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Assessing the Value of dynamic Pricing in Network Revenue Management

INFORMS JOURNAL ON COMPUTING 2013年第1期25卷 102-115页

作者： Zhang, Dan Lu, Zhaosong Univ Colorado Leeds Sch Business Boulder CO 80309 USA Simon Fraser Univ Dept Math Burnaby BC V5A 1S6 Canada

dynamic pricing for a network of resources over a finite selling horizon has received considerable attention in recent years, yet few papers provide effective computational approaches to solve the problem. We consider a resource decomposition approach to solve the problem and investigate the performance of the approach in a computational study. We compare the performance of the approach to static pricing and choice-based availability control. Our numerical results show that dynamic pricing policies from network resource decomposition can achieve significant revenue lift compared with choice-based availability control and static pricing, even when the latter is frequently resolved. As a by-product of our approach, network decomposition provides an upper bound in revenue, which is provably tighter than the well-known upper bound from a deterministic approximation.

关键词： revenue management dynamic pricing approximate dynamic programming choice models

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A novel actor-critic-identifier architecture for approximate optimal control of uncertain nonlinear systems

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AUTOMATICA 2013年第1期49卷 82-92页

作者： Bhasin, S. Kamalapurkar, R. Johnson, M. Vamvoudakis, K. G. Lewis, F. L. Dixon, W. E. Indian Inst Technol Dept Elect Engn Delhi India Univ Florida Dept Mech & Aerosp Engn Gainesville FL USA Univ Calif Santa Barbara Ctr Control Dynam Syst & Computat CCDC Santa Barbara CA 93106 USA Univ Texas Arlington Automat & Robot Res Inst Ft Worth TX 76118 USA

An online adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem for continuous-time uncertain nonlinear systems. A novel actor-critic-identifier (ACI) is proposed to approximate the Hamilton-Jacobi-Bellman equation using three neural network (NN) structures actor and critic NNs approximate the optimal control and the optimal value function, respectively, and a robust dynamic neural network identifier asymptotically approximates the uncertain system dynamics. An advantage of using the ACI architecture is that learning by the actor, critic, and identifier is continuous and simultaneous, without requiring knowledge of system drift dynamics. Convergence of the algorithm is analyzed using Lyapunov-based adaptive control methods. A persistence of excitation condition is required to guarantee exponential convergence to a bounded region in the neighborhood of the optimal control and uniformly ultimately bounded (UUB) stability of the closed-loop system. Simulation results demonstrate the performance of the actor-critic-identifier method for approximate optimal control. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Learning control Adaptive control Optimal control approximate dynamic programming Actor-critic-identifier

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Analysis of cross-price effects on markdown policies by using function approximation techniques

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KNOWLEDGE-BASED SYSTEMS 2013年第Nov.期53卷 173-184页

作者： Cosgun, Ozlem Kula, Ufuk Kahraman, Cengiz Fatih Univ Dept Ind Engn TR-34500 Istanbul Turkey Sakarya Univ Dept Ind Engn Sakarya Turkey Istanbul Tech Univ Dept Ind Engn TR-80626 Istanbul Turkey

Markdown policies for product groups having significant cross-price elasticity among each other should be jointly determined. However, finding optimal policies for product groups becomes computationally intractable as the number of products increases. Therefore, we formulate the problem as a Markov decision process and use approximate dynamic programming approach to solve it. Since the state space is multidimensional and very large, the number of iterations required to learn the state values is enormous. Therefore, we use aggregation and neural networks in order to approximate the value function and to determine the optimal markdown policies approximately. In a numerical study, we provide insights on the behavior of markdown policies when one product is expensive, the other is cheap and both have the same price. We also provide insights and compare the markdown policies for the cases in which there is a substitution effect between products and the products are independent. (C) 2013 Elsevier B.V. All rights reserved.

关键词： approximate dynamic programming Artificial neural networks Cross-price elasticity Markdown optimization dynamic pricing Aggregation

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Multi-objective optimal control for a class of nonlinear time-delay systems via adaptive dynamic programming

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SOFT COMPUTING 2013年第11期17卷 2109-2115页

作者： Song, Ruizhuo Xiao, Wendong Wei, Qinglai Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China Chinese Acad Sci State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China

A novel multi-objective adaptive dynamic programming (ADP) method is constructed to obtain the optimal controller of a class of nonlinear time-delay systems in this paper. Using the weighted sum technology, the original multi-objective optimal control problem is transformed to the single one. An ADP method is established for nonlinear time-delay systems to solve the optimal control problem. To demonstrate that the presented iterative performance index function sequence is convergent and the closed-loop system is asymptotically stable, the convergence analysis is also given. The neural networks are used to get the approximative control policy and the approximative performance index function, respectively. Two simulation examples are presented to illustrate the performance of the presented optimal control method.

关键词： Optimal control Adaptive dynamic programming Multi-objective approximate dynamic programming Time-delay

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Adaptive value function approximation for continuous-state stochastic dynamic programming

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COMPUTERS & OPERATIONS RESEARCH 2013年第4期40卷 1076-1084页

作者： Fan, Huiyuan Tarun, Prashant K. Chen, Victoria C. P. Rolls Royce Energy Syst Inc Mt Vernon OH 43050 USA Missouri Western State Univ Steven L Craig Sch Business St Joseph MO 64507 USA Univ Texas Arlington Arlington TX 76019 USA

approximate dynamic programming (ADP) commonly employs value function approximation to numerically solve complex dynamic programming problems. A statistical perspective of value function approximation employs a design and analysis of computer experiments (DACE) approach, where the "computer experiment" yields points on the value function curve. The DACE approach has been used to numerically solve high-dimensional, continuous-state stochastic dynamic programming, and performs two tasks primarily: (1) design of experiments and (2) statistical modeling. The use of design of experiments enables more efficient discretization. However, identifying the appropriate sample size is not straightforward. Furthermore, identifying the appropriate model structure is a well-known problem in. the field of statistics. In this paper, we present a sequential method that can adaptively determine both sample size and model structure. Number-theoretic methods (NTM) are used to sequentially grow the experimental design because of their ability to fill the design space. Feed-forward neural networks (NNs) are used for statistical modeling because of their adjustability in structure-complexity. This adaptive value function approximation (AVFA) method must be automated to enable efficient implementation within ADP. An AVFA algorithm is introduced, that increments the size of the state space training data in each sequential step, and for each sample size a successive model search process is performed to find an optimal NN model. The new algorithm is tested on a nine-dimensional inventory forecasting problem. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： approximate dynamic programming Sequential design of experiments Statistical modeling Neural network Number theoretic methods Inventory forecasting

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The finite-horizon optimal control for a class of time-delay affine nonlinear system

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NEURAL COMPUTING & APPLICATIONS 2013年第2期22卷 229-235页

作者： Song, Ruizhuo Zhang, Huaguang Northeastern Univ Sch Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Northeastern Univ Key Lab Integrated Automat Proc Ind Minist Educ Shenyang 110004 Liaoning Peoples R China

In this paper, a new iteration algorithm is proposed to solve the finite-horizon optimal control problem for a class of time-delay affine nonlinear systems with known system dynamic. First, we prove that the algorithm is convergent as the iteration step increases. Then, a theorem is presented to demonstrate that the limit of the iteration performance index function satisfies discrete-time Hamilton-Jacobi-Bellman (DTHJB) equation, and the finite-horizon iteration algorithm is presented with satisfactory accuracy error. At last, two neural networks are used to approximate the iteration performance index function and the corresponding control policy. In simulation part, an example is given to demonstrate the effectiveness of the proposed iteration algorithm.

关键词： Adaptive dynamic programming approximate dynamic programming Optimal control Finite horizon Neural network

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Multi-objective optimal control for a class of unknown nonlinear systems based on finite-approximation-error ADP algorithm

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NEUROCOMPUTING 2013年 119卷 212-221页

作者： Song, Ruizhuo Xiao, Wendong Zhang, Huaguang Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China Northeastern Univ Sch Informat Sci & Engn Shenyang Liaoning Peoples R China

In this paper, an optimal control method for a class of unknown discrete-time nonlinear systems with general multi-objective performance indices is proposed. In the design of the optimal controller, only available input output data are required instead of known system dynamics, and the data-based identifier is established with stability proof. By the weighted sum technology, the multi-objective optimal control problem is transformed into the single objective optimization. To obtain the solution of the HJB equation, the novel finite-approximation-error adaptive dynamic programming (ADP) algorithm is presented with convergence proof. The detailed theoretic analyses for the relationship of the approximation accuracy and the algorithm convergence are given. It is shown that, as convergence conditions are satisfied, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the proposed method. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Adaptive dynamic programming approximate dynamic programming Finite-approximation-error Neural networks Multi-objective Optimal control

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Comparison of deterministic and heuristic optimization solvers for water network scheduling problems

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WATER SCIENCE AND TECHNOLOGY-WATER SUPPLY 2013年第5期13卷 1367-1376页

作者： Bene, J. G. Selek, I. Hos, Cs Budapest Univ Technol & Econ Dept Hydrodynam Syst H-1521 Budapest Hungary Univ Oulu Syst Engn Lab FI-90014 Oulu Finland

This paper presents a novel approximate dynamic programming technique for solving the pump schedule optimization of real-water distribution networks. The method is based on the significant decreasing of the search space by splitting the optimization problem into smaller units. In addition, the state space of the main distribution system was further reduced to the most important reservoirs. The capabilities of the proposed technique are demonstrated on a real-life problem, the water distribution system of the town of Sopron, Hungary. Nine test cases were defined which represent different initial water level scenarios, thus the new application was easy to compare to a former developed genetic algorithm and to some world-leading optimization solvers which are available on the NEOS Server. The benefits and drawbacks of these deterministic and heuristic methods are highlighted.

关键词： approximate dynamic programming genetic algorithm pump schedule optimization

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Q-learning and policy iteration algorithms for stochastic shortest path problems

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ANNALS OF OPERATIONS RESEARCH 2013年第1期208卷 95-132页

作者： Yu, Huizhen Bertsekas, Dimitri P. MIT Informat & Decis Syst Lab Cambridge MA 02139 USA MIT Dept Elect Engn & Comp Sci Cambridge MA 02139 USA

We consider the stochastic shortest path problem, a classical finite-state Markovian decision problem with a termination state, and we propose new convergent Q-learning algorithms that combine elements of policy iteration and classical Q-learning/value iteration. These algorithms are related to the ones introduced by the authors for discounted problems in Bertsekas and Yu (Math. Oper. Res. 37(1):66-94, 2012). The main difference from the standard policy iteration approach is in the policy evaluation phase: instead of solving a linear system of equations, our algorithm solves an optimal stopping problem inexactly with a finite number of value iterations. The main advantage over the standard Q-learning approach is lower overhead: most iterations do not require a minimization over all controls, in the spirit of modified policy iteration. We prove the convergence of asynchronous deterministic and stochastic lookup table implementations of our method for undiscounted, total cost stochastic shortest path problems. These implementations overcome some of the traditional convergence difficulties of asynchronous modified policy iteration, and provide policy iteration-like alternative Q-learning schemes with as reliable convergence as classical Q-learning. We also discuss methods that use basis function approximations of Q-factors and we give an associated error bound.

关键词： Markov decision processes Q-learning approximate dynamic programming Value iteration Policy iteration Stochastic shortest paths Stochastic approximation

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Biologically inspired scheme for continuous-time approximate dynamic programming

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2008年第3-4期30卷 207-223页

作者： Vrabie, Draguna Lewis, Frank Abu-Khalaf, Murad Univ Texas Arlington Automat & Robot Res Inst Ft Worth TX 76118 USA Mathworks Inc Natick MA 01760 USA

Control system theory has been based oil certain well understood and accepted techniques, such as transfer function-based methods, adaptive control, robust control, non-linear systems theory, state-space methods, etc. However, recently, the hypothesis that methods of modelling and analysis of life science systems hold out the power of significantly improving the performance of man-made control systems has gained increased interest, while becoming more and more a fact. For instance, in the last few decades many successful results were obtained by combining the potential of artificial neural networks (ANNs) with classical control structures. It has been shown that certain types of ANN can extend the capabilities of adaptive controllers by making them applicable for more complex non-linear systems, and at the same time greatly improving the system performance. In this paper, we will present a biologically inspired structure that will learn the optimal state feedback controller for a linear system, while at the same time performing continuous-time online control for the system at hand. Being based on a reinforcement learning technique, the optimal controller will be obtained while only making use of the input-to-state system dynamics. Mathematically speaking, the solution of the algebraic Riccati equation underlying the control problem will be obtained without making use of any knowledge of the system internal dynamics.

关键词： Actor/Critic structures approximate dynamic programming linear quadratic regulation policy iteration

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