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A simulation-based algorithm for optimal pricing policy under demand uncertainty

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2014年第5期21卷 737-760页

作者： Chakravarty, Saswata Padakandla, Sindhu Bhatnagar, Shalabh Indian Inst Sci Dept Elect Engn Bangalore 560012 Karnataka India Indian Inst Sci Dept Comp Sci & Automat Bangalore 560012 Karnataka India

We propose a simulation-based algorithm for computing the optimal pricing policy for a product under uncertain demand dynamics. We consider a parameterized stochastic differential equation (SDE) model for the uncertain demand dynamics of the product over the planning horizon. In particular, we consider a dynamic model that is an extension of the Bass model. The performance of our algorithm is compared to that of a myopic pricing policy and is shown to give better results. Two significant advantages with our algorithm are as follows: (a) it does not require information on the system model parameters if the SDE system state is known via either a simulation device or real data, and (b) as it works efficiently even for high-dimensional parameters, it uses the efficient smoothed functional gradient estimator.

关键词： optimal pricing policy Bass model parameterized stochastic differential equation (SDE) stochastic approximation algorithm smoothed functional gradient estimates

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Detection of Homophilic Communities and Coordination of Interacting Meta-Agents: A Game-Theoretic Viewpoint

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IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS 2016年第1期2卷 84-101页

作者： Gharehshiran, Omid Namvar Hoiles, William Krishnamurthy, Vikram Univ Toronto Dept Stat Sci Toronto ON M5S 3G3 Canada Univ British Columbia Dept Elect & Comp Engn Vancouver BC V6T 1Z4 Canada

This paper studies two important signal processing aspects of homophilic behavior namely, detection of homophilic communities and the distributed coordination of meta-agents, which interact with the detected homophilic communities. First, the theory of revealed preferences from microeconomics is used to construct a nonparametric decision test for homophilic behavior using only the time series of external influences and associated agents' responses. These tests rely on rationalizing the dataset of agents' actions as the play from the Nash equilibrium of a concave potential game. A stochastic gradient algorithm is given to optimize the external influence signal in real time to minimize the Type-II error probabilities of the detection test subject to specified Type-I error probability. Using the decision test, methods are provided to detect for homophilic communities. Subsequently, a nonparametric algorithm is presented that uses the constructed potential function for the potential game to predict the preferences of the detected homophilic communities. Second, we present a non-cooperative game model for interaction of meta-agents that interact with the communities and propose an algorithm that prescribes meta-agents how to take actions based on the preference of the communities and past interaction information with other meta-agents. The proposed algorithm has two timescales: the slow timescale is the nonparametric preference learning presented in the first part, and the fast timescale is a regret-matching stochastic approximation algorithm. It is shown that, if all meta-agents follow the proposed algorithm, their collective behavior is attracted to the correlated equilibria set of the game. This means that meta-agents can co-ordinate their strategies in a distributed fashion as if there exists a centralized coordinating device that they all trust to follow. We provide a real-world example using the energy market, and a numerical example to detect malicious agents in a

关键词： Multiagent signal processing nonco-operative games correlated equilibrium homophily revealed preferences Afriat's theorem stochastic approximation algorithm

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A hierarchical decision and information system for multi-aircraft combat missions

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 2010年第G2期224卷 133-148页

作者： Lechevin, N. Rabbath, C. A. Def Res & Dev Canada Quebec City PQ G3J 1X5 Canada

Designing decision, control and information systems is motivated, in part, by the need to support the deployment of multiple aircraft, such as combat vehicles, unmanned combat air vehicles, unmanned aerial vehicles, and weapons, in missions taking place in a dynamic, although uncertain, environment. Such systems aim at ensuring mission success without overloading the operating crew, the pilots, and the commanders. One of the main design challenges lies in obtaining some sort of coherent behaviour of the fleet, by means of solutions to potentially NP-hard problems, given incomplete and imperfect information, and despite limited computational and communication capabilities. In this context, this article proposes a hierarchical decision and information system aiming at providing, in real-time, coordinated aircraft path planning and deceptive engagement assignments. The blue-red engagement policy is obtained by minimizing, and balancing, the energy expenditure among the vehicles while constraining information exchanges to a minimum defined by a risk of inconsistency. The proposed system relies on dynamic programming, online heuristic techniques and stochastic, consistency-checking methods. Numerical simulations show that the proposed approach compares advantageously to a random process and to a law that seeks to minimize the cost of the confrontation at a given time regardless of past moves. However, there is a trade-off between increasing the level of deception and the level of energy consumption.

关键词： autonomous vehicle path planning task assignment dynamic programming stochastic approximation algorithm

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Bias reduction in kernel density estimation

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JOURNAL OF NONPARAMETRIC STATISTICS 2018年第2期30卷 505-522页

作者： Slaoui, Yousri Univ Poitiers Lab Math & Applicat Futuroscope France

In this paper, we propose two kernel density estimators based on a bias reduction technique. We study the properties of these estimators and compare them with Parzen-Rosenblatt's density estimator and Mokkadem, A., Pelletier, M., and Slaoui, Y. (2009, The stochastic approximation method for the estimation of a multivariate probability density', J. Statist. Plann. Inference, 139, 2459-2478) is density estimators. It turns out that, with an adequate choice of the parameters of the two proposed estimators, the rate of convergence of two estimators will be faster than the two classical estimators and the asymptotic MISE (Mean Integrated Squared Error) will be smaller than the two classical estimators. We corroborate these theoretical results through simulations.

关键词： Density estimation stochastic approximation algorithm smoothing curve fitting bias reduction Primary: 62G07 62L20 Secondary: 65D10

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Recursive non-parametric kernel classification rule estimation for independent functional data

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COMPUTATIONAL STATISTICS 2021年第1期36卷 79-112页

作者： Slaoui, Yousri Univ Poitiers Lab Math & Applicat Poitiers France

In this paper we propose an automatic selection of the bandwidth of the recursive non-parametric estimation of the kernel classification rule function defined by the stochastic approximation algorithm, when the explanatory data are curves and the response is categorical. We established a central limit theorem for our proposed recursive estimators, the proposed recursive estimators will be very competitive to the non-recursive one in terms of estimation error but much better in terms of computational costs. The proposed estimators are used first on simulated waveform curves and then on real phoneme data.

关键词： stochastic approximation algorithm Asymptotic normality Functional data Regression estimation Supervised classification Smoothing Curve fitting

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Moderate deviation principles for nonparametric recursive distribution estimators using Bernstein polynomials

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REVISTA MATEMATICA COMPLUTENSE 2022年第1期35卷 147-158页

作者： Slaoui, Yousri Univ Poitiers Poitiers Poitou Charente France

In this paper we prove moderate deviations principles for the recursive estimators of a distribution function defined by the stochastic approximation algorithm based on Bernstein polynomials introduced by Jmaei el al. (J Nonparametr Stat 29:792-805, 2017). We show that the considered estimator gives the same pointwise moderate deviations principle (MDP) as the recursive kernel distribution estimator proposed in Slaoui (Math Methods Stat 23(4):306-325, 2014b) and whose large and moderate deviation principles were established by Slaoui (Stat Interface 12(3):439-455, 2009).

关键词： Bernstein polynomial Distribution estimation Large and moderate deviations principles stochastic approximation algorithm

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Shortfall Risk Minimization in Discrete Time Financial Market Models

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SIAM JOURNAL ON FINANCIAL MATHEMATICS 2014年第1期5卷 384-414页

作者： Frikha, N. Univ Paris Diderot LPMA F-75205 Paris France

In this paper, we study theoretical and computational aspects of risk minimization in financial market models operating in discrete time. To define the risk, we consider a class of convex risk measures defined on L-p(P) in terms of shortfall risk. Under mild assumptions, namely, the absence of arbitrage opportunity and the nondegeneracy of the price process, we prove the existence of an optimal strategy by performing a dynamic programming argument in a non-Markovian framework. In a Markovian framework, the shortfall risk and optimal dynamic strategies are estimated using three main tools: Newton-Raphson Monte Carlo-based procedure, stochastic approximation algorithm, and Markovian quantization scheme. Finally, we illustrate our approach by considering several shortfall risk measures and portfolios inspired by energy and financial markets.

关键词： shortfall risk measures risk minimization dynamic programming principle stochastic approximation algorithm vector quantization Monte Carlo simulation

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Self-healing umbrella sampling: convergence and efficiency

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STATISTICS AND COMPUTING 2017年第1期27卷 147-168页

作者： Fort, Gersende Jourdain, Benjamin Lelievre, Tony Stoltz, Gabriel CNRS LTCI 46 Rue Barrault F-75634 Paris 13 France Telecom Paris Tech 46 Rue Barrault F-75634 Paris 13 France Univ Paris Est CERMICS ENPC INRIA F-77455 Marne La Vallee France

The Self-Healing Umbrella Sampling (SHUS) algorithm is an adaptive biasing algorithm which has been proposed in Marsili et al. (J Phys Chem B 110(29):14011-14013, 2006) in order to efficiently sample a multimodal probability measure. We show that this method can be seen as a variant of the well-known Wang-Landau algorithm Wang and Landau (Phys Rev E 64:056101, 2001a;Phys Rev Lett 86(10):2050-2053, 2001b). Adapting results on the convergence of the Wang-Landau algorithm obtained in Fort et al. (Math Comput 84(295):2297-2327, 2014a), we prove the convergence of the SHUS algorithm. We also compare the two methods in terms of efficiency. We finally propose a modification of the SHUS algorithm in order to increase its efficiency, and exhibit some similarities of SHUS with the well-tempered metadynamics method Barducci et al. (Phys Rev Lett 100:020,603, 2008).

关键词： Wang-Landau algorithm stochastic approximation algorithm Free energy biasing techniques

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Two new nonparametric kernel distribution estimators based on a transformation of the data

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JOURNAL OF APPLIED STATISTICS 2021年第12期48卷 2065-2091页

作者： Slaoui, Yousri Univ Poitiers Lab Math & Applicat Futuroscope France

In this paper, we propose two kernel distribution estimators based on a data transformation. We study the properties of these estimators and we compare them with two conventional estimators. It appears that with an appropriate choice of the parameters of the two proposed estimators, the convergence rate of two estimators will be faster than that of the two conventional estimators and the Mean Integrated Square Error will be smaller than the two conventional estimators. We corroborate these theoretical results through simulations as well as a real data set.

关键词： Distribution estimation stochastic approximation algorithm smoothing curve fitt ing Bias reduction

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STRONGLY REINFORCED POLYA URNS WITH GRAPH-BASED COMPETITION

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ANNALS OF APPLIED PROBABILITY 2016年第4期26卷 2494-2539页

作者： van der Hofstad, Remco Holmes, Mark Kuznetsov, Alexey Ruszel, Wioletta Eindhoven Univ Technol Dept Math & Comp Sci POB 513 NL-5600 MB Eindhoven Netherlands Univ Auckland Dept Stat Private Bag 92019 Auckland 1142 New Zealand York Univ Dept Math & Stat 4700 Keele St Toronto ON Canada Delft Univ Technol Delft Inst Appl Math Mekelweg 4 NL-2628 CD Delft Netherlands

We introduce a class of reinforcement models where, at each time step t, one first chooses a random subset A(t) of colours (independently of the past) from n colours of balls, and then chooses a colour i from this subset with probability proportional to the number of balls of colour i in the urn raised to the power alpha > 1. We consider stability of equilibria for such models and establish the existence of phase transitions in a number of examples, including when the colours are the edges of a graph;a context which is a toy model for the formation and reinforcement of neural connections. We conjecture that for any graph G and all alpha sufficiently large, the set of stable equilibria is supported on so-called whisker-forests, which are forests whose components have diameter between 1 and 3.

关键词： Reinforcement model Polya urn stochastic approximation algorithm stable equilibria

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