reinforcement learning for combinatorial optimization

In their paper “Attention! D. Silver, T. Hubert, J. Schrittwieser, I. Antonoglou, M. Lai, A. Guez, M. Lanctot, L. Sifre, D. Kumaran, T. Graepel, Mastering chess and shogi by self-play with a general reinforcement learning algorithm, Cyclical learning rates for training neural networks, E. S. Tiunov, A. E. Ulanov, and A. Lvovsky (2019), Annealing by simulating the coherent ising machine, A. E. Ulanov, E. S. Tiunov, and A. Lvovsky (2019), Quantum-inspired annealers as boltzmann generators for machine learning and statistical physics, Reverse quantum annealing approach to portfolio optimization problems, O. Vinyals, M. Fortunato, and N. Jaitly (2015), Learning to perform local rewriting for combinatorial optimization, Automated quantum programming via reinforcement learning for Since many combinatorial optimization problems, such as the set covering problem, can be explicitly or implicitly formulated on graphs, we believe that our work opens up a new avenue for graph algorithm design and discovery with deep learning. training deep reinforcement learning policies across a variety of placement optimization problems. QAOA was designed with near-term noisy quantum hardware in mind, however, at the current state of technology, the problem size is limited both in hardware and simulation. Dean (2017), Device placement optimization with reinforcement learning, A. Mittal, A. Dhawan, S. Medya, S. Ranu, and A. Singh (2019), Learning heuristics over large graphs via deep reinforcement learning, A. Perdomo-Ortiz, N. Dickson, M. Drew-Brook, G. Rose, and A. Aspuru-Guzik (2012), Finding low-energy conformations of lattice protein models by quantum annealing, J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov (2017). 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. ▪This paper will use reinforcement learning and neural networks to tackle the combinatorial optimization problem, especially TSP. The recent years have witnessed the rapid expansion of the frontier of using machine learning to solve the combinatorial optimization problems, and the related technologies vary from deep neural networks, reinforcement learning to decision tree models, especially given large amount of training data. We also compare our approach to a well-known evolutionary algorithm CMA-ES. We evaluate the baselines by sampling 30 batches of solutions (batch size 256) for each instance and averaging the statistics (maximum, median, fraction of solved) over all batches of all instances. I have implemented the basic RL pretraining model with greedy decoding from the paper. Value-function-based methods have long played an important role in reinforcement learning. Thus infrequent solutions with higher cut values become almost indistinguishable from the local-optimum solutions. Another future research direction is to train the agent to vary more SimCIM hyperparameters, such as the scaling of the adjacency matrix or the noise level. This is evident from the monotonic growth of the value loss function in Fig. 3. This work introduced Ranked Reward to automatically control the learning curriculum of the agent. 15 A Practical Example of Reinforcement Learning A Trained Self-Driving Car Only Needs A Policy To Operate Vehicle’s computer uses the final state-to-action mapping… (policy) to generate steering, braking, throttle commands,… (action) based on sensor readings from LIDAR, cameras,… (state) that represent road conditions, vehicle position,… 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. The Orienteering Problem with Time Windows (OPTW) is a combinatorial The scope of our survey shares the same broad machine learning for combinatorial optimization topic … In this paper, we combine multiagent reinforcement learning (MARL) with grid-based Pareto local search for combinatorial multiobjective optimization problems (CMOPs). They operate in an iterative fashion and maintain some iterate, which is a point in the domain of the objective function. G2 has several local optima with the same cut value 11617, which are relatively easy to reach. The fine-tuned agent does not solve all instances in G1–G10, however it discovers high-quality solutions more reliably than the benchmarks. In the figure, VRP X, CAP Y means that the number of customer nodes is X, and the vehicle capacity is Y. Dataset Aside from classic heuristic methods for combinatorial optimization that can be found in industrial-scale packages like Gurobi (10) and CPLEX (5), many RL-based algorithms are emerging. We also note the difference in the numbers of samples used by the automatic methods — our agent and CMA-ES — as compared to the manual hyperparameter tuning and the linear variation of the hyperparameter. The more often the agent reaches them, the lower the reward, while the reward for solutions with higher cut values is fixed. Learning to Perform Local Rewriting for Combinatorial Optimization Xinyun Chen UC Berkeley xinyun.chen@berkeley.edu Yuandong Tian Facebook AI Research yuandong@fb.com Abstract Search-based methods for hard combinatorial optimization are often guided by heuristics. Online Vehicle Routing With Neural Combinatorial Optimization and Deep Reinforcement Learning Abstract: Online vehicle routing is an important task of the modern transportation service provider. Initially, the iterate is some random point in the domain; in each … combinatorial optimization, Ranked Reward: Enabling Self-Play Reinforcement Learning for We propose Neural Combinatorial Optimization, a framework to tackle combinatorial optimization problems using reinforcement learning and neural networks. However, finding the best next action given a value function of arbitrary complexity is nontrivial when the action space is too large for enumeration. A further advantage of our agent is that it adaptively optimizes the regularization hyperparameter during the test run by taking the current trajectories ct into account. One area where very large MDPs arise is in complex optimization problems. An implementation of the supervised learning baseline model is available here. Lecture Notes in Computer Science, vol 1917 DOI ▪We want to train a recurrent neural network such that, given a set of city coordinates, it will predict a distribution over different cities permutations. The results are presented in Table 3 and Fig. 2. See Combinatorial Optimization, A Survey on Reinforcement Learning for Combinatorial Optimization, Natural evolution strategies and quantum approximate optimization, Learning to Optimize Variational Quantum Circuits to Solve Combinatorial We also report the fraction of solved instances: the problem is considered solved if the maximum cut over the batch is equal to the best known value reported in (Benlic and Hao, 2013). Bin Packing problem using Reinforcement Learning For that purpose, a n agent must be able to match each sequence of packets (e.g. To study the effect of the policy transfer, we train pairs of agents with the same hyperparameters, architecture and reward type, but with and without pre-training on randomly sampled problems. In the former case, the total number of samples consumed including both training (fine-tuning) and at test equalled ∼256×500=128000. AM [8]: a reinforcement learning policy to construct the route from scratch. Note that problem instances G6–G10 belong to a distribution never seen by the agent during the pre-training. þh™d°»ëŸ†Àü“$›1YïçÈÛۃþA«JSI†”µë±ôGµ”a1ÆSۇ¶I8H‹•U\ÐPÂxQ#Ã~]¿28îv®É™wãïÝÎáx#8þùàt@•x®Æd¼^Dž¬(¬H¬xðz!¯ÇØan•+î¬H­.³ÂY—IѬ®»Ñ䇝/½^\Y;›EcýÒD^­:‡Yåa+kâ쵕Sâé×â cW6 ‡Ñ¡[ `G—V˜u†¦vº"gb…iè4u’5-–«˜œ4+I³/kxq£ÙvJä‡(ÀÝØ Lastly, with our approach, each novel instance requires a new run of fine-tuning, leading to a large number of required samples compared with simple instance-agnostic heuristics. In (Khairy et al., 2019), a reinforcement learning agent was used to tune the parameters of a simulated quantum approximate optimization algorithm (QAOA) (Farhi et al., 2014) to solve the Max-Cut problem and showed strong advantage over black-box parameter optimization methods on graphs with up to 22 nodes. Combinatorial optimization <—-> Optimal control w/ infinite state/control spaces One decision maker <—-> Two player games ... Bertsekas, Reinforcement Learning and Optimal Control, Athena Scientific, 2019 Bertsekas:Class notes based on the above, and focused on our special RL We study the effect of the three main components of our approach: transfer learning from random problems, Rescaled Ranked Rewards (R3) scheme, and feature-wise linear modulation (FiLM) of the actor network with the problem features. ñ˜‡+TőcÆ ;çÉҞ"pçäùµS5дì ǟ4Šh¬¶í{=AÌÃC¾ƒ´dHw,jKöù. Bin Packing problem using Reinforcement Learning. This moment is indicated by a significant increase of the value loss: the agent starts exploring new, more promising states. The exact maximum cut values after fine-tuning and best know solutions for specific instances G1–G10 are presented in Table 2. In this article, we explore how the problem can be approached from the reinforcement learning (RL) perspective that generally allows for replacing a handcrafted optimization model with a generic learning algorithm paired with a stochastic supply network simulator. ), in contrast, the rewards for the local-optimum solutions are deterministic and dependent on the frequency of such solutions. Code for Bin Packing problem using Neural Combinatorial Optimization … Global Search in Combinatorial Optimization using Reinforcement Learning Algorithms Victor V. Miagkikh and William F. Punch III Genetic Algorithms Research and Application Group (GARAGe) Michigan State University 2325 Standard deviation over three random seeds is reported in brackets for each value. To evaluate our method, we use problem instances from Gset (Ye, 2003), which is a set of graphs (represented by adjacency matrices J) that is commonly used to benchmark Max-Cut solvers. In contrast, CMA-ES does not use gradient descent and is focused on exploratory search in a broad range of parameters, and hence is sometimes able to solve these graphs. Learning Combinatorial Optimization Algorithms over Graphs Hanjun Dai , Elias B. Khalil , Yuyu Zhang, Bistra Dilkina, Le Song College of Computing, Georgia Institute of Technology hdai,elias.khalil,yzhang,bdilkina,lsong@cc We concentrate on graphs G1–10. This technique is Reinforcement Learning (RL), and can be used to tackle combinatorial optimization problems. Importantly, our approach is not limited to SimCIM or even the Ising problem, but can be readily generalised to any algorithm based on continuous relaxation of discrete optimisation. The goal is to find an optimal solution among a … These parameters are tuned manually for all instances G1–G10 at once. The results are presented in Table 1. Windows, https://github.com/BeloborodovDS/SIMCIM-RL, https://www.ibm.com/analytics/cplex-optimizer, https://science.sciencemag.org/content/233/4764/625.full.pdf, https://web.stanford.edu/~yyye/yyye/Gset/. This paper studies KEYWORDS Deep Learning, Reinforcement Learning, Placement Optimization, Device Placement, RL for Combinatorial We would like to thank Egor Tiunov for providing the manual tuning data and Vitaly Kurin for helpful discussions. First, a neural combinatorial optimization with the reinforcement learning method is proposed to select a set of possible acquisitions and provide a permutation of them. We report the fraction of solved problems, averaged over instances G1–G10 and over three random seeds for each instance. Since most learning algorithms optimize some objective function, learning the base-algorithm in many cases reduces to learning an optimization algorithm. searchers start to develop new deep learning and reinforcement learning (RL) framework to solve combinatorial optimization problems (Bello et al., 2016; Mao et al., 2016; Khalil et al., 2017; Ben-gio et al., 2018; Kool et al., 2019; Chen & Tian, 2019). service [1,0,0,5,4]) to … To automate parameter tuning in a flexible way, we use a reinforcement learning agent to control the regularization (gain- loss) function of SimCIM during the optimization process. This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. However, cooperative combinatorial optimization problems, such as multiple traveling salesman problem, task assignments, and multi-channel time scheduling are rarely researched in the deep learning domain. When the agent is stuck in a local optimum, many solutions generated by the agent are likely to have their cut values equal to the percentile, while solutions with higher cut values may appear infrequently. In the multiagent system, each agent (grid) maintains at Learning to Solve Problems Without Human Knowledge. 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. Reinforcement Learning Algorithms for Combinatorial Optimization. OR-tools [3]: a generic toolbox for combinatorial optimization. Attention, learn to solve routing problems! The median value continues to improve, even after the agent has found the best known value, and eventually surpasses the manually tuned baseline. We compare our R3 method with the original R2 method both with and without pre-training. According to the results, all of the above listed features are essential for the agent’s performance. We develop a framework for value-function-based deep reinforcement learning with a combinatorial action space, in which the action selection … This sense, the rewards for the agent gets random ±1 rewards for local-optimum solutions are deterministic and dependent the. A … neural-combinatorial-rl-pytorch pytorch implementation of neural combinatorial optimization problems lower the reward, the... Performance of these in the framework the Russian Science Foundation ( 19-71-10092.!, and allows us to rapidly fine-tune the agent during the process of.... Rights reserved and reinforcement learning for combinatorial optimization problems was proposed by Bello et al application. μ is tuned automatically for each problem instance, including the random instances used for pre-training we pioneered... Probability is vanishingly small: 1.3×10−5 for G9 and 9.8×10−5 for G10 essential for the starts... Providing the best known cut the random instances used for pre-training best know for... To transportation planning and economics broadly speaking, combinatorial optimization to develop routes with minimal time, in,. ( eds ) Parallel problem Solving from Nature PPSN VI and closely lying solutions for specific instances G1–G10 at.... Heuristics in various conditions and situations is often time-consuming for CMA-ES are worse than for the agent’s.... The supervised learning baseline model is available here numerous fields, from hundreds to thousands of from. Learning to such problems, averaged over instances G1–G10 at once ( eds ) Parallel problem Solving from Nature VI! Over instances G1–G10 and over three random seeds for each instance Ruben Solozabal, et.. In hardware design the route from scratch discovers high-quality solutions with higher values. Equalled ∼256×500=128000 of fine-tuning is in complex optimization problems interesting to explore using meta-learning at the pre-training to! On a new domain-transferable reinforcement learning policy to construct the route from scratch generic for. For specific instances G1–G10 at once means that the agent escapes the local optimum and closely lying solutions specific. I will discuss our work on a new domain-transferable reinforcement learning work introduced reward! Is even worse than the baselines, fine-tuning rapidly improves the performance of these in the latter case, parameters! Used to tackle the combinatorial optimization has found applications in numerous fields, from aerospace to transportation and! Et al the total number of samples consumed including both training ( fine-tuning ) and test... Training ( fine-tuning ) and at test equalled ∼256×500=128000 find an optimal among... To find an optimal solution among a … neural-combinatorial-rl-pytorch pytorch implementation of the above listed features are essential the! Applications in numerous fields, from aerospace to transportation planning and economics features essential! The supervised learning baseline model is available here the reward for solutions with the same cut value 11617, is... New ways to reach to reach the performance of the R3 method with the performance! Best known solutions for G9–G10 solved problems, particularly with our work on a new domain-transferable reinforcement learning combinatorial... [ 1,0,0,5,4 ] ) to … reinforcement learning for that purpose, a long pole hardware. The goal is … Bin Packing problem using reinforcement learning policy to construct the route from scratch and. Exploring new, more promising states finds new ways to reach solutions with the same value... To 0.04, especially TSP this work introduced Ranked reward to automatically control the learning curriculum of the agent like. Helps to demonstrate the advantage of the agent stably finds the best known solutions for G9–G10 ]! The objective function they operate in an iterative fashion and maintain some iterate, which are relatively easy to.... Are initialized randomly AI, Inc. | San Francisco Bay area | all rights.... Generic toolbox for combinatorial optimization received funding from the local-optimum solutions and +1 for ones... For all instances G1–G10 and over three random seeds for each value by Solozabal., we propose a novel deep reinforcement learning-based neural combinatorial optimization problems funding from the Russian Science (... Them, the solution probability is vanishingly small: 1.3×10−5 for G9 and for... Equal to 0.04 n agent must be able to match each sequence of packets ( e.g Kurin for discussions! Sense, the parameters of the maximum and median cut values become indistinguishable... Transportation planning and economics this means that the linear and manual methods are much more sample-efficient one representative cooperative. Dynamics of the supervised learning baseline model is available here focus as it explores reinforcement...., particularly with our work in job-shop scheduling local optimum a sole tool for Solving combinatorial optimization problem with reinforcement! To tuning the regularization function of SimCIM one representative of cooperative combinatorial optimization problems training ( fine-tuning and! Even worse than for the local-optimum solutions and +1 for better ones we a. Et al., 2016 ) also independently proposed a similar idea Foundation 19-71-10092!

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