43, No. The material in this book is motivated by numerous industrial applications undertaken at CASTLE Lab, as well as a number of undergraduate senior theses. An Approximate Dynamic Programming Algorithm for Monotone Value Functions Daniel R. Jiang, Warren B. Powell Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08540 {drjiang@princeton.edu, powell@princeton.edu} Warren B. Powell. The book is written at a level that is accessible to advanced undergraduates, masters students and practitioners Powell, “An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, II: Multiperiod Travel Times,” Transportation Science, Vol. 210-237 (2009). 4.4 Real-Time Dynamic Programming, 126. Ryzhov, I. O., W. B. Powell, “Approximate Dynamic Programming with Correlated Bayesian Beliefs,” Forty-Eighth Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, Sept. 29-Oct. 1, 2010. 2079-2111 (2008). Our result is compared to other deterministic formulas as well as stochastic stepsize rules which are proven to be convergent. Day, A. George, T. Gifford, J. Nienow, W. B. Powell, “An Approximate Dynamic Programming Algorithm for Large-Scale Fleet Management: A Case Application,” Transportation Science, Vol. 9, No. Approximate Dynamic Programming for Planning a Ride-Sharing System using Autonomous Fleets of Electric Vehicles Citation: (15)L. Al-Kanj, J. Nascimento, and W. B. Powell, “ Approximate Dynamic Programming for Planning a Ride-Sharing System using Autonomous Fleets of Electric Vehicles ,” ArXiv Preprint,.arxiv:1810.08124, 2018. An Approximate Dynamic Programming Algorithm for Large-Scale Fleet Management: A Case Application Hugo P. Simao Jeff Day Abraham P. George Ted Gifford John Nienow Warren B. Powell Department of Operations Research and Financial Engineering Princeton University, Princeton, NJ 08544 February 25, 2007 What is surprising is that the weighting scheme works so well. 3, pp. (c) Informs. 178-197 (2009). Approximate Dynamic Programming Solving the Curses of Dimensionality Second Edition Warren B. Powell Princeton University The Department of Operations Research and Financial Engineering 56, No. Why would we approximate a problem that is easy to solve to optimality? M.A. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. Applications in revenue management, fleet management and pricing. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Approximate dynamic programming (ADP) is a broad umbrella for a modeling and algorithmic strategy for solving problems that are sometimes large and complex, and are usually (but not always) stochastic. 22, No. (c) Informs. All the problems are stochastic, dynamic optimization problems. Stochastic resource allocation problems produce dynamic programs with state, information and action variables with thousands or even millions of dimensions, a characteristic we refer to as the “three curses of dimensionality.” Powell, “An Adaptive Dynamic Programming Algorithm for a Stochastic Multiproduct Batch Dispatch Problem,” Naval Research Logistics, Vol. on Power Systems (to appear), W. B. Powell, Stephan Meisel, "Tutorial on Stochastic Optimization in Energy II: An energy storage illustration", IEEE Trans. A formula is provided when these quantities are unknown. and T. Carvalho, “Dynamic Control of Logistics Queueing Networks for Large Scale Fleet Management,” Transportation Science, Vol. Powell, W.B., A. George, B. Bouzaiene-Ayari and H. Simao, “Approximate Dynamic Programming for High Dimensional Resource Allocation Problems,” Proceedings of the IJCNN, Montreal, August 2005. programming has often been dismissed because it suffers from "the curse Dynamic It then summarizes four fundamental classes of policies called policy function approximations (PFAs), policies based on cost function approximations (CFAs), policies based on value function approximations (VFAs), and lookahead policies. Approximate dynamic programming involves iteratively simulating a system. Using the contextual domain of transportation and logistics, this paper describes the fundamentals of how to model sequential decision processes (dynamic programs), and outlines four classes of policies. The dynamic programming literature primarily deals with problems with low dimensional state and action spaces, which allow the use of discrete dynamic programming techniques. 3, pp. CONTENTS Preface xi Acknowledgments xv 1 The challenges of dynamic programming 1 1, No. Ryzhov, I. and W. B. Powell, “Bayesian Active Learning with Basis Functions,” IEEE Workshop on Adaptive Dynamic Programming and Reinforcement Learning, Paris, April, 2011. A stochastic system consists of 3 components: • State x t - the underlying state of the system. “Approximate dynamic programming” has been discovered independently by different communities under different names: » Neuro-dynamic programming » Reinforcement learning » Forward dynamic programming » Adaptive dynamic programming » Heuristic dynamic programming » Iterative dynamic programming Approximate dynamic programming is emerging as a powerful tool for certain classes of multistage stochastic, dynamic problems that arise in operations research. The remainder of the paper uses a variety of applications from transportation and logistics to illustrate the four classes of policies. We address the issue of ine cient sampling for risk applications in simulated settings and present a procedure, based on importance sampling, to direct samples toward the “risky region” as the ADP algorithm progresses. Abstract:Approximate dynamic programming (ADP) is a broad umbrella for a modeling and algorithmic strategy for solving problems that are sometimes large and complex, and are usually (but not always) stochastic. This is the first book to bridge the growing field of approximate dynamic programming with operations research. 34, No. The challenge of dynamic programming: Problem: Curse of dimensionality tt tt t t t t max ( , ) ( )|({11}) x VS C S x EV S S++ ∈ =+ X Three curses State space Outcome space Action space (feasible region) Powell, Approximate Dynamic Programming, John Wiley and Sons, 2007. When demands are uncertain, we vary the degree to which the demands become known in advance. 3, pp. Powell, “Exploiting structure in adaptive dynamic programming algorithms for a stochastic batch service problem,” European Journal of Operational Research, Vol. There is also a section that discusses “policies”, which is often used by specific subcommunities in a narrow way. All of these methods are tested on benchmark problems that are solved optimally, so that we get an accurate estimate of the quality of the policies being produced. Approximate dynamic programming has evolved, initially independently, within operations research, computer science and the engineering controls community, all searching for practical tools for solving sequential stochastic optimization problems. 167-198, (2006). This technique worked very well for single commodity problems, but it was not at all obvious that it would work well for multicommodity problems, since there are more substitution opportunities. 4.3 Q-Learning and SARSA, 122. 4 Introduction to Approximate Dynamic Programming 111 4.1 The Three Curses of Dimensionality (Revisited), 112 4.2 The Basic Idea, 114 4.3 Q-Learning and SARSA, 122 4.4 Real-Time Dynamic Programming, 126 4.5 Approximate Value Iteration, 127 4.6 The Post-Decision State Variable, 129 4.7 Low-Dimensional Representations of Value Functions, 144 Approximate Dynamic Programming for High-Dimensional Resource Allocation Problems. Powell, W. B. Daniel Jiang, Thuy Pham, Warren B. Powell, Daniel Salas, Warren Scott, “A Comparison of Approximate Dynamic Programming Techniques on Benchmark Energy Storage Problems: Does Anything Work?,” IEEE Symposium Series on Computational Intelligence, Workshop on Approximate Dynamic Programming and Reinforcement Learning, Orlando, FL, December, 2014. that scale to real-world applications. ‪Princeton University‬ - ‪Cited by 20,130‬ - ‪Stochastic optimization‬ - ‪dynamic programming‬ - ‪approximate dynamic programming‬ - ‪reinforcement learning‬ - ‪stochastic programming‬ 9, pp. 109-137, November, 2014, http://dx.doi.org/10.1287/educ.2014.0128. Tutorial articles - A list of articles written with a tutorial style. “Approximate dynamic programming” has been discovered independently by different communities under different names: » Neuro-dynamic programming » Reinforcement learning » Forward dynamic programming » Adaptive dynamic programming » Heuristic dynamic programming » Iterative dynamic programming We then describe some recent research by the authors on approximate policy iteration algorithms that offer convergence guarantees (with technical assumptions) for both parametric and nonparametric architectures for the value function. (c) Informs. Powell, “Dynamic Programming Approximations for Stochastic, Time-Staged Integer Multicommodity Flow Problems,” Informs Journal on Computing, Vol. 814-836 (2004). A list of articles written with a tutorial style. (Click here to go to Amazon.com to order the book - to purchase an electronic copy, click here.) Approximate Dynamic Programming in Transportation and Logistics: A Unied Framework Warren B. Powell, Hugo P. Simao and Belgacem Bouzaiene-Ayari Department of Operations Research and Financial Engineering Princeton University, Princeton, NJ 08544 European J. of Transportation and Logistics, Vol. This article is a brief overview and introduction to approximate dynamic programming, with a bias toward operations research. For the advanced Ph.D., there is an introduction to fundamental proof techniques in “why does it work” sections. It describes a new algorithm dubbed the Separable Projective Approximation Routine (SPAR) and includes 1) a proof that the algorithm converges when we sample all intervals infinitely often, 2) a proof that the algorithm produces an optimal solution when we only sample the optimal solution of our approximation at each iteration, when applied to separable problems, 3) a bound when the algorithm is applied to nonseparable problems such as two-stage stochastic programs with network resource, and 4) computational comparisons against deterministic approximations and variations of Benders decomposition (which is provably optimal). Stochastic resource allocation problems produce dynamic programs with state, information and action variables with thousands or even millions of dimensions, a characteristic we refer to as the “three curses of dimensionality.” A fifth problem shows that in some cases a hybrid policy is needed. 65, No. A few years ago we proved convergence of this algorithmic strategy for two-stage problems (click here for a copy). This paper also used linear approximations, but in the context of the heterogeneous resource allocation problem. Backward Approximate Dynamic Programming Crossing State Stochastic Model Energy Storage Optimization Risk-Directed Importance Sampling Stochastic Dual Dynamic Programming: Subjects: Operations research Energy: Issue Date: 2020: Publisher: Princeton, NJ : Princeton … In fact, there are up to three curses of dimensionality: the state space, the outcome space and the action space. The dynamic programming literature primarily deals with problems with low dimensional state and action spaces, which allow the use of discrete dynamic programming techniques. Relationship to Reinforcement Learning. First, it provides a simple, five-part canonical form for modeling stochastic dynamic programs (drawing off established notation from the controls community), with a thorough discussion of state variables. Dynamic Programming with Missing or Incomplete Models. Approximate Dynamic Programming Much of our work falls in the intersection of stochastic programming and dynamic programming. Cornell ORIE. 38, No. Powell, W. B., “Approximate Dynamic Programming I: Modeling,” Encyclopedia of Operations Research and Management Science, John Wiley and Sons, (to appear). We derive a near-optimal time-dependent policy using backward approximate dynamic programming (ADP), which overcomes the computational hurdles of exact backward dynamic programming, with higher quality solutions than more familiar forward ADP methods. We show that an approximate dynamic programming strategy using linear value functions works quite well and is computationally no harder than a simple myopic heuristics (once the iterative learning is completed). Please download: Clearing the Jungle of Stochastic Optimization (c) Informs - This is a tutorial article, with a better section on the four classes of policies, as well as a fairly in-depth section on lookahead policies (completely missing from the ADP book). An Optimal Approximate Dynamic Programming Algorithm for the Economic Dispatch Problem with Grid-Level Storage Juliana M. Nascimento and Warren B. Powell 1 January 12, 2012 1Department of Operations Research and Financial Engineering, Princeton University. Powell, W. B., “Approximate Dynamic Programming: Lessons from the field,” Invited tutorial, Proceedings of the 40th Conference on Winter Simulation, pp. Please see each event's listing for details about how to view or participate. 2, pp. 2995-3010. http://dx.doi.org/10.1109/TAC.2013.2272973 (2013). This paper uses two variations on energy storage problems to investigate a variety of algorithmic strategies from the ADP/RL literature. The experiments show that the SPAR algorithm, even when applied to nonseparable approximations, converges much more quickly than Benders decomposition. Ma, J. and W. B. Powell, “A convergent recursive least squares policy iteration algorithm for multi-dimensional Markov decision process with continuous state and action spaces,” IEEE Conference on Approximate Dynamic Programming and Reinforcement Learning (part of IEEE Symposium on Computational Intelligence), March, 2009. “What you should know about approximate dynamic programming,” Naval Research Logistics, Vol. 12, pp. of dimensionality." 399-419 (2004). In this chapter, we consider a base perimeter patrol stochastic control problem. Experimental Issues. This is a major application paper, which summarizes several years of development to produce a model based on approximate dynamic programming which closely matches historical performance. 1, pp. Using two different algorithms developed for each problem setting, backward approximate dynamic programming for the first case and risk-directed importance sampling in stochastic dual dynamic programming with partially observable states for the second setting, in combination with improved stochastic modeling for wind forecast errors, we develop control policies that are more cost-effective … Thus, a decision made at a single state can provide us with information about many states, making each individual observation much more powerful. So Just What is Approximate Dynamic Programming? Simao, H. P. and W. B. Powell, “Approximate Dynamic Programming for Management of High Value Spare Parts”, Journal of Manufacturing Technology Management Vol. 5 - Modeling - Good problem solving starts with good modeling. Princeton University. This paper introduces the use of linear approximations of value functions that are learned adaptively. Instead, it describes the five fundamental components of any stochastic, dynamic system. The book includes dozens of algorithms written at a level that can be directly translated to code. Approximate Dynamic Programming for High-Dimensional Resource Allocation Problems Warren Powell Department of Operations Research and Financial Engineering Princeton University Wednesday, May 2, 2007 4:30 - 5:30 PM Terman Engineering Center, Room 453 Abstract: Dynamic Programming (DP) is known to be a standard optimization tool for solving Stochastic Optimal Control (SOC) problems, either over a finite or an infinite horizon of stages. It highlights the major dimensions of an ADP algorithm, some strategies for approximating value functions, and brief discussions of good (and bad) modeling and algorithmic strategies. (c) Informs. One encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for large scale controlled Markov chains. Test datasets are available at http://www.castlelab.princeton.edu/datasets.htm. This paper is a lite version of the paper above, submitted for the Wagner competition. This is an easy introduction to the use of approximate dynamic programming for resource allocation problems. A series of short introductory articles are also available. 58, No. The AI community often works on problems with a single, complexity entity (e.g. Due to the Covid-19 pandemic, all events are online unless otherwise noted. Research and Data. Under very general assumptions, commonly employed numerical algorithms are based on approximations of the cost-to-go functions, by means of suitable parametric models built from a set of sampling points in the … Design/methodology/approach – The problem is solved using approximate dynamic programming (ADP), but this requires developing new methods for approximating value functions in the presence of low/frequency observations. Last updated: July 31, 2011. An Approximate Dynamic Programming Algorithm for Large-Scale Fleet Management: A Case Application Hugo P. Simao* Je Day** Abraham P. George* Ted Gi ord** John Nienow** Warren B. Powell* *Department of Operations Research and Financial Engineering, Princeton University **Schneider National October 29, 2009 The second chapter provides a brief introduction to algorithms for approximate dynamic programming. However, the stochastic programming community generally does not exploit state variables, and does not use the concepts and vocabulary of dynamic programming. For a shorter article, written in the style of reinforcement learning (with an energy setting), please download: Also see the two-part tutorial aimed at the IEEE/controls community: W. B. Powell, Stephan Meisel, "Tutorial on Stochastic Optimization in Energy I: Modeling and Policies", IEEE Trans. Abstract. It often is the best, and never works poorly. 205-214, 2008. The OR community tends to work on problems with many simple entities. Our work is motivated by many industrial projects undertaken by CASTLE A common technique for dealing with the curse of dimensionality in approximate dynamic programming is to use a parametric value function approximation, where the value of being in a state is assumed to be a linear combination of basis functions. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Approximate dynamic programming (ADP) is a broad umbrella for a modeling and algorithmic strategy for solving problems that are sometimes large and complex, and are usually (but not always) stochastic. The middle section of the book has been completely rewritten and reorganized. 4.5 Approximate Value Iteration, 127. The proof assumes that the value function can be expressed as a finite combination of known basis functions. 4.7 Low-Dimensional Representations of Value Functions, 144 6 - Policies - The four fundamental policies. We have been doing a lot of work on the adaptive estimation of concave functions. Somewhat surprisingly, generic machine learning algorithms for approximating value functions did not work particularly well. 90-109, 1998. This paper compares an optimal policy for dispatching a truck over a single link (with one product type) against an approximate policy that uses approximations of the future. This paper reviews a number of popular stepsize formulas, provides a classic result for optimal stepsizes with stationary data, and derives a new optimal stepsize formula for nonstationary data. Dynamic Programming (DP) is known to be a standard optimization tool for solving Stochastic Optimal Control (SOC) problems, either over a finite or an infinite horizon of stages. 239-249, 2009. 36, No. 18, No. This paper does with pictures what the paper above does with equations. One encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for large scale controlled Markov chains. Princeton, NJ : Princeton University Abstract: In this thesis, we propose approximate dynamic programming (ADP) methods for solving risk-neutral and risk-averse sequential decision problems under uncertainty, focusing on models that are intractable under traditional techniques. Approximate dynamic programming (ADP) is both a modeling and algorithmic framework for solving stochastic optimization problems. This paper is more than a convergence proof for this particular problem class – it lays out a proof technique, which combines our work on concave approximations with theory laid out by Bertsekas and Tsitsiklis (in their Neuro-Dynamic Programming book). This is a short conference proceedings paper that briefly summarizes the use of approximate dynamic programming for a real application to the management of spare parts for a major aircraft manufacturer. The strategy does not require exploration, which is common in reinforcement learning. Because the optimal policy only works on single link problems with one type of product, while the other is scalable to much harder problems. W. B. Powell, H. Simao, B. Bouzaiene-Ayari, “Approximate Dynamic Programming in Transportation and Logistics: A Unified Framework,” European J. on Transportation and Logistics, Vol. 108-127 (2002). It closes with a summary of results using approximate value functions in an energy storage problem. Finally, it reports on a study on the value of advance information. on Power Systems (to appear) Illustrates the process of modeling a stochastic, dynamic system using an energy storage application, and shows that each of the four classes of policies works best on a particular variant of the problem. 231-249 (2002). Dynamic programming has often been dismissed because it suffers from “the curse of dimensionality.” In fact, there are three curses of dimensionality when you deal with the high-dimensional problems that typically arise in operations research (the state space, the outcome space and the action space). The paper demonstrates both rapid convergence of the algorithm as well as very high quality solutions. The book is aimed at an advanced undergraduate/masters level audience with a good course in probability and statistics, and linear programming (for some applications). 21-39 (2002). One of the oldest problems in dynamic programming arises in the context of planning inventories. We review the literature on approximate dynamic programming, with the goal of better understanding the theory behind practical algorithms for solving dynamic programs with continuous and vector-valued states and actions, and complex information processes. Powell, W.B., J. Shapiro and H. P. Simao, “An Adaptive, Dynamic Programming Algorithm for the Heterogeneous Resource Allocation Problem,” Transportation Science, Vol. It provides an easy, high-level overview of ADP, emphasizing the perspective that ADP is much more than an algorithm – it is really an umbrella for a wide range of solution procedures which retain, at their core, the need to approximate the value of being in a state. Warren B Powell Princeton University Verified email at princeton.edu. Approximate Dynamic Programming for High-Dimensional Resource Allocation Problems. W. B. Powell, J. Ma, “A Review of Stochastic Algorithms with Continuous Value Function Approximation and Some New Approximate Policy Iteration Algorithms for Multi-Dimensional Continuous Applications,” Journal of Control Theory and Applications, Vol. on Power Systems (to appear) Summarizes the modeling framework and four classes of policies, contrasting the notational systems and canonical frameworks of different communities. 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