Combinatorial optimization problem (COP) over graphs is a fundamental challenge in optimization. Reinforcement learning (RL) has recently emerged as a new framework to tackle these problems and has demonstrated promising results. However, most RL solutions employ a greedy manner to construct the solution incrementally, thus inevitably pose unnecessary dependency on action sequences and need a lot of problem-specific designs. We propose a general RL framework that not only exhibits state-of-the-art empirical performance but also generalizes to a variety class of COPs. Specifically, we define state as a solution to a problem instance and action as a perturbation to this solution. We utilize graph neural networks (GNN) to extract latent representations for given problem instances for state-action encoding, and then apply deep Q-learning to obtain a policy that gradually refines the solution by flipping or swapping vertex labels. Experiments are conducted on Maximum $k$-Cut and Traveling Salesman Problem and performance improvement is achieved against a set of learning-based and heuristic baselines.
Beijing National Laboratory for Molecular Sciences (BNLMS)（北京分子科学国家实验室）
Most algorithms for the multi-armed bandit problem in reinforcement learning aimed to maximize the expected reward, which are thus useful in searching the optimized candidate with the highest reward (function value) for diverse applications (e.g., AlphaGo). However, in some typical application scenaios such as drug discovery, the aim is to search a diverse set of candidates with high reward. Here we propose a reversible upper confidence bound (rUCB) algorithm for such a purpose, and demonstrate its application in virtual screening upon intrinsically disordered proteins (IDPs). It is shown that…
Combinatorial optimization problems (COPs) on the graph with real-life applications are canonical challenges in Computer Science. The difficulty of finding quality labels for problem instances holds back leveraging supervised learning across combinatorial problems. Reinforcement learning (RL) algorithms have recently been adopted to solve this challenge automatically. The underlying principle of this approach is to deploy a graph neural network (GNN) for encoding both the local information of the nodes and the graph-structured data in order to capture the current state of the environment. Then…
Symmetric Replay Training: Enhancing Sample Efficiency in Deep Reinforcement Learning for Combinatorial Optimization
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院（KAIST））；Pohang University of Science and Technology (POSTECH)（浦项科技大学（POSTECH））；OMELET
We develop a general method for incentive-based programming of hybrid quantum-classical computing systems using reinforcement learning, and apply this to solve combinatorial optimization problems on both simulated and real gate-based quantum computers. Relative to a set of randomly generated problem instances, agents trained through reinforcement learning techniques are capable of producing short quantum programs which generate high quality solutions on both types of quantum resources. We observe generalization to problems outside of the training set, as well as generalization from the simulat…
Google Brain（谷歌大脑）；University of Cambridge（剑桥大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；UC Berkeley（加州大学伯克利分校）
Deep reinforcement learning algorithms can learn complex behavioral skills, but real-world application of these methods requires a large amount of experience to be collected by the agent. In practical settings, such as robotics, this involves repeatedly attempting a task, resetting the environment between each attempt. However, not all tasks are easily or automatically reversible. In practice, this learning process requires extensive human intervention. In this work, we propose an autonomous method for safe and efficient reinforcement learning that simultaneously learns a forward and reset pol…
University of the Basque Country（巴斯克大学）；Lehigh University（理海大学）
This paper presents a framework to tackle constrained combinatorial optimization problems using deep Reinforcement Learning (RL). To this end, we extend the Neural Combinatorial Optimization (NCO) theory in order to deal with constraints in its formulation. Notably, we propose defining constrained combinatorial problems as fully observable Constrained Markov Decision Processes (CMDP). In that context, the solution is iteratively constructed based on interactions with the environment. The model, in addition to the reward signal, relies on penalty signals generated from constraint dissatisfactio…
Combinatorial Multivariant Multi-Armed Bandits with Applications to Episodic Reinforcement Learning and Beyond
The Chinese University of Hong Kong（香港中文大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Microsoft Research（微软研究院）；Shanghai Jiao Tong University（上海交通大学）
University of Washington（华盛顿大学）；Microsoft Research（微软研究院）
We introduce an online popularity prediction and tracking task as a benchmark task for reinforcement learning with a combinatorial, natural language action space. A specified number of discussion threads predicted to be popular are recommended, chosen from a fixed window of recent comments to track. Novel deep reinforcement learning architectures are studied for effective modeling of the value function associated with actions comprised of interdependent sub-actions. The proposed model, which represents dependence between sub-actions through a bi-directional LSTM, gives the best performance acr…
University of Alberta（阿尔伯塔大学）；ETH Zurich（苏黎世联邦理工学院）；University College London（伦敦大学学院）；DeepMind（深度思维）
A practical challenge in reinforcement learning are combinatorial action spaces that make planning computationally demanding. For example, in cooperative multi-agent reinforcement learning, a potentially large number of agents jointly optimize a global reward function, which leads to a combinatorial blow-up in the action space by the number of agents. As a minimal requirement, we assume access to an argmax oracle that allows to efficiently compute the greedy policy for any Q-function in the model class. Building on recent work in planning with local access to a simulator and linear function ap…
This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city coordinates, predicts a distribution over different city permutations. Using negative tour length as the reward signal, we optimize the parameters of the recurrent network using a policy gradient method. We compare learning the network parameters on a set of training graphs against learning them on individual test graphs. Despite the computational expense, without …
Columbia University（哥伦比亚大学）；Cornell University（康奈尔大学）
In this work, we introduce Graph Pointer Networks (GPNs) trained using reinforcement learning (RL) for tackling the traveling salesman problem (TSP). GPNs build upon Pointer Networks by introducing a graph embedding layer on the input, which captures relationships between nodes. Furthermore, to approximate solutions to constrained combinatorial optimization problems such as the TSP with time windows, we train hierarchical GPNs (HGPNs) using RL, which learns a hierarchical policy to find an optimal city permutation under constraints. Each layer of the hierarchy is designed with a separate rewar…
MIT Operations Research Center（麻省理工学院运筹学中心）；Google Research（谷歌研究院）
Value-function-based methods have long played an important role in reinforcement learning. However, finding the best next action given a value function of arbitrary complexity is nontrivial when the action space is too large for enumeration. We develop a framework for value-function-based deep reinforcement learning with a combinatorial action space, in which the action selection problem is explicitly formulated as a mixed-integer optimization problem. As a motivating example, we present an application of this framework to the capacitated vehicle routing problem (CVRP), a combinatorial optimiz…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Zyfra（兹夫特拉）；Criteo AI Lab（Criteo人工智能实验室）
Many traditional algorithms for solving combinatorial optimization problems involve using hand-crafted heuristics that sequentially construct a solution. Such heuristics are designed by domain experts and may often be suboptimal due to the hard nature of the problems. Reinforcement learning (RL) proposes a good alternative to automate the search of these heuristics by training an agent in a supervised or self-supervised manner. In this survey, we explore the recent advancements of applying RL frameworks to hard combinatorial problems. Our survey provides the necessary background for operations…
In sponsored search, keyword recommendations help advertisers to achieve much better performance within limited budget. Many works have been done to mine numerous candidate keywords from search logs or landing pages. However, the strategy to select from given candidates remains to be improved. The existing relevance-based, popularity-based and regular combinatorial strategies fail to take the internal or external competitions among keywords into consideration. In this paper, we regard keyword recommendations as a combinatorial optimization problem and solve it with a modified pointer network s…
University of Alberta（阿尔伯塔大学）；Huawei Technologies Canada Co., Ltd.（华为技术加拿大有限公司）
Branch-and-bound is a systematic enumerative method for combinatorial optimization, where the performance highly relies on the variable selection strategy. State-of-the-art handcrafted heuristic strategies suffer from relatively slow inference time for each selection, while the current machine learning methods require a significant amount of labeled data. We propose a new approach for solving the data labeling and inference latency issues in combinatorial optimization based on the use of the reinforcement learning (RL) paradigm. We use imitation learning to bootstrap an RL agent and then use P…
Ecole Polytechnique de Montréal（蒙特利尔综合理工学院）；Element AI（Element AI公司）；University of Toronto Scarborough（多伦多大学士嘉堡分校）
Combinatorial optimization has found applications in numerous fields, from aerospace to transportation planning and economics. The goal is to find an optimal solution among a finite set of possibilities. The well-known challenge one faces with combinatorial optimization is the state-space explosion problem: the number of possibilities grows exponentially with the problem size, which makes solving intractable for large problems. In the last years, deep reinforcement learning (DRL) has shown its promise for designing good heuristics dedicated to solve NP-hard combinatorial optimization problems.…
POSTECH（浦项科技大学）；University of Guelph（圭尔夫大学）；Vector Institute（矢量研究所）；POSCO（浦项制铁公司）
Discovering a solution in a combinatorial space is prevalent in many real-world problems but it is also challenging due to diverse complex constraints and the vast number of possible combinations. To address such a problem, we introduce a novel formulation, combinatorial construction, which requires a building agent to assemble unit primitives (i.e., LEGO bricks) sequentially -- every connection between two bricks must follow a fixed rule, while no bricks mutually overlap. To construct a target object, we provide incomplete knowledge about the desired target (i.e., 2D images) instead of exact …
With the advancement of deep learning techniques, major cloud providers and niche machine learning service providers start to offer their cloud-based machine learning tools, also known as machine learning as a service (MLaaS), to the public. According to our measurement, for the same task, these MLaaSes from different providers have varying performance due to the proprietary datasets, models, etc. Federating different MLaaSes together allows us to improve the analytic performance further. However, naively aggregating results from different MLaaSes not only incurs significant momentary cost but…
University of Oxford（牛津大学）；Facebook AI Research（Facebook AI研究院）；Russian Quantum Center（俄罗斯量子中心）
Many real-world problems can be reduced to combinatorial optimization on a graph, where the subset or ordering of vertices that maximize some objective function must be found. With such tasks often NP-hard and analytically intractable, reinforcement learning (RL) has shown promise as a framework with which efficient heuristic methods to tackle these problems can be learned. Previous works construct the solution subset incrementally, adding one element at a time, however, the irreversible nature of this approach prevents the agent from revising its earlier decisions, which may be necessary give…
Russian Quantum Center（俄罗斯量子中心）；University of Oxford（牛津大学）
Quantum hardware and quantum-inspired algorithms are becoming increasingly popular for combinatorial optimization. However, these algorithms may require careful hyperparameter tuning for each problem instance. We use a reinforcement learning agent in conjunction with a quantum-inspired algorithm to solve the Ising energy minimization problem, which is equivalent to the Maximum Cut problem. The agent controls the algorithm by tuning one of its parameters with the goal of improving recently seen solutions. We propose a new Rescaled Ranked Reward (R3) method that enables stable single-player vers…
The formal semantics of an interpreted first-order logic (FOL) statement can be given in Tarskian Semantics or a basically equivalent Game Semantics. The latter maps the statement and the interpretation into a two-player semantic game. Many combinatorial problems can be described using interpreted FOL statements and can be mapped into a semantic game. Therefore, learning to play a semantic game perfectly leads to the solution of a specific instance of a combinatorial problem. We adapt the AlphaZero algorithm so that it becomes better at learning to play semantic games that have different chara…
Adversarial self-play in two-player games has delivered impressive results when used with reinforcement learning algorithms that combine deep neural networks and tree search. Algorithms like AlphaZero and Expert Iteration learn tabula-rasa, producing highly informative training data on the fly. However, the self-play training strategy is not directly applicable to single-player games. Recently, several practically important combinatorial optimisation problems, such as the travelling salesman problem and the bin packing problem, have been reformulated as reinforcement learning problems, increas…
Illinois Institute of Technology（伊利诺伊理工学院）；Clemson University（克莱姆森大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Argonne National Laboratory（阿贡国家实验室）
Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can outperform classical state-of-the-art methods in the near term. QAOA is a hybrid quantum-classical algorithm that combines a parameterized quantum state evolution with a classical optimization routine to approximately solve combinatorial problems. The quality of the solution obtained by QAOA within a fixed budget of calls to the quantum computer depends on the per…
Graph problems such as traveling salesman problem, or finding minimal Steiner trees are widely studied and used in data engineering and computer science. Typically, in real-world applications, the features of the graph tend to change over time, thus, finding a solution to the problem becomes challenging. The dynamic version of many graph problems are the key for a plethora of real-world problems in transportation, telecommunication, and social networks. In recent years, using deep learning techniques to find heuristic solutions for NP-hard graph combinatorial problems has gained much interest …
We introduce robustness in \textit{restless multi-armed bandits} (RMABs), a popular model for constrained resource allocation among independent stochastic processes (arms). Nearly all RMAB techniques assume stochastic dynamics are precisely known. However, in many real-world settings, dynamics are estimated with significant \emph{uncertainty}, e.g., via historical data, which can lead to bad outcomes if ignored. To address this, we develop an algorithm to compute minimax regret -- robust policies for RMABs. Our approach uses a double oracle framework (oracles for \textit{agent} and \textit{nat…
Transform then Explore: a Simple and Effective Technique for Exploratory Combinatorial Optimization with Reinforcement Learning
College of Systems Engineering, National University of Defense Technology（国防科技大学系统工程学院）；Washington University in St. Louis（圣路易斯华盛顿大学）；Huaxia Bank（华夏银行）；University of International Business and Economics（对外经济贸易大学）
Synergizing Reinforcement Learning and Genetic Algorithms for Neural Combinatorial Optimization
C 2 DL, Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）；School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences（中国科学院大学先进交叉学科学院）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）
KAIST（韩国科学技术院）；King’s College London（伦敦国王学院）；Naver Corporation（Naver公司）
We consider the Markov Decision Process (MDP) of selecting a subset of items at each step, termed the Select-MDP (S-MDP). The large state and action spaces of S-MDPs make them intractable to solve with typical reinforcement learning (RL) algorithms especially when the number of items is huge. In this paper, we present a deep RL algorithm to solve this issue by adopting the following key ideas. First, we convert the original S-MDP into an Iterative Select-MDP (IS-MDP), which is equivalent to the S-MDP in terms of optimal actions. IS-MDP decomposes a joint action of selecting K items simultaneou…
Inverse Reinforcement Learning (IRL) is a powerful way of learning from demonstrations. In this paper, we address IRL problems with the availability of prior knowledge that optimal policies will never violate certain constraints. Conventional approaches ignoring these constraints need many demonstrations to converge. We propose XOR-Maximum Entropy Constrained Inverse Reinforcement Learning (X-MEN), which is guaranteed to converge to the optimal policy in linear rate w.r.t. the number of learning iterations. X-MEN embeds XOR-sampling -- a provable sampling approach that transforms the #P comple…
Research Centre in Digital Services (CISeD)（数字服务研究中心（CISeD））；Polytechnic Institute of Viseu（维塞乌理工学院）；Rockets of Awesome
The Orienteering Problem with Time Windows (OPTW) is a combinatorial optimization problem where the goal is to maximize the total score collected from different visited locations. The application of neural network models to combinatorial optimization has recently shown promising results in dealing with similar problems, like the Travelling Salesman Problem. A neural network allows learning solutions using reinforcement learning or supervised learning, depending on the available data. After the learning stage, it can be generalized and quickly fine-tuned to further improve performance and perso…
RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmark
Leuphana University（吕贝克大学）；MIT（麻省理工学院）；Southeast University（东南大学）；Peking University（北京大学）；Bielefeld University（比勒菲尔德大学）；Nanyang Technological University（南洋理工大学）；Soochow University（苏州大学）；City University of Hong Kong（香港城市大学）；University of Brescia（布雷西亚大学）；ORTEC（ORTEC公司）；Singapore Management University（新加坡管理学院）；Brandenburg University of Technology（勃兰登堡技术大学）
Combinatorial optimisation problems framed as mixed integer linear programmes (MILPs) are ubiquitous across a range of real-world applications. The canonical branch-and-bound algorithm seeks to exactly solve MILPs by constructing a search tree of increasingly constrained sub-problems. In practice, its solving time performance is dependent on heuristics, such as the choice of the next variable to constrain ('branching'). Recently, machine learning (ML) has emerged as a promising paradigm for branching. However, prior works have struggled to apply reinforcement learning (RL), citing sparse rewar…
Network-on-chip (NoC) architectures rely on buffers to store flits to cope with contention for router resources during packet switching. Recently, reversible multi-function channel (RMC) buffers have been proposed to simultaneously reduce power and enable adaptive NoC buffering between adjacent routers. While adaptive buffering can improve NoC performance by maximizing buffer utilization, controlling the RMC buffer allocations requires a congestion-aware, scalable, and proactive policy. In this work, we present RACE, a novel reinforcement learning (RL) framework that utilizes better awareness …
