We study combinatorial problems with real world applications such as machine scheduling, routing, and assignment. We propose a method that combines Reinforcement Learning (RL) and planning. This method can equally be applied to both the offline, as well as online, variants of the combinatorial problem, in which the problem components (e.g., jobs in scheduling problems) are not known in advance, but rather arrive during the decision-making process. Our solution is quite generic, scalable, and leverages distributional knowledge of the problem parameters. We frame the solution process as an MDP, and take a Deep Q-Learning approach wherein states are represented as graphs, thereby allowing our trained policies to deal with arbitrary changes in a principled manner. Though learned policies work well in expectation, small deviations can have substantial negative effects in combinatorial settings. We mitigate these drawbacks by employing our graph-convolutional policies as non-optimal heuristics in a compatible search algorithm, Monte Carlo Tree Search, to significantly improve overall performance. We demonstrate our method on two problems: Machine Scheduling and Capacitated Vehicle Routing. We show that our method outperforms custom-tailored mathematical solvers, state of the art learning-based algorithms, and common heuristics, both in computation time and performance.
Combinatorial optimization serves as an essential part in many modern industrial applications. A great number of the problems are offline setting due to safety and/or cost issues. While simulation-based approaches appear difficult to realise for complicated systems, in this research, we propose DeepCO, an offline combinatorial optimization framework utilizing deep learning. We also design an offline variation of Travelling Salesman Problem (TSP) to model warehouse operation sequence optimization problem for evaluation. With only limited historical data, novel proposed distribution regularized …
Tsinghua University（清华大学）；Microsoft Research Asia（微软亚洲研究院）
In this paper, we study the application of the Thompson sampling (TS) methodology to the stochastic combinatorial multi-armed bandit (CMAB) framework. We first analyze the standard TS algorithm for the general CMAB model when the outcome distributions of all the base arms are independent, and obtain a distribution-dependent regret bound of $O(m\log K_{\max}\log T / Δ_{\min})$, where $m$ is the number of base arms, $K_{\max}$ is the size of the largest super arm, $T$ is the time horizon, and $Δ_{\min}$ is the minimum gap between the expected reward of the optimal solution and any non-optimal so…
A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to combinatorial constraints, and then observes stochastic weights of these items and receives their sum as a payoff. In this paper, we consider efficient learning in large-scale combinatorial semi-bandits with linear generalization, and as a solution, propose two learning algorithms called Combinatorial Linear Thompson Sampling (CombLinTS) and Combinatorial Linear UCB (CombLinUCB). Both algorithms are computationally efficient as long as the offline…
Coordinating Ride-Pooling with Public Transit using Reward-Guided Conservative Q-Learning: An Offline Training and Online Fine-Tuning Reinforcement Learning Framework
The Hong Kong University of Science and Technology（香港科技大学）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
The Chinese University of Hong Kong（香港中文大学）；Carnegie Mellon University（卡内基梅隆大学）；Bytedance（字节跳动）；Microsoft Research（微软研究院）
Multi-layered network exploration (MuLaNE) problem is an important problem abstracted from many applications. In MuLaNE, there are multiple network layers where each node has an importance weight and each layer is explored by a random walk. The MuLaNE task is to allocate total random walk budget $B$ into each network layer so that the total weights of the unique nodes visited by random walks are maximized. We systematically study this problem from offline optimization to online learning. For the offline optimization setting where the network structure and node weights are known, we provide gre…
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…
We propose a sample-efficient alternative for importance weighting for situations where one only has sample access to the probability distribution that generates the observations. Our new method, called Geometric Resampling (GR), is described and analyzed in the context of online combinatorial optimization under semi-bandit feedback, where a learner sequentially selects its actions from a combinatorial decision set so as to minimize its cumulative loss. In particular, we show that the well-known Follow-the-Perturbed-Leader (FPL) prediction method coupled with Geometric Resampling yields the fi…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University Innsbruck（因斯布鲁克大学）
The ability to form complex plans based on raw visual input is a litmus test for current capabilities of artificial intelligence, as it requires a seamless combination of visual processing and abstract algorithmic execution, two traditionally separate areas of computer science. A recent surge of interest in this field brought advances that yield good performance in tasks ranging from arcade games to continuous control; these methods however do not come without significant issues, such as limited generalization capabilities and difficulties when dealing with combinatorially hard planning instan…
UC Berkeley（加州大学伯克利分校）；Meta AI Research（Meta人工智能研究院）；Princeton University（普林斯顿大学）；UT Austin（德克萨斯大学奥斯汀分校）
Object rearrangement is a challenge for embodied agents because solving these tasks requires generalizing across a combinatorially large set of configurations of entities and their locations. Worse, the representations of these entities are unknown and must be inferred from sensory percepts. We present a hierarchical abstraction approach to uncover these underlying entities and achieve combinatorial generalization from unstructured visual inputs. By constructing a factorized transition graph over clusters of entity representations inferred from pixels, we show how to learn a correspondence bet…
A combinatorial recommender (CR) system feeds a list of items to a user at a time in the result page, in which the user behavior is affected by both contextual information and items. The CR is formulated as a combinatorial optimization problem with the objective of maximizing the recommendation reward of the whole list. Despite its importance, it is still a challenge to build a practical CR system, due to the efficiency, dynamics, personalization requirement in online environment. In particular, we tear the problem into two sub-problems, list generation and list evaluation. Novel and practical…
An efficient algorithm for learning with semi-bandit feedback
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；MTA SZTAKI Institute for Computer Science and Control（MTA SZTAKI计算机科学与控制研究所）；ETH Zürich（苏黎世联邦理工学院）
Thompson sampling (TS) has attracted a lot of interest in the bandit area. It was introduced in the 1930s but has not been theoretically proven until recent years. All of its analysis in the combinatorial multi-armed bandit (CMAB) setting requires an exact oracle to provide optimal solutions with any input. However, such an oracle is usually not feasible since many combinatorial optimization problems are NP-hard and only approximation oracles are available. An example (Wang and Chen, 2018) has shown the failure of TS to learn with an approximation oracle. However, this oracle is uncommon and i…
Microsoft Research（微软研究院）；Tsinghua University（清华大学）
In this paper, we study combinatorial pure exploration for dueling bandits (CPE-DB): we have multiple candidates for multiple positions as modeled by a bipartite graph, and in each round we sample a duel of two candidates on one position and observe who wins in the duel, with the goal of finding the best candidate-position matching with high probability after multiple rounds of samples. CPE-DB is an adaptation of the original combinatorial pure exploration for multi-armed bandit (CPE-MAB) problem to the dueling bandit setting. We consider both the Borda winner and the Condorcet winner cases. F…
Microsoft Research（微软研究院）；Peking University（北京大学）；Princeton University（普林斯顿大学）；Kuaishou Inc.（快手公司）
In this paper, we investigate the non-stationary combinatorial semi-bandit problem, both in the switching case and in the dynamic case. In the general case where (a) the reward function is non-linear, (b) arms may be probabilistically triggered, and (c) only approximate offline oracle exists \cite{wang2017improving}, our algorithm achieves $\tilde{\mathcal{O}}(\sqrt{\mathcal{S} T})$ distribution-dependent regret in the switching case, and $\tilde{\mathcal{O}}(\mathcal{V}^{1/3}T^{2/3})$ in the dynamic case, where $\mathcal S$ is the number of switchings and $\mathcal V$ is the sum of the total …
Guangzhou University（广州大学）；Zhejiang University（浙江大学）；The University of Hong Kong（香港大学）
Recent studies have revealed that neural combinatorial optimization (NCO) has advantages over conventional algorithms in many combinatorial optimization problems such as routing, but it is less efficient for more complicated optimization tasks such as packing which involves mutually conditioned action spaces. In this paper, we propose a Recurrent Conditional Query Learning (RCQL) method to solve both 2D and 3D packing problems. We first embed states by a recurrent encoder, and then adopt attention with conditional queries from previous actions. The conditional query mechanism fills the informa…
Microsoft Research（微软研究院）；Princeton University（普林斯顿大学）；The University of Texas at Austin（得克萨斯大学奥斯汀分校）；Tsinghua University（清华大学）；Shanghai University of Finance and Economics（上海财经大学）
In this paper, we study the stochastic combinatorial multi-armed bandit (CMAB) framework that allows a general nonlinear reward function, whose expected value may not depend only on the means of the input random variables but possibly on the entire distributions of these variables. Our framework enables a much larger class of reward functions such as the $\max()$ function and nonlinear utility functions. Existing techniques relying on accurate estimations of the means of random variables, such as the upper confidence bound (UCB) technique, do not work directly on these functions. We propose a …
We define a general framework for a large class of combinatorial multi-armed bandit (CMAB) problems, where subsets of base arms with unknown distributions form super arms. In each round, a super arm is played and the base arms contained in the super arm are played and their outcomes are observed. We further consider the extension in which more based arms could be probabilistically triggered based on the outcomes of already triggered arms. The reward of the super arm depends on the outcomes of all played arms, and it only needs to satisfy two mild assumptions, which allow a large class of nonli…
Beihang University（北京航空航天大学）；MIRA Lab, USTC（中国科学技术大学 MIRA 实验室）；Huawei Cloud Co.（华为云计算有限公司）
Most combinatorial optimization problems can be formulated as mixed integer linear programming (MILP), in which branch-and-bound (B\&B) is a general and widely used method. Recently, learning to branch has become a hot research topic in the intersection of machine learning and combinatorial optimization. In this paper, we propose a novel reinforcement learning-based B\&B algorithm. Similar to offline reinforcement learning, we initially train on the demonstration data to accelerate learning massively. With the improvement of the training effect, the agent starts to interact with the environmen…
Chicago Booth School of Business（芝加哥大学布斯商学院）；MIT Sloan School of Management（麻省理工学院斯隆管理学院）；Google Research（谷歌研究院）
Motivated by online decision-making in time-varying combinatorial environments, we study the problem of transforming offline algorithms to their online counterparts. We focus on offline combinatorial problems that are amenable to a constant factor approximation using a greedy algorithm that is robust to local errors. For such problems, we provide a general framework that efficiently transforms offline robust greedy algorithms to online ones using Blackwell approachability. We show that the resulting online algorithms have $O(\sqrt{T})$ (approximate) regret under the full information setting. W…
Duke University（杜克大学）；Purdue University（普渡大学）；George Washington University（乔治华盛顿大学）；University of Michigan（密歇根大学）
We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this…
Divide and Learn: Multi-Objective Combinatorial Optimization at Scale
Department of Computer Science & Engineering UC San Diego（计算机科学与工程系，圣地亚哥大学）；Department of Statistics Stanford University（统计学系，斯坦福大学）；Halıcıoğlu Data Science Institute UC San Diego（Halıcıoğlu数据科学研究所，圣地亚哥大学）
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；National Technical University of Athens（雅典国立技术大学）
We study various discrete nonlinear combinatorial optimization problems in an online learning framework. In the first part, we address the question of whether there are negative results showing that getting a vanishing (or even vanishing approximate) regret is computational hard. We provide a general reduction showing that many (min-max) polynomial time solvable problems not only do not have a vanishing regret, but also no vanishing approximation $α$-regret, for some $α$ (unless $NP=BPP$). Then, we focus on a particular min-max problem, the min-max version of the vertex cover problem which is …
Many network applications can be formulated as NP-hard combinatorial optimization problems of community detection (CD). Due to the NP-hardness, to balance the CD quality and efficiency remains a challenge. Most existing CD methods are transductive, which are independently optimized only for the CD on a single graph. Some of these methods use advanced machine learning techniques to obtain high-quality CD results but usually have high complexity. Other approaches use fast heuristic approximation to ensure low runtime but may suffer from quality degradation. In contrast to these transductive meth…
Distributed Constraint Optimization Problems (DCOPs) are an important subclass of combinatorial optimization problems, where information and controls are distributed among multiple autonomous agents. Previously, Machine Learning (ML) has been largely applied to solve combinatorial optimization problems by learning effective heuristics. However, existing ML-based heuristic methods are often not generalizable to different search algorithms. Most importantly, these methods usually require full knowledge about the problems to be solved, which are not suitable for distributed settings where central…
