Monte Carlo Tree Search is a popular method for solving decision making problems. Faster implementations allow for more simulations within the same wall clock time, directly improving search performance. To this end, we present an alternative array-based implementation of the classic Upper Confidence bounds applied to Trees algorithm. Our method preserves the logic of the original algorithm, but eliminates the need for branch prediction, enabling faster performance on pipelined processors, and up to a factor of 2.8 times better scaling with search depth in our numerical simulations.

Failure-Directed Search (FDS) is a significant complete generic search algorithm used in Constraint Programming (CP) to efficiently explore the search space, proven particularly effective on scheduling problems. This paper analyzes FDS's properties, showing that minimizing the size of its search tree guided by ranked branching decisions is closely related to the Multi-armed bandit (MAB) problem. Building on this insight, MAB reinforcement learning algorithms are applied to FDS, extended with problem-specific refinements and parameter tuning, and evaluated on the two most fundamental scheduling problems, the Job Shop Scheduling Problem (JSSP) and Resource-Constrained Project Scheduling Problem (RCPSP). The resulting enhanced FDS, using the best extended MAB algorithm and configuration, performs 1.7 times faster on the JSSP and 2.1 times faster on the RCPSP benchmarks compared to the original implementation in a new solver called OptalCP, while also being 3.5 times faster on the JSSP and 2.1 times faster on the RCPSP benchmarks than the current state-of-the-art FDS algorithm in IBM CP Optimizer 22.1. Furthermore, using only a 900-second time limit per instance, the enhanced FDS improved the existing state-of-the-art lower bounds of 78 of 84 JSSP and 226 of 393 RCPSP standard open benchmark instances while also completely closing a few of them.

Bidirectional motion planning often reduces planning time compared to its unidirectional counterparts. It requires connecting the forward and reverse search trees to form a continuous path. However, this process could fail and restart the asymmetric bidirectional search due to the limitations of lazy-reverse search. To address this challenge, we propose Greedy GuILD Grafting Trees (G3T*), a novel path planner that grafts invalid edge connections at both ends to re-establish tree-based connectivity, enabling rapid path convergence. G3T* employs a greedy approach using the minimum Lebesgue measure of guided incremental local densification (GuILD) subsets to optimize paths efficiently. Furthermore, G3T* dynamically adjusts the sampling distribution between the informed set and GuILD subsets based on historical and current cost improvements, ensuring asymptotic optimality. These features enhance the forward search's growth towards the reverse tree, achieving faster convergence and lower solution costs. Benchmark experiments across dimensions from R^2 to R^8 and real-world robotic evaluations demonstrate G3T*'s superior performance compared to existing single-query sampling-based planners. A video showcasing our experimental results is available at: https://youtu.be/3mfCRL5SQIU

Path planning has long been an important and active research area in robotics. To address challenges in high-dimensional motion planning, this study introduces the Force Direction Informed Trees (FDIT*), a sampling-based planner designed to enhance speed and cost-effectiveness in pathfinding. FDIT* builds upon the state-of-the-art informed sampling planner, the Effort Informed Trees (EIT*), by capitalizing on often-overlooked information in invalid vertices. It incorporates principles of physical force, particularly Coulomb's law. This approach proposes the elliptical $k$-nearest neighbors search method, enabling fast convergence navigation and avoiding high solution cost or infeasible paths by exploring more problem-specific search-worthy areas. It demonstrates benefits in search efficiency and cost reduction, particularly in confined, high-dimensional environments. It can be viewed as an extension of nearest neighbors search techniques. Fusing invalid vertex data with physical dynamics facilitates force-direction-based search regions, resulting in an improved convergence rate to the optimum. FDIT* outperforms existing single-query, sampling-based planners on the tested problems in R^4 to R^16 and has been demonstrated on a real-world mobile manipulation task.

Machine learning (ML) is increasingly employed in real-world applications like medicine or economics, thus, potentially affecting large populations. However, ML models often do not perform homogeneously, leading to underperformance or, conversely, unusually high performance in certain subgroups (e.g., sex=female AND marital_status=married). Identifying such subgroups can support practical decisions on which subpopulation a model is safe to deploy or where more training data is required. However, an efficient and coherent framework for effective search is missing. Consequently, we introduce SubROC, an open-source, easy-to-use framework based on Exceptional Model Mining for reliably and efficiently finding strengths and weaknesses of classification models in the form of interpretable population subgroups. SubROC incorporates common evaluation measures (ROC and PR AUC), efficient search space pruning for fast exhaustive subgroup search, control for class imbalance, adjustment for redundant patterns, and significance testing. We illustrate the practical benefits of SubROC in case studies as well as in comparative analyses across multiple datasets.

Bayesian Optimization (BO) has been widely applied to optimize expensive black-box functions while retaining sample efficiency. However, scaling BO to high-dimensional spaces remains challenging. Existing literature proposes performing standard BO in multiple local trust regions (TuRBO) for heterogeneous modeling of the objective function and avoiding over-exploration. Despite its advantages, using local Gaussian Processes (GPs) reduces sampling efficiency compared to a global GP . To enhance sampling efficiency while preserving heterogeneous modeling, we propose to construct multiple local quadratic models using gradients and Hessians from a global GP, and select new sample points by solving the bound-constrained quadratic program. Additionally, we address the issue of vanishing gradients of GPs in high-dimensional spaces. We provide a convergence analysis and demonstrate through experimental results that our method enhances the efficacy of TuRBO and outperforms a wide range of high-dimensional BO techniques on synthetic functions and real-world applications.

We give a reduction from $(1+\varepsilon)$-approximate Earth Mover's Distance (EMD) to $(1+\varepsilon)$-approximate Closest Pair (CP). As a consequence, we improve the fastest known approximation algorithm for high-dimensional EMD. Here, given $p\in [1, 2]$ and two sets of $n$ points $X,Y \subseteq (\mathbb R^d,\ell_p)$, their EMD is the minimum cost of a perfect matching between $X$ and $Y$, where the cost of matching two vectors is their $\ell_p$ distance. Further, CP is the basic problem of finding a pair of points realizing $\min_{x \in X, y\in Y} ||x-y||_p$. Our contribution is twofold: we show that if a $(1+\varepsilon)$-approximate CP can be computed in time $n^{2-ϕ}$, then a $1+O(\varepsilon)$ approximation to EMD can be computed in time $n^{2-Ω(ϕ)}$; plugging in the fastest known algorithm for CP [Alman, Chan, Williams FOCS'16], we obtain a $(1+\varepsilon)$-approximation algorithm for EMD running in time $n^{2-\tildeΩ(\varepsilon^{1/3})}$ for high-dimensional point sets, which improves over the prior fastest running time of $n^{2-Ω(\varepsilon^2)}$ [Andoni, Zhang FOCS'23]. Our main technical contribution is a sublinear implementation of the Multiplicative Weights Update framework for EMD. Specifically, we demonstrate that the updates can be executed without ever explicitly computing or storing the weights; instead, we exploit the underlying geometric structure to perform the updates implicitly.

This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one optimal, to solve this problem. We also generate a benchmark to cover different instances of SSMP varying in complexity, and carry out an experimental evaluation to assess the performance of the approaches.

Optimal path planning requires finding a series of feasible states from the starting point to the goal to optimize objectives. Popular path planning algorithms, such as Effort Informed Trees (EIT*), employ effort heuristics to guide the search. Effective heuristics are accurate and computationally efficient, but achieving both can be challenging due to their conflicting nature. This paper proposes Direction Informed Trees (DIT*), a sampling-based planner that focuses on optimizing the search direction for each edge, resulting in goal bias during exploration. We define edges as generalized vectors and integrate similarity indexes to establish a directional filter that selects the nearest neighbors and estimates direction costs. The estimated direction cost heuristics are utilized in edge evaluation. This strategy allows the exploration to share directional information efficiently. DIT* convergence faster than existing single-query, sampling-based planners on tested problems in R^4 to R^16 and has been demonstrated in real-world environments with various planning tasks. A video showcasing our experimental results is available at: https://youtu.be/2SX6QT2NOek

Weisfeiler-Leman Features (WLFs) are a recently introduced classical machine learning tool for learning to plan and search. They have been shown to be both theoretically and empirically superior to existing deep learning approaches for learning value functions for search in symbolic planning. In this paper, we introduce new WLF hyperparameters and study their various tradeoffs and effects. We utilise the efficiency of WLFs and run planning experiments on single core CPUs with a sample size of 1,000,000 to understand the effect of hyperparameters on training and planning. Our experimental analysis show that there is a robust and best set of hyperparameters for WLFs across the tested planning domains. We find that the best WLF hyperparameters for learning heuristic functions minimise execution time rather than maximise model expressivity. We further statistically analyse and observe no significant correlation between training and planning metrics.