Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programming

Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), which formulate many important real-world applications. Cut selection heavily depends on (P1) which cuts to prefer and (P2) how many cuts to select. Although modern MILP solvers tackle (P1)-(P2) by human-designed heuristics, machine learning carries the potential to learn more effective heuristics. However, many existing learning-based methods learn which cuts to prefer, neglecting the importance of learning how many cuts to select. Moreover, we observe that (P3) what order of selected cuts to prefer significantly impacts the efficiency of MILP solvers as well. To address these challenges, we propose a novel hierarchical sequence/set model (HEM) to learn cut selection policies. Specifically, HEM is a bi-level model: (1) a higher-level module that learns how many cuts to select, (2) and a lower-level module -- that formulates the cut selection as a sequence/set to sequence learning problem -- to learn policies selecting an ordered subset with the cardinality determined by the higher-level module. To the best of our knowledge, HEM is the first data-driven methodology that well tackles (P1)-(P3) simultaneously. Experiments demonstrate that HEM significantly improves the efficiency of solving MILPs on eleven challenging MILP benchmarks, including two Huawei's real problems.

Learning to Stop Cut Generation for Efficient Mixed-Integer Linear Programming

Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), as they significantly tighten the dual bounds and improve the solving performance. A key problem for cuts is when to stop cuts generation, which is important for the efficiency of solving MILPs. However, many modern MILP solvers employ hard-coded heuristics to tackle this problem, which tends to neglect underlying patterns among MILPs from certain applications. To address this challenge, we formulate the cuts generation stopping problem as a reinforcement learning problem and propose a novel hybrid graph representation model (HYGRO) to learn effective stopping strategies. An appealing feature of HYGRO is that it can effectively capture both the dynamic and static features of MILPs, enabling dynamic decision-making for the stopping strategies. To the best of our knowledge, HYGRO is the first data-driven method to tackle the cuts generation stopping problem. By integrating our approach with modern solvers, experiments demonstrate that HYGRO significantly improves the efficiency of solving MILPs compared to competitive baselines, achieving up to 31% improvement.

Machine Learning Insides OptVerse AI Solver: Design Principles and Applications

In an era of digital ubiquity, efficient resource management and decision-making are paramount across numerous industries. To this end, we present a comprehensive study on the integration of machine learning (ML) techniques into Huawei Cloud's OptVerse AI Solver, which aims to mitigate the scarcity of real-world mathematical programming instances, and to surpass the capabilities of traditional optimization techniques. We showcase our methods for generating complex SAT and MILP instances utilizing generative models that mirror multifaceted structures of real-world problem. Furthermore, we introduce a training framework leveraging augmentation policies to maintain solvers' utility in dynamic environments. Besides the data generation and augmentation, our proposed approaches also include novel ML-driven policies for personalized solver strategies, with an emphasis on applications like graph convolutional networks for initial basis selection and reinforcement learning for advanced presolving and cut selection. Additionally, we detail the incorporation of state-of-the-art parameter tuning algorithms which markedly elevate solver performance. Compared with traditional solvers such as Cplex and SCIP, our ML-augmented OptVerse AI Solver demonstrates superior speed and precision across both established benchmarks and real-world scenarios, reinforcing the practical imperative and effectiveness of machine learning techniques in mathematical programming solvers.

Accelerate Presolve in Large-Scale Linear Programming via Reinforcement Learning

Large-scale LP problems from industry usually contain much redundancy that severely hurts the efficiency and reliability of solving LPs, making presolve (i.e., the problem simplification module) one of the most critical components in modern LP solvers. However, how to design high-quality presolve routines -- that is, the program determining (P1) which presolvers to select, (P2) in what order to execute, and (P3) when to stop -- remains a highly challenging task due to the extensive requirements on expert knowledge and the large search space. Due to the sequential decision property of the task and the lack of expert demonstrations, we propose a simple and efficient reinforcement learning (RL) framework -- namely, reinforcement learning for presolve (RL4Presolve) -- to tackle (P1)-(P3) simultaneously. Specifically, we formulate the routine design task as a Markov decision process and propose an RL framework with adaptive action sequences to generate high-quality presolve routines efficiently. Note that adaptive action sequences help learn complex behaviors efficiently and adapt to various benchmarks. Experiments on two solvers (open-source and commercial) and eight benchmarks (real-world and synthetic) demonstrate that RL4Presolve significantly and consistently improves the efficiency of solving large-scale LPs, especially on benchmarks from industry. Furthermore, we optimize the hard-coded presolve routines in LP solvers by extracting rules from learned policies for simple and efficient deployment to Huawei's supply chain. The results show encouraging economic and academic potential for incorporating machine learning to modern solvers.

A Circuit Domain Generalization Framework for Efficient Logic Synthesis in Chip Design

Logic Synthesis (LS) plays a vital role in chip design -- a cornerstone of the semiconductor industry. A key task in LS is to transform circuits -- modeled by directed acyclic graphs (DAGs) -- into simplified circuits with equivalent functionalities. To tackle this task, many LS operators apply transformations to subgraphs -- rooted at each node on an input DAG -- sequentially. However, we found that a large number of transformations are ineffective, which makes applying these operators highly time-consuming. In particular, we notice that the runtime of the Resub and Mfs2 operators often dominates the overall runtime of LS optimization processes. To address this challenge, we propose a novel data-driven LS operator paradigm, namely PruneX, to reduce ineffective transformations. The major challenge of developing PruneX is to learn models that well generalize to unseen circuits, i.e., the out-of-distribution (OOD) generalization problem. Thus, the major technical contribution of PruneX is the novel circuit domain generalization framework, which learns domain-invariant representations based on the transformation-invariant domain-knowledge. To the best of our knowledge, PruneX is the first approach to tackle the OOD problem in LS operators. We integrate PruneX with the aforementioned Resub and Mfs2 operators. Experiments demonstrate that PruneX significantly improves their efficiency while keeping comparable optimization performance on industrial and very large-scale circuits, achieving up to $3.1\times$ faster runtime.

Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model

Cutting planes (cuts) are important for solving mixed-integer linear programs (MILPs), which formulate a wide range of important real-world applications. Cut selection -- which aims to select a proper subset of the candidate cuts to improve the efficiency of solving MILPs -- heavily depends on (P1) which cuts should be preferred, and (P2) how many cuts should be selected. Although many modern MILP solvers tackle (P1)-(P2) by manually designed heuristics, machine learning offers a promising approach to learn more effective heuristics from MILPs collected from specific applications. However, many existing learning-based methods focus on learning which cuts should be preferred, neglecting the importance of learning the number of cuts that should be selected. Moreover, we observe from extensive empirical results that (P3) what order of selected cuts should be preferred has a significant impact on the efficiency of solving MILPs as well. To address this challenge, we propose a novel hierarchical sequence model (HEM) to learn cut selection policies via reinforcement learning. Specifically, HEM consists of a two-level model: (1) a higher-level model to learn the number of cuts that should be selected, (2) and a lower-level model -- that formulates the cut selection task as a sequence to sequence learning problem -- to learn policies selecting an ordered subset with the size determined by the higher-level model. To the best of our knowledge, HEM is the first method that can tackle (P1)-(P3) in cut selection simultaneously from a data-driven perspective. Experiments show that HEM significantly improves the efficiency of solving MILPs compared to human-designed and learning-based baselines on both synthetic and large-scale real-world MILPs, including MIPLIB 2017. Moreover, experiments demonstrate that HEM well generalizes to MILPs that are significantly larger than those seen during training.

Efficient Exploration in Resource-Restricted Reinforcement Learning

In many real-world applications of reinforcement learning (RL), performing actions requires consuming certain types of resources that are non-replenishable in each episode. Typical applications include robotic control with limited energy and video games with consumable items. In tasks with non-replenishable resources, we observe that popular RL methods such as soft actor critic suffer from poor sample efficiency. The major reason is that, they tend to exhaust resources fast and thus the subsequent exploration is severely restricted due to the absence of resources. To address this challenge, we first formalize the aforementioned problem as a resource-restricted reinforcement learning, and then propose a novel resource-aware exploration bonus (RAEB) to make reasonable usage of resources. An appealing feature of RAEB is that, it can significantly reduce unnecessary resource-consuming trials while effectively encouraging the agent to explore unvisited states. Experiments demonstrate that the proposed RAEB significantly outperforms state-of-the-art exploration strategies in resource-restricted reinforcement learning environments, improving the sample efficiency by up to an order of magnitude.

Sample-Efficient Reinforcement Learning via Conservative Model-Based Actor-Critic

Model-based reinforcement learning algorithms, which aim to learn a model of the environment to make decisions, are more sample efficient than their model-free counterparts. The sample efficiency of model-based approaches relies on whether the model can well approximate the environment. However, learning an accurate model is challenging, especially in complex and noisy environments. To tackle this problem, we propose the conservative model-based actor-critic (CMBAC), a novel approach that achieves high sample efficiency without the strong reliance on accurate learned models. Specifically, CMBAC learns multiple estimates of the Q-value function from a set of inaccurate models and uses the average of the bottom-k estimates -- a conservative estimate -- to optimize the policy. An appealing feature of CMBAC is that the conservative estimates effectively encourage the agent to avoid unreliable "promising actions" -- whose values are high in only a small fraction of the models. Experiments demonstrate that CMBAC significantly outperforms state-of-the-art approaches in terms of sample efficiency on several challenging tasks, and the proposed method is more robust than previous methods in noisy environments.

Random Pairwise Shapelets Forest

Shapelet is a discriminative subsequence of time series. An advanced shapelet-based method is to embed shapelet into accurate and fast random forest. However, it shows several limitations. First, random shapelet forest requires a large training cost for split threshold searching. Second, a single shapelet provides limited information for only one branch of the decision tree, resulting in insufficient accuracy and interpretability. Third, randomized ensemble causes interpretability declining. For that, this paper presents Random Pairwise Shapelets Forest (RPSF). RPSF combines a pair of shapelets from different classes to construct random forest. It omits threshold searching to be more efficient, includes more information for each node of the forest to be more effective. Moreover, a discriminability metric, Decomposed Mean Decrease Impurity (DMDI), is proposed to identify influential region for every class. Extensive experiments show RPSF improves the accuracy and training speed of shapelet-based forest. Case studies demonstrate the interpretability of our method.