. We revisit this default in a controlled setting and find that it misestimates the cross-task correlation even in the simplest non-trivial case, affinely related source and target tasks, where a working transfer learning method should obviously succeed. We trace the failure to two independent structural mechanisms. Per-task standardization, the textbook fix for the affine slice ambiguity, propagates a finite-sample alignment error into the recovered correlation. The marginal likelihood itself identifies the correlation only at a per-sample rate that a Gaussian process at non-overlapping designs further dilutes. We propose three conservative remedies that follow from the analysis: promoting per-task means and scales to model parameters, restricting the task covariance to non-negative correlations, and co-locating part of the source and target designs. Across synthetic multi-task problems and surrogate-based hyperparameter tuning transfer, these remedies recover the target-only baseline on the simple instances, while the broader failure persists on harder instances and across most rank-based and latent-context variants.
A unified framework, KENDO (Kernel ENsemble Disagreement-aware Operator), is proposed that integrates Ensemble Gaussian Processes (EGP) with disagreement-aware acquisition strategies and extends the approach to multi-objective optimization via random scalarization that preserves the single-optimizer conditioning structure.
Heng Zhang, Haotian Xiang, Qin Lu et al.· 0 citations
It is shown that TabPFN v2 (Hollmann et al., 2025), a pretrained tabular foundation model never trained on Bayesian optimization data, can serve as a drop-in zero-shot BO surrogate, eliminating the per-task fitting step.
In multi-task learning (MTL) negative transfer is often considered as an optimization artifact, but it can also be viewed as a consequence of limited shared capacity and weak task redundancy. We investigate this effect through a Capacity--Redundancy (CR) identity that decomposes the sum of per-task predictive informations into joint predictive information that includes label redundancy defined via total correlation (TC), and a residual coupling term that quantifies interference left unresolved by the shared representation. Additionally, we show two key results: (i) a clustering-gap decomposition that gives a necessary and sufficient condition for clustered sharing to outperform global sharing, and (ii) a gradient--TC bridge in a Gaussian multi-task model that formally justifies gradient cosine similarity as a proxy for redundancy ordering. Empirically, we estimate the residual coupling $\Delta$ from validation residual correlations, showing that clustered LoRA substantially reduces $\widehat{\Delta}$, outperforms size-matched random partitions, and results in statistically significant gains with multi-seed confidence intervals.
The performance of Large Language Models (LLMs) is fundamentally influenced by the distributional composition of multi-domain pre-training data. While manual heuristics were prevalent in early models, they increasingly fail to capture the intricate synergies between domains as data complexity grows. To overcome the issue, a dominant approach seeks to fit a proxy function mapping between domain weights and their corresponding validation losses, and then find the optimal domain weights to minimize validation losses. These methods rely on strong structural assumptions, such as rank invariance or scaling laws, which are often violated, resulting in non-negligible estimation bias. A promising approach is to directly optimize the weighting scheme from data. However, it suffers from unstable optimization trajectory and prohibitive computational overhead, limiting its potential to search better domain weights configurations. This paper presents a Bayesian domain weighting method to infer the weights from a Dirichlet distribution via introducing Gamma prior information learned from observations. Experimental results demonstrate that proposed method could achieve stable and efficient domain weights learning, and identifies optimal mixtures while consuming substantially less data than search-based function-fitting methods, revitalizing optimization-based domain weighting for large-scale applications.
Xiang Yuan, Kaiqing Lei, Zhenyu Jin et al.· 0 citations
ReBRAC-v2 is introduced, which directly trains an exact-likelihood normalizing flow as the RL actor, combines likelihood, MSE, and MAE behavior regularization, and integrates a classification-based residual critic, staged optimization, and multi-sample test-time action selection, and ranks first in eight categories.
Discrete diffusion models have become a strong, widely adopted class of generators for sequence data, and steering them toward a downstream reward at inference time, without any retraining, is increasingly important. Such training-free steering is done by gradient guidance, by search, or by combining the two. We study the combined regime and identify two weaknesses in how it is usually run: the guided proposal estimates its gradient from a single noisy sample, and the search then resamples particles at a fixed temperature that ignores how rewards spread across each denoising step. We address both with a small set of changes that add no denoiser cost. For the proposal, we lower the estimator variance with a Rao-Blackwellized reveal for differentiable rewards and a leave-one-out baseline for non-differentiable ones; for the search, we standardize the per-step values into a group-relative advantage and prove it collapses to a single active ingredient, an adaptive resampling temperature. We call the resulting method Guided Reduced-variance proposals and Adaptive Selection (GRAS). GRAS is simple yet effective: across regulatory DNA and protein design it attains the best training-free reward, outperforming prior training-free methods and matching or surpassing a reward-fine-tuned model, and it remains effective even for non-differentiable rewards.