The 2023 Big ANNChallenge, held at NeurIPS'23, aimed at advancing the stateof-the-art in indexing data structures and search algorithms. It focused for practical variants of Approximate Nearest Neighbor (ANN) search that reflect the growing complexity and diversity of workloads. Unlike prior challenges that emphasized scaling up classical ANN search [21], this competition addressed filtered search, out-of-distribution data, sparse and streaming variants of ANNS. Participants developed and submitted innovative solutions that were evaluated on new standard datasets with constrained computational resources.

Online bidding is a classic optimization problem, with several applications in online decision-making, the design of interruptible systems, and the analysis of approximation algorithms. In this work, we study online bidding under learningaugmented settings that incorporate stochasticity, in either the prediction oracle or the algorithm itself. In the first part, we study bidding under distributional predictions, and find Pareto-optimal algorithms that offer the best-possible tradeoff between the consistency and the robustness of the algorithm. In the second part, we study the power and limitations of randomized bidding algorithms, by presenting upper and lower bounds on the consistency/robustness tradeoffs. Previous works focused predominantly on oracles that do not leverage stochastic information on the quality of the prediction, and deterministic algorithms.

Clustering is a fundamental problem that has been extensively studied over past few decades, with most research focusing on point-based clustering such as kmeans, k-median, and k-center. However, numerous real-world applications, such as motion analysis, computer vision, and missing data analysis, require clustering over structured data, including lines, time series and affine subspaces (flats), where traditional point-based clustering algorithms often fall short. In this paper, we study the k-means of lines problem, where the input is a set L of lines in Rd, and the goal is to find k centers C in Rd such that the sum of squared distances from each line in L to its nearest center in C is minimized. The local search algorithm is a well-established strategy for point-based k-means clustering, known for its efficiency and provable approximation guarantees. However, extending local search algorithm to the k-means of lines problem is nontrivial, as the capture relation used in point-based clustering does not generalize to the line setting.

Matrix preconditioning is a critical technique to accelerate the solution of linear systems, where performance heavily depends on the selection of preconditioning parameters. Traditional parameter selection approaches often define fixed constants for specific scenarios. However, they rely on domain expertise and fail to consider the instance-wise features for individual problems, limiting their performance. In contrast, machine learning (ML) approaches, though promising, are hindered by high inference costs and limited interpretability. To combine the strengths of both approaches, we propose a symbolic discovery framework-namely, Symbolic Matrix Preconditioning (SymMaP)-to learn efficient symbolic expressions for preconditioning parameters. Specifically, we employ a neural network to search the high-dimensional discrete space for expressions that can accurately predict the optimal parameters. The learned expression allows for high inference efficiency and excellent interpretability (expressed in concise symbolic formulas), making it simple and reliable for deployment. Experimental results show that SymMaP consistently outperforms traditional strategies across various benchmarks 1.

The fundamental limitation of the behavioral cloning (BC) approach to imitation learning is that it only teaches an agent what the expert did at states the expert visited. This means that when a BC agent makes a mistake which takes them out of the support of the demonstrations, they often don't know how to recover from it. In this sense, BC is akin to giving the agent the fish - giving them dense supervision across a narrow set of states - rather than teaching them to fish: to be able to reason independently about achieving the expert's outcome even when faced with unseen situations at test-time. In response, we explore learning to search (L2S) from expert demonstrations, i.e. learning the components required to, at test time, plan to match expert outcomes, even after making a mistake. These include (1) a world model and (2) a reward model. We carefully ablate the set of algorithmic and design decisions required to combine these and other components for stable and sample/interaction-efficient learning of recovery behavior without additional human corrections. Across a dozen visual manipulation tasks from three benchmarks, our approach SAILORconsistently out-performs state-of-the-art Diffusion Policies trained via BC on the same data. Furthermore, scaling up the amount of demonstrations used for BC by 5-10 still leaves a performance gap. We find that SAILORcan identify nuanced failures and is robust to reward hacking.

While large language models (LLMs) have emerged as promising tools for CO--either by directly generating solutions or synthesizing solver-specific codes--existing approaches often neglect critical structural priors inherent to CO problems, leading to suboptimality and iterative inefficiency. Inspired by human experts' success in leveraging CO structures for algorithm design, we propose STRCMP, a novel structure-aware LLM-based algorithm discovery framework that systematically integrates structure priors to enhance solution quality and solving efficiency. Our framework combines a graph neural network (GNN) for extracting structural embeddings from CO instances with an LLM conditioned on these embeddings to identify high-performing algorithms in the form of solver-specific codes. This composite architecture ensures syntactic correctness, preserves problem topology, and aligns with natural language objectives, while an evolutionary refinement process iteratively optimizes generated algorithm. Extensive evaluations across Mixed Integer Linear Programming and Boolean Satisfiability problems, using nine benchmark datasets, demonstrate that our proposed STRCMPoutperforms five strong neural and LLM-based methods by a large margin, in terms of both solution optimality and computational efficiency.

Foundation Models (FMs) have demonstrated remarkable success in fields like computer vision and natural language processing, yet their application to combinatorial optimization remains underexplored. Optimization problems, often modeled as graphs, pose unique challenges due to their diverse structures, varying distributions, and NP-hard complexity. To address these challenges, we propose OPTFM, the first graph foundation model for general combinatorial optimization. OPTFM introduces a scalable multi-view graph transformer with hybrid self-attention and cross-attention to model large-scale heterogeneous graphs in O(N)time complexity while maintaining semantic consistency throughout the attention computation.

In recent years, neural network-guided heuristic search algorithms, such as MonteCarlo tree search and A search, have achieved significant advancements across diverse practical applications. Due to the challenges stemming from high statespace complexity, sparse training datasets, and incomplete environmental modeling, heuristic estimations manifest uncontrolled inherent biases towards the actual expected evaluations, thereby compromising the decision-making quality of search algorithms. Sampling exploration enhanced A (SeeA) was proposed to improve the efficiency of A search by constructing an dynamic candidate subset through random sampling, from which the expanded node was selected.

The Asymmetric Traveling Salesman Problem (ATSP) is one of the most fundamental and notoriously challenging problems in combinatorial optimization. We propose a novel continuous relaxation framework for ATSP that leverages differentiable constraints to encourage acyclic structures and valid permutations.

In human-AI interaction, effective communication relies on aligning the AI agent's model with the human user's mental model, a process known as model reconciliation. However, existing model reconciliation approaches predominantly assume deterministic models, overlooking the fact that human knowledge is often uncertain or probabilistic. To bridge this gap, we present a probabilistic model reconciliation framework that resolves inconsistencies in MPE outcome probabilities between an agent's and a user's models. Our approach is built on probabilistic logic programming (PLP) using ProbLog, where explanations are generated as cost-optimal model updates that reconcile these probabilistic differences. We develop two search algorithms - a generic baseline and an optimized version. The latter is guided by theoretical insights and further extended with greedy and weighted variants to enhance scalability and efficiency. Our approach is validated through a user study on explanation types and computational experiments showing that the optimized version consistently outperforms the generic baseline.