A key requirement is the ability to handle continuous state and action spaces while remaining within a limited time and resource budget. Enhance particle swarm portfolio optimization with Calmar ratio as fitness function. operating horizon as a Constrained Markov Decision Process (CMDP). For this reason, we compute the time required by the solver to obtain a solution comparable with that of the RL model. Producing, therefore, for each operation, a representation of the remaining operations until the job is completed. The easiest solution would be to create a single reward function that takes both of those signals into account. Constrained Reinforcement Learning from Intrinsic and Extrinsic Rewards 157 where N K and N T denote the number of episode and the maximum time step, respectively. Shortest Processing Time (SPT): it is one of the most used heuristics for solving the JSP problem. The less work remaining in a job, the earlier it is scheduled. A popular alternative is the use of a learned value function or critic ^v(x,θν), where the parameters θν are learnt from observations Grondman et al. To validate the proposed framework, we optimize two relevant and well-known constrained combinatorial problems: a Job Shop Problem Garey et al. For both cases, constrained variants of the problems were considered. (2018). For example, from the state s1the action a1moves the agent to … Through interactions within the constrained space, the reinforcement learning agent is trained to optimize the manipulation skills according to a defined reward function. The results were considerable worst than those obtained by the iterative alternative. As the goal of reinforcement learning agents is to maximize the accumulated reward, they often find loopholes and misspecifications in the reward signal which lead to unwanted behavior. methods. Multi-objectivization and ensembles of shapings in reinforcement learning Tim Brys a, ... 4 Constrained optimization problemsare where one needs optimize a given objective function with respect to a set of variables, given constraints on the values of these variables. Increasing customer lifetime value. share. This procedure is repeated until all operations are assigned. This study extends a recurrent reinforcement portfolio allocation and rebalancing management system with complex portfolio constraints using particle swarm algorithms. r... Section 2 gives some background of basic reinforcement learning and constrained Q-learning. ofComputerScience HarvardSEAS Abstract Manymedicaldecision-makingtaskscanbe framed as partially observed Markov deci-sionprocesses(POMDPs). Optimization Problem To this end, they introduced the Pointer Network (PN), a neural architecture that enables permutations of the input sequence. Introduction The most widely-adopted optimization criterion for Markov decision processes (MDPs) is repre-sented by the risk-neutral expectation of a cumulative cost. This is calculated as the sum of the energy required to power up the servers plus the energy consumption of the virtual machines. Pages 75–84. The basic framework is the same with standard CE methods: In each iteration, we This problem is motivated by the fact that for most robotic systems, the dynamics may not always be known. Previous Chapter Next Chapter. share, The Orienteering Problem with Time Windows (OPTW) is a combinatorial In that case, the output corresponds to a sequence indicating the job to be scheduled first. However, in the large-scale setting i.e., nis very large in (1.2), batch methods become in-tractable. We observe that in the classic JSP, our approach is competitive in terms of the quality of the solution against the compared heuristics and the GA, especially for small and medium problems instances JSP10x10 and JSP15x15. Learning to soar: Resource-constrained exploration in reinforcement learning Show all authors. ∙ To reduce the variance of the gradients, and therefore, to speed up the convergence, we include a baseline estimator, Self-competing baseline estimator. The objective function is therefore defined as. It is, therefore, the number of samples we used hereof. Abstract: Learning from demonstration is increasingly used for transferring operator manipulation skills to robots. By contrast, the proposed neural network presents similarities with traditional RL models used for solving fully observable MDPs. In this case, the model is able to extract the features of the infrastructure and the services in order to infer a policy that almost suits perfectly on the problem instances. We conclude, therefore, that the model is robust in the sense that the results are consistent in performance. Z. Leibo, D. Silver, and K. Kavukcuoglu (2016), Reinforcement learning with unsupervised auxiliary tasks, Adam: a method for stochastic optimization, W. Kool, H. van Hoof, and M. Welling (2018). This is clear. A service function f is defined by the number of cores Vcpuf it requires to run, and the bandwidth Vbwf of the flow it processes. In the Virtual Resource Allocation Problem (VRAP), a service is required to be allocated in a pool of server hosts H={H0,H1,...,Hn−1}. Conducted experiments on the constrained Job Shop and Resource 1. In this paper, we argue that sequence-to-sequence models Sutskever et al. For each operation Oi,j, the machine Mi,j and the duration time Di,j associated are defined. Least Work Remaining (LWR): it is also an extension of SPT, this rule dictates the operation to be scheduled according to the processing time remaining before the job is completed. As shown in the picture, the RL model consistently predicts close to the optimal allocation sequences, outperforming the GA. Abstract: Reinforcement learning (RL) is a control approach that can handle nonlinear stochastic optimal control problems. In addition, the sum of ingress/egress bandwidth required by the virtual machines allocated in a server cannot exceed its bandwidth capabilities Hbwi. For small size instances, the solver is able to compute the optimal solution. Comparison of the distance to the optimal solution in the Resource Allocation Problem between a Genetic Algorithm and our RL model. problems with temporal dependencies. (2012). For every instance, there is a heading that indicates the number of jobs n and the number of machines m. Then, there is a one line for each job, listing the machine number and processing time for each operation. In that work, the greedy output of the neural network is hybridized with a local search to infer better results. (DeepRL)... the constrained setting. Request PDF | Constrained-Space Optimization and Reinforcement Learning for Complex Tasks | Learning from Demonstration is increasingly used for transferring operator manipulation skills to robots. The service composed by a sequence of VMs, each one represented by its specific features, is encoded using an RNN. This article presents a constrained-space optimization and reinforcement learning scheme for managing complex tasks. In this problem, services are located one at a time, and they are formed by sequences of no more than a few virtual machines. Reinforcement Learning with Convex Constraints ... (2019) reward constrained policy optimization (RCPO) follows a two-timescale primal-dual approach, giving guarantees for the convergence to a fixed point. Constrained optimization is a well studied problem in su-pervised machine learning and optimization. . Lastly, the gradient is approximated via Monte-Carlo sampling, where B problem instances are drawn from the problem distribution s1,s2,…,sB∼S, . This is due two main factors: firstly, the size of the sequences, which determine the number of iterations with the environment, is much shorter in the VRAP; and secondly, the number of parameters used in the neural model is considerably lower. The model at each time-step t, computes a binary action deciding whether the next operation for each job is scheduled. Prove effectiveness of the method through an efficient frontier and a cost analysis. 06/02/2020 ∙ by Quentin Cappart, et al. Q-learning, the improved Q-learning provides 73% and 14% reduction in power and latency respectively. For the problem JSP15x15 and larger, However, for larger instances or when the number of restrictions is higher, as it is the case of the limited idle time variant, computing the optimal solution becomes intractable. The algorithm is described below: During the experimentation a sequence-to-sequence model based on a recurrent encoder-decoder architecture was also tested. Reinforcement learning is a technique for determining solutions to dynamic optimization problems by measuring input–output data online and without knowing the system dynamics. In particular, we propose to use a combination of recurrent reinforcement learning (RRL) and particle swarm algorithm (PSO) with Calmar ratio for both asset allocation and constraint optimization. It is combined with the state of the environment to feed the neural network that iteratively decides the server in which each VM in the chain is going to be located. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. A constrained portfolio trading system using particle swarm algorithm and recurrent reinforcement learning. The datasets used in the experimentation are included along the code. ∙ representation, M. Deudon, P. Cournut, A. Lacoste, Y. Adulyasak, and L. Rousseau (2018), Learning heuristics for the tsp by policy gradient, International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research, P. Dhariwal, C. Hesse, O. Klimov, A. Nichol, M. Plappert, A. Radford, J. Schulman, S. Sidor, Y. Wu, and P. Zhokhov (2017), M. R. Garey, D. S. Johnson, and R. Sethi (1976), The complexity of flowshop and jobshop scheduling, Computers and intractability: a guide to the theory of np-completeness, F. A. Gers, J. Schmidhuber, and F. Cummins (1999), Learning to forget: continual prediction with lstm, Understanding the difficulty of training deep feedforward neural networks, Proceedings of the thirteenth international conference on artificial intelligence and statistics, I. Grondman, L. Busoniu, G. A. Lopes, and R. Babuska (2012), A survey of actor-critic reinforcement learning: standard and natural policy gradients, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), Neural computation of decisions in optimization problems, M. Jaderberg, V. Mnih, W. M. Czarnecki, T. Schaul, J. Tuning Optimizers for Time-Constrained Problems using Reinforcement Learning Paul Ruvolo Department of Computer Science University of California San Diego La Jolla, CA 92093 pruvolo@cs.ucsd.edu Ian Fasel Department of Computer Sciences University of Texas at Austin ianfasel@cs.utexas.edu Javier Movellan Machine Perception Laboratory Remark 2: We argue that combinatorial problems can be defined as a fully observable CMDP. Trajectory Optimization using 1 Reinforcement Learning for Map Exploration Thomas Kollar and Nicholas Roy, Abstract—Automatically building maps from sensor data is a necessary and fundamental skill for mobile robots; as a result, considerable research attention has focused on the technical challenges inherent in the mapping problem. L(y|x)=R(y|x)−ξ(y|x)=R(y|x)−∑iλi⋅Ci(y|x) With illustrative purposes, let us considerate that two operations of different jobs are competing at a time-step for the same machine to be released. This approach benefits from not requiring memory-based architectures to compute the solutions, which improves the quality of the results obtained. In this problem, a set of services is required to be allocated in a pool of server nodes. Despite their positive results, using supervised learning to solve combinatorial problems is not trivial, as acquiring a training set implies the ability to solve a large number of instances optimally. 0 Prediction Constrained Reinforcement Learning JosephFutoma MichaelC.Hughes FinaleDoshi-Velez HarvardSEAS TuftsUniversity,Dept. To this end, we extend the Neural Combinatorial Optimization (NCO) theory in order to deal with constraints in its formulation. Further details on the implementation of the model can be seen in Appendix B. Although the solver performed better than the RL model, the time required in each case is totally different, so carrying out a fair comparison is tricky. Fig. Enhancing SAT Based Planning with Landmark Knowledge However,prevail-ing two-stage approaches that first learn a Le et al. The VRAP presents some differences when compared to the JSP. UPV/EHU By comparing with multiple PSO based long only constrained portfolios, we propose an optimal portfolio trading system that is capable of generating both long and short signals and handling the common portfolio constraints. [14] applied reinforcement learning (RL) in DNN pruning by formulating the pruning ratio as a continuous action and the accuracy as the reward. This point is reflected in a lower number of parameters of the neural network and faster training times. (2019) describe a batch off-policy A baseline estimator performs in the following way, the advantage function Lπ(y|x)−b(x) is positive if the sampled solution is better that the baseline, causing these actions to be reinforced, and vice-versa. Proceedings of the 34th International Conference on Machine Learning-Volume 70. trained a Deep Neural Network (DNN) to solve the Euclidean TSP using supervised learning. The results are summarized in Table 1. This appendix B completes the details on the Virtual Resource Allocation Problem (VRAP). Remember that the operations for a job must be assigned in a specific order; that is operation cannot be scheduled until the previous one has finished. We explore different constrained optimization strategies using these surrogates such as the use of gradient-based techniques (useful when the surrogates are differentiable such as neural networks), and gradient-free techniques such as reinforcement learning and Bayesian optimization. The state of the problem is defined by the state of the machines and the operations currently being process at the decision time. To minimize delivery costs, you'd want to start out defining your reward function like: R(.) To this end, we extend the Neural Combinatorial Optimization (NCO) theory in order to deal with constraints in its formulation. In addition to the JSP, to prove the validity of the proposed framework, we evaluate its performance on the Virtual Resource Allocation Problem (VRAP) Beloglazov et al. Let us represent each instance of the problem as a static feature vector, Non-maskable constraints are incorporated into (9) using the Lagrange relaxation technique. 0 211–212, 2014. ∙ 0 ∙ share Teaching agents to perform tasks using Reinforcement Learning is no easy feat. both the environment and the agent are implemented as tensor operations. approaches. In this project, an attentional sequence-to-sequence model is used to predict real-time solutions on a highly constrained … ∙ OptLayer is fully differentiable, enabling future end-to-end learning under safety constraints. The Robot Learning Lab at Imperial College London. This procedure is computed once and stored to be used during the interaction with the environment. ∙ The resulting gradient equation is, where share, In this work, we introduce Graph Pointer Networks (GPNs) trained using representation during the optimization process allows us to rely on memory-less Reinforcement learning is a technique for determining solutions to dynamic optimization problems by measuring input–output data online and without knowing the system dynamics. 04/07/2020 ∙ by Benjamin van Niekerk, et al. In the Job Shop Problem (JSP) there exist a number of n jobs J={J0,J1...Jn−1} and a set m machines M={M0,M1...Mm−1}. ∙ Joshua Achiam Jul 6, 2017 (Based on joint work with David Held, Aviv Tamar, and Pieter Abbeel.) 3.1. The resulting vector represents the static part of our input. 1 However, there are different PSO approaches in the constrained portfolio problem context where one may use the recurrent reinforcement learning method to generate long/short signals for dynamic portfolio optimization. For example, your problem, if I understand your pseudo-code, looks something like this: Generating smooth, dynamically feasible trajectories could be difficult for such systems. This is clear. In practice, it is important to cater for limited data and imperfect human demonstrations, as well as underlying safety constraints. Combinatorial optimization is the science that studies finding the optimal solution from a finite set of discrete possibilities. ∙ architectures, enhancing the results obtained in previous sequence-to-sequence Constrained Combinatorial Optimization with Reinforcement Learning. Dynamic Programming (DP) provides standard algorithms to solve Markov Decision Processes.However, these algorithms generally do not optimize a scalar objective function. Tuning Optimizers for Time-Constrained Problems using Reinforcement Learning Paul Ruvolo Department of Computer Science University of California San Diego La Jolla, CA 92093 pruvolo@cs.ucsd.edu Ian Fasel Department of Computer Sciences University of Texas at Austin ianfasel@cs.utexas.edu Javier Movellan Machine Perception Laboratory step as a solution of a constrained optimization problem to compute the new policy ˇi+1. Optimizing debt collections using constrained reinforcement learning. 2 shows the optimality gap for the instances in which the optimal solution can be obtained in a reasonable time: JSP10x10 and JSP15x15. Many of these works demonstrate the capability of RL algorithms to learn a control law independently from a nominal The only requirement is that evaluating the objective function must not be time-consuming. ... Kollar, T, Roy, N (2008) Trajectory optimization using reinforcement learning for map exploration. ∙ 6 ∙ share . This vector is embedded and sequentially encoded. This benefits the results as accessing the fully observable state of the problem is more reliable than doing on memories. Combine recurrent reinforcement learning and particle swarm for portfolio trading. Under that constraint, for any machine, the period between finishing operation and starting the next operation (idle time) cannot exceed a certain threshold Tth. Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. The authors applied the Hopfield-network for solving instances of the Traveller Salesman Problem (TSP). To include non-maskable restrictions, the JSP variant with limited idle time was considered. Section 3 explains our problem formulation and policy optimization using constrained indicated in the JSP except for small details. It has been in the last few years with the rise of deep learning that this topic has again attracted the attention of the artificial intelligence community. 0 Although this problem adds no much complexity, the computation time required by OR-Tools increases significantly, in this case, a slight increase in the number of constraints in the problem is enough to prevent the solver from getting good approximations in the short time. This leads to a model that is more difficult to train in comparison to the proposed alternative. Constrained Policy Optimization. It will provide a forum for establishing a mutually accessible introduction to current research on this integration, and allow exploration of recent advances in optimization for potential application in reinforcement learning. optimization problems using deep Reinforcement Learning (RL). Resource Allocation Problem. The proposed model presents two different input sources: the instance of the problem s, which is defined by the M and D feature matrices, and the state of the environment dt, represented by the state of the machines and the time for the previous operations to finish. Optimizing debt collections using constrained reinforcement learning. This comes naturally in this proposal with the self-competing strategy, therefore it does not add overhead to the model. The iteration process has a fixed number of steps, which corresponds to the length of the service. ∙ UPV/EHU ∙ 0 ∙ share. share, We present Ecole, a new library to simplify machine learning research fo... We study the safe reinforcement learning problem with nonlinear function approx- imation, where policy optimization is formulated as a constrained optimization problem with both the objective and the constraint being nonconvex functions. This paper presents a framework to tackle constrained combinatorial Nevertheless, things turn around when the limited idle time variant is considered. ∙ Code of the paper: Virtual Network Function placement optimization with Deep Reinforcement Learning. search of using black-box optimization for hyper-parameter search can be directly adopted [41]. Therefore, and as shown in the previous example, these constraints are relaxed and introduced as penalty terms into the objective function. Since most learning algorithms optimize some objective function, learning the base-algorithm in many cases reduces to learning an optimization algorithm. Conversely, they are not guaranteed to do it in polynomial time, and thus, when large problems are optimized, exact methods are no longer a feasible option. This paper proposes a reinforcement learning-based algorithm for trajectory optimization for constrained dynamical systems. In that process, an index vector it points at the current operation to be scheduled and the feature vector eij is gathered for each job to create the context vector ct. Lastly, the DNN decoder consists in multiple dense layers with a ReLU activation. 2009) which has worse performance Residual gradient (Baird 1995) is applying SGD to the rst term. Published in IROS, 2019. Many studies in the current literature apply PSO to solve the constrained portfolio problem for a long only portfolio. Dean (2017), Device placement optimization with reinforcement learning, M. Nazari, A. Oroojlooy, L. Snyder, and M. Takác (2018), Reinforcement learning for solving the vehicle routing problem, A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer (2017), S. Paternain, L. Chamon, M. Calvo-Fullana, and A. Ribeiro (2019), Constrained reinforcement learning has zero duality gap, I. Sutskever, O. Vinyals, and Q. V. Le (2014), Sequence to sequence learning with neural networks, Advances in neural information processing systems, C. Tessler, D. J. Mankowitz, and S. Mannor (2018), A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin (2017), O. Vinyals, M. Fortunato, and N. Jaitly (2015), Simple statistical gradient-following algorithms for connectionist Reinforcement Learning, Combining Reinforcement Learning and Constraint Programming for For each operation Oij, these values are concatenated to create the static input, denoted as sij in the paper. We note that soon after our paper appeared, (Andrychowicz et al., 2016) also independently proposed a similar idea. The gradient of the Lagrangian objective function JπL(θ) is derived using the log-likelihood method. Develop a dynamic adaptive long/short constrained portfolio trading system. Vˇ(s) = T (s);u(s) = T (s) it reduces to gradient-TD2 (Sutton et al. As the goal of reinforcement learning agents is to maximize the accumulated reward, they often find loopholes and misspecifications in the reward signal which lead to unwanted behavior.