Machine Learning-based heuristics have recently shown impressive performance in solving a variety of hard combinatorial optimization problems (COPs). However they generally rely on a separate neural model, specialized and trained for each single problem. Any variation of a problem requires adjustment of its model and re-training from scratch. In this paper, we propose GOAL (for Generalist combinatorial Optimization Agent Learning), a generalist model capable of efficiently solving multiple COPs and which can be fine-tuned to solve new COPs. GOAL consists of a single backbone plus light-weight problem-specific adapters, mostly for input and output processing. The backbone is based on a new form of mixed-attention blocks which allows to handle problems defined on graphs with arbitrary combinations of node, edge and instance-level features. Additionally, problems which involve heterogeneous nodes or edges, such as in multi-partite graphs, are handled through a novel multi-type transformer architecture, where the attention blocks are duplicated to attend only the relevant combination of types while relying on the same shared parameters. We train GOAL on a set of routing, scheduling and classic graph problems and show that it is only slightly inferior to the specialized baselines while being the first multi-task model that solves a variety of COPs. Finally, we showcase the strong transfer learning capacity of GOAL by fine-tuning or learning the adapters for new problems, with only few shots and little data.

These problems focus on identifying designs, represented as discrete objects like strings or graphs, that optimize multiple Active learning is increasingly adopted for expensive attributes, often requiring substantial resources for accurate multi-objective combinatorial optimization assessment (Ehrgott, 2005; Gómez-Bombarelli et al., 2016; problems, but it involves a challenging subset Stanton et al., 2022; Winter et al., 2019; Mirhoseini et al., selection problem, optimizing the batch acquisition 2021). Active learning frameworks, which iteratively propose score that quantifies the goodness of a batch of candidates and learn from the attributes a batch for evaluation. Due to the excessively evaluated on those candidates, are increasingly employed in large search space of the subset selection problem, these fields due to their query efficiency, which is a critical prior methods optimize the batch acquisition component to handling expensive evaluation costs (Aggarwal on the latent space, which has discrepancies with et al., 2014; Jain et al., 2022; Gruver et al., 2023; Zhu the actual space, or optimize individual acquisition et al., 2023; Agnesina et al., 2023). In active learning, each scores without considering the dependencies round entails an internal problem of selecting a proposal among candidates in a batch instead of directly batch of candidates for querying, formulated by cardinalityconstrained optimizing the batch acquisition.

Recently, machine learning (ML) methods have been developed for increasing the accuracy of robot mechanisms. Complex mechanical issues such as non-linear friction, backlash, flexibility of structure transmission elements can cause these errors and they are hard to model. ML requires training data and the above mechanical phenomena are highly dependent on position of the robot in the workspace and also on its velocity, especially near zero velocity in both directions where non-linearities such as Streibek and Coulomb friction are most pronounced. It is well known that success of ML methods depends on amount of training data and it is expensive/time consuming to collect data from physical robot motion. We therefore address the problem of searching for trajectories in the 6D space of positions and velocities which collect the most information in the least amount of time. This reduces to a special case of the traveling-salesman problem in that the robot must be programmed to visit sampled points in the position-velocity phase space most efficiently. Two goals of this work are 1) Computationally study the difficulty of the TSP in this application by applying it to X, Y, Z motion in 3D space (6D phase space) and 2) assess the effectiveness of an extremely simple Nearest Neighbor search algorithm compared to random sampling of the search space. Results confirm that Nearest Neighbor heuristic searching produces significantly better trajectories than random sampling in this application.

Large language models have demonstrated remarkable capabilities, but their performance is heavily reliant on effective prompt engineering. Automatic prompt optimization (APO) methods are designed to automate this and can be broadly categorized into those targeting instructions (instruction optimization, IO) vs. those targeting exemplars (exemplar selection, ES). Despite their shared objective, these have evolved rather independently, with IO recently receiving more research attention. This paper seeks to bridge this gap by comprehensively comparing the performance of representative IO and ES techniques, both isolation and combination, on a diverse set of challenging tasks. Our findings reveal that intelligently reusing model-generated input-output pairs obtained from evaluating prompts on the validation set as exemplars consistently improves performance over IO methods but is currently under-investigated. We also find that despite the recent focus on IO, how we select exemplars can outweigh how we optimize instructions, with ES strategies as simple as random search outperforming state-of-the-art IO methods with seed instructions without any optimization. Moreover, we observe synergy between ES and IO, with optimal combinations surpassing individual contributions. We conclude that studying exemplar selection as a standalone method and its optimal combination with instruction optimization remains a crucial aspect of APO and deserves greater consideration in future research, even in the era of highly capable instruction-following models.

Grouped-query attention (GQA) has been widely adopted in LLMs to mitigate the complexity of multi-head attention (MHA). To transform an MHA to a GQA, neighbour queries in MHA are evenly split into groups where each group shares the value and key layers. In this work, we propose AsymGQA, an activation-informed approach to asymmetrically grouping an MHA to a GQA for better model performance. Our AsymGQA outperforms the GQA within the same model size budget. For example, AsymGQA LLaMA-2-7B has an accuracy increase of 7.5% on MMLU compared to neighbour grouping. Our approach addresses the GQA's trade-off problem between model performance and hardware efficiency.

In this paper, we study the contextual multinomial logit (MNL) bandit problem in which a learning agent sequentially selects an assortment based on contextual information, and user feedback follows an MNL choice model. There has been a significant discrepancy between lower and upper regret bounds, particularly regarding the maximum assortment size $K$. Additionally, the variation in reward structures between these bounds complicates the quest for optimality. Under uniform rewards, where all items have the same expected reward, we establish a regret lower bound of $\Omega(d\sqrt{\smash[b]{T/K}})$ and propose a constant-time algorithm, OFU-MNL+, that achieves a matching upper bound of $\tilde{O}(d\sqrt{\smash[b]{T/K}})$. Under non-uniform rewards, we prove a lower bound of $\Omega(d\sqrt{T})$ and an upper bound of $\tilde{O}(d\sqrt{T})$, also achievable by OFU-MNL+. Our empirical studies support these theoretical findings. To the best of our knowledge, this is the first work in the contextual MNL bandit literature to prove minimax optimality -- for either uniform or non-uniform reward setting -- and to propose a computationally efficient algorithm that achieves this optimality up to logarithmic factors.

While the recent literature has seen a surge in the study of constrained bandit problems, all existing methods for these begin by assuming the feasibility of the underlying problem. We initiate the study of testing such feasibility assumptions, and in particular address the problem in the linear bandit setting, thus characterising the costs of feasibility testing for an unknown linear program using bandit feedback. Concretely, we test if $\exists x: Ax \ge 0$ for an unknown $A \in \mathbb{R}^{m \times d}$, by playing a sequence of actions $x_t\in \mathbb{R}^d$, and observing $Ax_t + \mathrm{noise}$ in response. By identifying the hypothesis as determining the sign of the value of a minimax game, we construct a novel test based on low-regret algorithms and a nonasymptotic law of iterated logarithms. We prove that this test is reliable, and adapts to the `signal level,' $\Gamma,$ of any instance, with mean sample costs scaling as $\widetilde{O}(d^2/\Gamma^2)$. We complement this by a minimax lower bound of $\Omega(d/\Gamma^2)$ for sample costs of reliable tests, dominating prior asymptotic lower bounds by capturing the dependence on $d$, and thus elucidating a basic insight missing in the extant literature on such problems.

The recent past has witnessed a notable surge in on-demand food delivery (OFD) services, offering delivery fulfillment within dozens of minutes after an order is placed. In OFD, pooling multiple orders for simultaneous delivery in real-time order assignment is a pivotal efficiency source, which may in turn extend delivery time. Constructing high-quality order pooling to harmonize platform efficiency with the experiences of consumers and couriers, is crucial to OFD platforms. However, the complexity and real-time nature of order assignment, making extensive calculations impractical, significantly limit the potential for order consolidation. Moreover, offline environment is frequently riddled with unknown factors, posing challenges for the platform's perceptibility and pooling decisions. Nevertheless, delivery behaviors of skilled couriers (SCs) who know the environment well, can improve system awareness and effectively inform decisions. Hence a SC delivery network (SCDN) is constructed, based on an enhanced attributed heterogeneous network embedding approach tailored for OFD. It aims to extract features from rich temporal and spatial information, and uncover the latent potential for order combinations embedded within SC trajectories. Accordingly, the vast search space of order assignment can be effectively pruned through scalable similarity calculations of low-dimensional vectors, making comprehensive and high-quality pooling outcomes more easily identified in real time. SCDN has now been deployed in Meituan dispatch system. Online tests reveal that with SCDN, the pooling quality and extent have been greatly improved. And our system can boost couriers'efficiency by 45-55% during noon peak hours, while upholding the timely delivery commitment.

Solving Olympiad-level mathematical problems represents a significant advancement in machine intelligence and automated reasoning. Current machine learning methods, however, struggle to solve Olympiad-level problems beyond Euclidean plane geometry due to a lack of large-scale, high-quality datasets. The challenge is even greater in algebraic systems, which involve infinite reasoning spaces within finite conditions. To address these issues, we propose AIPS, an Algebraic Inequality Proving System capable of autonomously generating complex inequality theorems and effectively solving Olympiad-level inequality problems without requiring human demonstrations. During proof search in a mixed reasoning manner, a value curriculum learning strategy on generated datasets is implemented to improve proving performance, demonstrating strong mathematical intuitions. On a test set of 20 International Mathematical Olympiad-level inequality problems, AIPS successfully solved 10, outperforming state-of-the-art methods. Furthermore, AIPS automatically generated a vast array of non-trivial theorems without human intervention, some of which have been evaluated by professional contestants and deemed to reach the level of the International Mathematical Olympiad. Notably, one theorem was selected as a competition problem in a major city 2024 Mathematical Olympiad.

Recent years have witnessed a growing trend toward employing deep reinforcement learning (Deep-RL) to derive heuristics for combinatorial optimization (CO) problems on graphs. Maximum Coverage Problem (MCP) and its probabilistic variant on social networks, Influence Maximization (IM), have been particularly prominent in this line of research. In this paper, we present a comprehensive benchmark study that thoroughly investigates the effectiveness and efficiency of five recent Deep-RL methods for MCP and IM. These methods were published in top data science venues, namely S2V-DQN, Geometric-QN, GCOMB, RL4IM, and LeNSE. Our findings reveal that, across various scenarios, the Lazy Greedy algorithm consistently outperforms all Deep-RL methods for MCP. In the case of IM, theoretically sound algorithms like IMM and OPIM demonstrate superior performance compared to Deep-RL methods in most scenarios. Notably, we observe an abnormal phenomenon in IM problem where Deep-RL methods slightly outperform IMM and OPIM when the influence spread nearly does not increase as the budget increases. Furthermore, our experimental results highlight common issues when applying Deep-RL methods to MCP and IM in practical settings. Finally, we discuss potential avenues for improving Deep-RL methods. Our benchmark study sheds light on potential challenges in current deep reinforcement learning research for solving combinatorial optimization problems.