adaptive projection selection

This work addresses the challenge of high-dimensional Bayesian optimization, where conventional Thompson sampling suffers from exponentially sparse coverage due to its reliance on a fixed set of discrete candidate points, hindering effective approximation of the optimum. To overcome this limitation, the paper proposes Adaptive Candidate Thompson Sampling (ACTS), which innovatively leverages gradient information from samples of the Gaussian process surrogate model to dynamically refine the sampling subspace. This approach significantly enhances both sampling density and the quality of sampled maxima without increasing the number of candidate points. ACTS integrates seamlessly into existing Thompson sampling frameworks and demonstrates consistent superiority over state-of-the-art methods across multiple synthetic and real-world benchmarks, achieving notable improvements in both optimization efficiency and solution quality.

In Bayesian optimization, global optimization of posterior sample paths becomes computationally intractable in high dimensions, severely limiting the performance of sampling-based acquisition functions such as GP-TS. To address this, we propose a novel paradigm for posterior sample optimization grounded in global root finding: using only a minimal number of initial points (typically one per sample), it achieves high-probability convergence to the global optimum, effectively circumventing the curse of dimensionality. Our method integrates gradient-based optimization, robust global root-finding techniques, and a newly designed tunable, sample-averaged GP-TS formulation. Experiments demonstrate substantial improvements in both inner- and outer-loop optimization efficiency, outperforming EI and GP-UCB across multiple benchmarks, while achieving near-linear scalability in high dimensions. This work establishes the first efficient, reliable, and theoretically grounded framework for posterior sample optimization in high-dimensional Bayesian optimization.

Efficiently identifying the Pareto-optimal set for multi-objective black-box functions over high-dimensional continuous design spaces remains challenging due to the exponential growth of candidate solutions. Method: This paper proposes Adaptive ε-PAL, the first algorithm integrating tree-based adaptive discretization with Gaussian process (GP) Bayesian optimization. It leverages GP surrogate modeling, Pareto front estimation, and information-theoretic analysis of compact metric spaces to dynamically partition the input space—thereby avoiding exhaustive enumeration. Contribution/Results: We establish a provably tight upper bound on the ε-accurate sample complexity. Empirical evaluation across multiple benchmarks demonstrates substantial reductions in function evaluations compared to state-of-the-art Pareto-set identification methods. The core contribution is a theoretically grounded, adaptive multi-objective optimization framework that simultaneously ensures rigorous convergence guarantees and practical efficiency.

This paper addresses complex pure-exploration objectives beyond best-arm identification—such as threshold testing and ε-optimal arm identification—by establishing the first duality-based minimax-optimal sampling allocation framework. It provides the first necessary and sufficient conditions for optimal sampling allocation in pure exploration; generalizes the top-two paradigm to arbitrary pure-exploration problems; and proposes a hyperparameter-free, information-directed selection rule driven by KL divergence and entropy. The rule is rigorously proven to achieve asymptotic optimality in Gaussian settings and resolves the long-standing open problem of asymptotic optimality for top-two Thompson sampling. Experiments demonstrate substantial improvements in sampling efficiency across Gaussian best-arm identification, threshold-bandwidth testing, and ε-optimal arm identification, consistently outperforming state-of-the-art methods.

Bayesian inverse problems and rare-event simulation under expensive likelihood evaluations face the challenge that the posterior concentrates in sparse, a priori unknown regions of the parameter space, making it difficult for conventional methods to balance accuracy and efficiency. Method: We propose an adaptive sequential Monte Carlo (SMC) algorithm that jointly optimizes a surrogate model—based on reduced-basis approximation for elliptic PDE solutions—and a temperature annealing schedule. Our method introduces a novel posterior-entropy-driven adaptive inverse-temperature selection mechanism, dynamically coupling surrogate error estimation with temperature scheduling to enable snapshot-wise accurate likelihood evaluation and uncertainty-aware surrogate refinement in critical regions. Contribution/Results: Theoretical analysis guarantees convergence. Numerical experiments on PDE inverse problems demonstrate approximately tenfold reduction in computational cost while preserving posterior statistical accuracy.

This work addresses the challenge of performing efficient and accurate Bayesian inference when likelihood evaluations are computationally expensive and budgets are limited. The authors propose the Sampling-adaptive Active Learning (SALE) framework, which employs a Gaussian process surrogate model and introduces expected posterior as a unified acquisition criterion to dynamically allocate evaluation resources between Bayesian optimization and uncertainty reduction. SALE integrates a state-dependent sampling strategy, an annealed objective function to balance bias and stability, and a tractable rule for quantifying uncertainty reduction. Experimental results demonstrate that SALE significantly reduces total variation error across multiple benchmark and synthetic tasks, avoids failure modes observed in existing methods, and exhibits strong empirical performance in real-world applications from econometrics and astrophysics.

This work addresses the trade-off in X-ray computed tomography between reconstruction quality and the costs associated with increased projection numbers, including prolonged acquisition time, higher experimental expense, and elevated radiation dose. To mitigate these drawbacks, the authors propose a reconstruction-free sequential experimental design method that directly identifies edge-aligned informative measurements from sinograms. By employing an adaptive beam selection strategy, the approach dynamically balances exploration and exploitation to efficiently select the most informative projections across the full measurement space. Notably, this method circumvents the conventional reliance on iterative reconstructions for edge localization, thereby substantially improving computational efficiency and reducing sensitivity to reconstruction errors. Experimental results demonstrate that the proposed technique achieves comparable or superior reconstruction quality with significantly fewer projections, effectively lowering both experimental overhead and radiation burden.

研究通过有限标记预算最小化多类零一分类风险，提出基于参数方向和贝叶斯决策边界的标签获取准则，并开发了两阶段自适应程序以实现最优风险标准。

该研究通过分析不同切片查找方案下混合切片采样的平均目标密度评估次数，提出了自动适应性调优方案，解决了切片采样中初始设置依赖问题。

This study addresses the issue that redundant views increase computational overhead and degrade reconstruction quality in feed-forward novel view synthesis. We propose a lightweight, rendering-free keyframe selector that integrates geometric and image features to construct a multi-criteria scoring system based on coverage, redundancy, and clarity. By employing a genetic algorithm for offline optimal subset search and knowledge distillation to train a compact network, our method breaks away from the conventional selection paradigm that relies on reconstruction feedback. Experiments across six datasets demonstrate that the proposed approach outperforms existing baselines while significantly reducing selection costs. Notably, the curated subsets achieve superior performance compared to full-sequence inputs and exhibit strong cross-paradigm generalization capabilities.