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 given the complexity of the optimization task. We instead propose that the agent should seek to continuously improve the solution by learning to explore at test time. Our approach of exploratory combinatorial optimization (ECO-DQN) is, in principle, applicable to any combinatorial problem that can be defined on a graph. Experimentally, we show our method to produce state-of-the-art RL performance on the Maximum Cut problem. Moreover, because ECO-DQN can start from any arbitrary configuration, it can be combined with other search methods to further improve performance, which we demonstrate using a simple random search.
High-dimensional observations and complex real-world dynamics present major challenges in reinforcement learning for both function approximation and exploration. We address both of these challenges with two complementary techniques: First, we develop a gradient-boosting style, non-parametric function approximator for learning on $Q$-function residuals. And second, we propose an exploration strategy inspired by the principles of state abstraction and information acquisition under uncertainty. We demonstrate the empirical effectiveness of these techniques, first, as a preliminary check, on two s…
Saliency maps are frequently used to support explanations of the behavior of deep reinforcement learning (RL) agents. However, a review of how saliency maps are used in practice indicates that the derived explanations are often unfalsifiable and can be highly subjective. We introduce an empirical approach grounded in counterfactual reasoning to test the hypotheses generated from saliency maps and assess the degree to which they correspond to the semantics of RL environments. We use Atari games, a common benchmark for deep RL, to evaluate three types of saliency maps. Our results show the exten…
New York University（纽约大学）；Facebook AI Research（脸书人工智能研究院）；UC Berkeley（加州大学伯克利分校）
Recent progress in deep learning has relied on access to large and diverse datasets. Such data-driven progress has been less evident in offline reinforcement learning (RL), because offline RL data is usually collected to optimize specific target tasks limiting the data's diversity. In this work, we propose Exploratory data for Offline RL (ExORL), a data-centric approach to offline RL. ExORL first generates data with unsupervised reward-free exploration, then relabels this data with a downstream reward before training a policy with offline RL. We find that exploratory data allows vanilla off-po…
Meta-reinforcement learning (meta-RL) aims to quickly solve new tasks by leveraging knowledge from prior tasks. However, previous studies often assume a single mode homogeneous task distribution, ignoring possible structured heterogeneity among tasks. Leveraging such structures can better facilitate knowledge sharing among related tasks and thus improve sample efficiency. In this paper, we explore the structured heterogeneity among tasks via clustering to improve meta-RL. We develop a dedicated exploratory policy to discover task structures via divide-and-conquer. The knowledge of the identifi…
Exploratory Diffusion Model for Unsupervised Reinforcement Learning
Department of Computer Science & Technology, Institute for AI, BNRist Center, Tsinghua-Bosch Joint ML Center, THBI Lab, Tsinghua University（计算机科学与技术系、人工智能研究院、BNRist中心、清华-博世联合机器学习中心、THBI实验室、清华大学）
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 …
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）
New York University（纽约大学）；Facebook AI Research（脸书人工智能研究院）
Learning effective representations in image-based environments is crucial for sample efficient Reinforcement Learning (RL). Unfortunately, in RL, representation learning is confounded with the exploratory experience of the agent -- learning a useful representation requires diverse data, while effective exploration is only possible with coherent representations. Furthermore, we would like to learn representations that not only generalize across tasks but also accelerate downstream exploration for efficient task-specific training. To address these challenges we propose Proto-RL, a self-supervise…
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…
Tel Aviv University（特拉维夫大学）；Google Research（谷歌研究院）
We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory conditions.We present a computationally efficient policy optimization algorithm for the challenging general setting of unknown dynamics and bandit feedback, featuring a combination of mirror-descent and least squares policy evaluation in an auxiliary MDP used to compute exploration bonuses.Our algorithm obtains an $\widetilde O(K^{6/7})$ regret bound, improving signifi…
ANEO；Centre Borelli - ENS Paris-saclay（巴黎萨克雷高等师范学院博雷利中心）；Criteo AI Lab（科韬人工智能实验室）；Crest, ENSAE（法国国立统计与经济管理学院 Crest 研究中心）
The objective of offline RL is to learn optimal policies when a fixed exploratory demonstrations data-set is available and sampling additional observations is impossible (typically if this operation is either costly or rises ethical questions). In order to solve this problem, off the shelf approaches require a properly defined cost function (or its evaluation on the provided data-set), which are seldom available in practice. To circumvent this issue, a reasonable alternative is to query an expert for few optimal demonstrations in addition to the exploratory data-set. The objective is then to l…
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…
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…
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…
Recent research on structured exploration placed emphasis on identifying novel states in the state space and incentivizing the agent to revisit them through intrinsic reward bonuses. In this study, we question whether the performance boost demonstrated through these methods is indeed due to the discovery of structure in exploratory schedule of the agent or is the benefit largely attributed to the perturbations in the policy and reward space manifested in pursuit of structured exploration. In this study we investigate the effect of perturbations in policy and reward spaces on the exploratory be…
Applied Artificial Intelligence Institute, Deakin University（迪肯大学应用人工智能研究所）
Prior access to domain knowledge could significantly improve the performance of a reinforcement learning agent. In particular, it could help agents avoid potentially catastrophic exploratory actions, which would otherwise have to be experienced during learning. In this work, we identify consistently undesirable actions in a set of previously learned tasks, and use pseudo-rewards associated with them to learn a prior policy. In addition to enabling safer exploratory behaviors in subsequent tasks in the domain, we show that these priors are transferable to similar environments, and can be learne…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
MDPs with low-rank transitions -- that is, the transition matrix can be factored into the product of two matrices, left and right -- is a highly representative structure that enables tractable learning. The left matrix enables expressive function approximation for value-based learning and has been studied extensively. In this work, we instead investigate sample-efficient learning with density features, i.e., the right matrix, which induce powerful models for state-occupancy distributions. This setting not only sheds light on leveraging unsupervised learning in RL, but also enables plug-in solu…
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…
Let it Calm: Exploratory Annealed Decoding for Verifiable Reinforcement Learning
Department of Computer Science, University of Chicago（芝加哥大学计算机科学系）；Department of Statistics, University of Chicago（芝加哥大学统计系）；Toyota Technological Insitute at Chicago（芝加哥丰田技术研究所）；Data Science Institute, University of Chicago（芝加哥大学数据科学研究所）；Meta AI
In reinforcement learning (RL) algorithms, exploratory control inputs are used during learning to acquire knowledge for decision making and control, while the true dynamics of a controlled object is unknown. However, this exploring property sometimes causes undesired situations by violating constraints regarding the state of the controlled object. In this paper, we propose an automatic exploration process adjustment method for safe RL in continuous state and action spaces utilizing a linear nominal model of the controlled object. Specifically, our proposed method automatically selects whether …
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…
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…
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…
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…
We propose to solve large scale Markowitz mean-variance (MV) portfolio allocation problem using reinforcement learning (RL). By adopting the recently developed continuous-time exploratory control framework, we formulate the exploratory MV problem in high dimensions. We further show the optimality of a multivariate Gaussian feedback policy, with time-decaying variance, in trading off exploration and exploitation. Based on a provable policy improvement theorem, we devise a scalable and data-efficient RL algorithm and conduct large scale empirical tests using data from the S&P 500 stocks. We foun…
We study an exploration method for model-free RL that generalizes the counter-based exploration bonus methods and takes into account long term exploratory value of actions rather than a single step look-ahead. We propose a model-free RL method that modifies Delayed Q-learning and utilizes the long-term exploration bonus with provable efficiency. We show that our proposed method finds a near-optimal policy in polynomial time (PAC-MDP), and also provide experimental evidence that our proposed algorithm is an efficient exploration method.
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…
This paper is both an introduction and an invitation. It is an introduction to CARLE, a Life-like cellular automata simulator and reinforcement learning environment. It is also an invitation to Carle's Game, a challenge in open-ended machine exploration and creativity. Inducing machine agents to excel at creating interesting patterns across multiple cellular automata universes is a substantial challenge, and approaching this challenge is likely to require contributions from the fields of artificial life, AI, machine learning, and complexity, at multiple levels of interest. Carle's Game is base…
Indian Institute of Technology Delhi（德里印度理工学院）；Northwestern University（西北大学）；University of California Santa Barbara（加州大学圣巴巴拉分校）
There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused on obtaining high-quality solutions, scalability to billion-sized graphs has not been adequately addressed. In addition, the impact of budget-constraint, which is necessary for many practical scenarios, remains to be studied. In this paper, we propose a framework called GCOMB to bridge these gaps. GCOMB trains a Graph Convolutional Network (GCN) using a novel probabilistic greedy mechanism to predict the quality of a node…
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 …
Offline reinforcement learning (RL) aims at learning a good policy from a batch of collected data, without extra interactions with the environment during training. However, current offline RL benchmarks commonly have a large reality gap, because they involve large datasets collected by highly exploratory policies, and the trained policy is directly evaluated in the environment. In real-world situations, running a highly exploratory policy is prohibited to ensure system safety, the data is commonly very limited, and a trained policy should be well validated before deployment. In this paper, we …
Exploratory data analytics (EDA) is a sequential decision making process where analysts choose subsequent queries that might lead to some interesting insights based on the previous queries and corresponding results. Data processing systems often execute the queries on samples to produce results with low latency. Different downsampling strategy preserves different statistics of the data and have different magnitude of latency reductions. The optimum choice of sampling strategy often depends on the particular context of the analysis flow and the hidden intent of the analyst. In this paper, we ar…
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…
Efficient exploration remains a challenging research problem in reinforcement learning, especially when an environment contains large state spaces, deceptive local optima, or sparse rewards. To tackle this problem, we present a diversity-driven approach for exploration, which can be easily combined with both off- and on-policy reinforcement learning algorithms. We show that by simply adding a distance measure to the loss function, the proposed methodology significantly enhances an agent's exploratory behaviors, and thus preventing the policy from being trapped in local optima. We further propo…
