Batched Bayesian optimization with correlated candidate uncertainties

Batched Bayesian optimization (BO) can accelerate molecular design by efficiently identifying top-performing compounds from a large chemical library. Existing acquisition strategies for batch design in BO aim to balance exploration and exploitation. This often involves optimizing non-additive batch acquisition functions, necessitating approximation via myopic construction and/or diversity heuristics. In this work, we propose an acquisition strategy for discrete optimization that is motivated by pure exploitation, qPO (multipoint Probability of Optimality). qPO maximizes the probability that the batch includes the true optimum, which is expressible as the sum over individual acquisition scores and thereby circumvents the combinatorial challenge of optimizing a batch acquisition function. We differentiate the proposed strategy from parallel Thompson sampling and discuss how it implicitly captures diversity. Finally, we apply our method to the model-guided exploration of large chemical libraries and provide empirical evidence that it performs better than or on par with state-of-the-art methods in batched Bayesian optimization.

LinSATNet: The Positive Linear Satisfiability Neural Networks

Encoding constraints into neural networks is attractive. This paper studies how to introduce the popular positive linear satisfiability to neural networks. We propose the first differentiable satisfiability layer based on an extension of the classic Sinkhorn algorithm for jointly encoding multiple sets of marginal distributions. We further theoretically characterize the convergence property of the Sinkhorn algorithm for multiple marginals. In contrast to the sequential decision e.g.\ reinforcement learning-based solvers, we showcase our technique in solving constrained (specifically satisfiability) problems by one-shot neural networks, including i) a neural routing solver learned without supervision of optimal solutions; ii) a partial graph matching network handling graphs with unmatchable outliers on both sides; iii) a predictive network for financial portfolios with continuous constraints. To our knowledge, there exists no one-shot neural solver for these scenarios when they are formulated as satisfiability problems. Source code is available at https://github.com/Thinklab-SJTU/LinSATNet

Double-Ended Synthesis Planning with Goal-Constrained Bidirectional Search

Computer-aided synthesis planning (CASP) algorithms have demonstrated expert-level abilities in planning retrosynthetic routes to molecules of low to moderate complexity. However, current search methods assume the sufficiency of reaching arbitrary building blocks, failing to address the common real-world constraint where using specific molecules is desired. To this end, we present a formulation of synthesis planning with starting material constraints. Under this formulation, we propose Double-Ended Synthesis Planning (DESP), a novel CASP algorithm under a bidirectional graph search scheme that interleaves expansions from the target and from the goal starting materials to ensure constraint satisfiability. The search algorithm is guided by a goal-conditioned cost network learned offline from a partially observed hypergraph of valid chemical reactions. We demonstrate the utility of DESP in improving solve rates and reducing the number of search expansions by biasing synthesis planning towards expert goals on multiple new benchmarks. DESP can make use of existing one-step retrosynthesis models, and we anticipate its performance to scale as these one-step model capabilities improve.

Rethinking and Benchmarking Predict-then-Optimize Paradigm for Combinatorial Optimization Problems

Numerous web applications rely on solving combinatorial optimization problems, such as energy cost-aware scheduling, budget allocation on web advertising, and graph matching on social networks. However, many optimization problems involve unknown coefficients, and improper predictions of these factors may lead to inferior decisions which may cause energy wastage, inefficient resource allocation, inappropriate matching in social networks, etc. Such a research topic is referred to as "Predict-Then-Optimize (PTO)" which considers the performance of prediction and decision-making in a unified system. A noteworthy recent development is the end-to-end methods by directly optimizing the ultimate decision quality which claims to yield better results in contrast to the traditional two-stage approach. However, the evaluation benchmarks in this field are fragmented and the effectiveness of various models in different scenarios remains unclear, hindering the comprehensive assessment and fast deployment of these methods. To address these issues, we provide a comprehensive categorization of current approaches and integrate existing experimental scenarios to establish a unified benchmark, elucidating the circumstances under which end-to-end training yields improvements, as well as the contexts in which it performs ineffectively. We also introduce a new dataset for the industrial combinatorial advertising problem for inclusive finance to open-source. We hope the rethinking and benchmarking of PTO could facilitate more convenient evaluation and deployment, and inspire further improvements both in the academy and industry within this field.

GMTR: Graph Matching Transformers

Vision transformers (ViTs) have recently been used for visual matching beyond object detection and segmentation. However, the original grid dividing strategy of ViTs neglects the spatial information of the keypoints, limiting the sensitivity to local information. Therefore, we propose \textbf{QueryTrans} (Query Transformer), which adopts a cross-attention module and keypoints-based center crop strategy for better spatial information extraction. We further integrate the graph attention module and devise a transformer-based graph matching approach \textbf{GMTR} (Graph Matching TRansformers) whereby the combinatorial nature of GM is addressed by a graph transformer neural GM solver. On standard GM benchmarks, GMTR shows competitive performance against the SOTA frameworks. Specifically, on Pascal VOC, GMTR achieves $\mathbf{83.6\%}$ accuracy, $\mathbf{0.9\%}$ higher than the SOTA framework. On Spair-71k, GMTR shows great potential and outperforms most of the previous works. Meanwhile, on Pascal VOC, QueryTrans improves the accuracy of NGMv2 from $80.1\%$ to $\mathbf{83.3\%}$, and BBGM from $79.0\%$ to $\mathbf{84.5\%}$. On Spair-71k, QueryTrans improves NGMv2 from $80.6\%$ to $\mathbf{82.5\%}$, and BBGM from $82.1\%$ to $\mathbf{83.9\%}$. Source code will be made publicly available.

Rethinking Cross-Domain Sequential Recommendation under Open-World Assumptions

Cross-Domain Sequential Recommendation (CDSR) methods aim to tackle the data sparsity and cold-start problems present in Single-Domain Sequential Recommendation (SDSR). Existing CDSR works design their elaborate structures relying on overlapping users to propagate the cross-domain information. However, current CDSR methods make closed-world assumptions, assuming fully overlapping users across multiple domains and that the data distribution remains unchanged from the training environment to the test environment. As a result, these methods typically result in lower performance on online real-world platforms due to the data distribution shifts. To address these challenges under open-world assumptions, we design an \textbf{A}daptive \textbf{M}ulti-\textbf{I}nterest \textbf{D}ebiasing framework for cross-domain sequential recommendation (\textbf{AMID}), which consists of a multi-interest information module (\textbf{MIM}) and a doubly robust estimator (\textbf{DRE}). Our framework is adaptive for open-world environments and can improve the model of most off-the-shelf single-domain sequential backbone models for CDSR. Our MIM establishes interest groups that consider both overlapping and non-overlapping users, allowing us to effectively explore user intent and explicit interest. To alleviate biases across multiple domains, we developed the DRE for the CDSR methods. We also provide a theoretical analysis that demonstrates the superiority of our proposed estimator in terms of bias and tail bound, compared to the IPS estimator used in previous work.

Mind Your Solver! On Adversarial Attack and Defense for Combinatorial Optimization

Combinatorial optimization (CO) is a long-standing challenging task not only in its inherent complexity (e.g. NP-hard) but also the possible sensitivity to input conditions. In this paper, we take an initiative on developing the mechanisms for adversarial attack and defense towards combinatorial optimization solvers, whereby the solver is treated as a black-box function and the original problem's underlying graph structure (which is often available and associated with the problem instance, e.g. DAG, TSP) is attacked under a given budget. In particular, we present a simple yet effective defense strategy to modify the graph structure to increase the robustness of solvers, which shows its universal effectiveness across tasks and solvers.

A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs

Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the solution quality. Currently, machine learning for combinatorial optimization (MLCO) has become a trending research topic, but most existing MLCO methods treat CO as a single-level optimization by directly learning the end-to-end solutions, which are hard to scale up and mostly limited by the capacity of ML models given the high complexity of CO. In this paper, we propose a hybrid approach to combine the best of the two worlds, in which a bi-level framework is developed with an upper-level learning method to optimize the graph (e.g. add, delete or modify edges in a graph), fused with a lower-level heuristic algorithm solving on the optimized graph. Such a bi-level approach simplifies the learning on the original hard CO and can effectively mitigate the demand for model capacity. The experiments and results on several popular CO problems like Directed Acyclic Graph scheduling, Graph Edit Distance and Hamiltonian Cycle Problem show its effectiveness over manually designed heuristics and single-level learning methods.

Deep Reinforcement Learning of Graph Matching

Graph matching under node and pairwise constraints has been a building block in areas from combinatorial optimization, machine learning to computer vision, for effective structural representation and association. We present a reinforcement learning solver that seeks the node correspondence between two graphs, whereby the node embedding model on the association graph is learned to sequentially find the node-to-node matching. Our method differs from the previous deep graph matching model in the sense that they are focused on the front-end feature and affinity function learning while our method aims to learn the backend decision making given the affinity objective function whatever obtained by learning or not. Such an objective function maximization setting naturally fits with the reinforcement learning mechanism, of which the learning procedure is label-free. Besides, the model is not restricted to a fixed number of nodes for matching. These features make it more suitable for practical usage. Extensive experimental results on both synthetic datasets, natural images, and QAPLIB showcase the superior performance regarding both matching accuracy and efficiency. To our best knowledge, this is the first deep reinforcement learning solver for graph matching.

Combinatorial Learning of Graph Edit Distance via Dynamic Embedding

Graph Edit Distance (GED) is a popular similarity measurement for pairwise graphs and it also refers to the recovery of the edit path from the source graph to the target graph. Traditional A* algorithm suffers scalability issues due to its exhaustive nature, whose search heuristics heavily rely on human prior knowledge. This paper presents a hybrid approach by combing the interpretability of traditional search-based techniques for producing the edit path, as well as the efficiency and adaptivity of deep embedding models to achieve a cost-effective GED solver. Inspired by dynamic programming, node-level embedding is designated in a dynamic reuse fashion and suboptimal branches are encouraged to be pruned. To this end, our method can be readily integrated into A* procedure in a dynamic fashion, as well as significantly reduce the computational burden with a learned heuristic. Experimental results on different graph datasets show that our approach can remarkably ease the search process of A* without sacrificing much accuracy. To our best knowledge, this work is also the first deep learning-based GED method for recovering the edit path.