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Jason L. Speyer - One of the best experts on this subject based on the ideXlab platform.
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On the LQG Game With Nonclassical Information Pattern Using a Direct Solution Method
IEEE Transactions on Automatic Control, 2020Co-Authors: Joshua W. Clemens, Jason L. SpeyerAbstract:A two-sided (simultaneous) optimization technique is presented for the two-player linear quadratic Gaussian multistage game. This direct solution method naturally decomposes the solution into separate deterministic and stochastic terms, which provides insight into the optimal control strategies. We use the optimal governing equations to derive a compact expression for the optimal performance index value. We prove that this two-sided linear solution is indeed optimal out of all possible strategies (linear and nonlinear) by way of a saddle point proof. In addition, we provide some numerical results to show how system noises affect the optimal control strategies and optimal performance index value.
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ACC - The LQG game with nonclassical Information Pattern using a direct solution method
2017 American Control Conference (ACC), 2017Co-Authors: Joshua W. Clemens, Jason L. SpeyerAbstract:A two-sided (simultaneous) optimization technique is presented for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of results as compared to previously used formal solution methods. For example, this direct solution method naturally decomposes the problem into separate deterministic and stochastic terms. This decomposition provides insight into the resulting optimal control strategies. In addition to the optimal control strategies, we derive a Lagrange multiplier (influence) sequence and an expression for the performance index differential, as well as an expression for the optimal performance index value.
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Centralized and decentralized solutions of the linear-exponential-Gaussian problem
IEEE Transactions on Automatic Control, 1994Co-Authors: C.-h. Fan, Jason L. Speyer, C.r. JaenschAbstract:A particular class of stochastic control problems constrained to different Information Patterns is considered. This class consists of minimizing the expectation of an exponential cost criterion with quadratic argument subject to a discrete-time Gauss-Markov dynamic system, i.e., the linear-exponential-Gaussian (LEG) control problem. Besides the one-step delayed Information Pattern previously considered, the classical and the one-step delayed Information-sharing (OSDIS) Patterns are assumed. After determining the centralized controller based upon the classical Information Pattern, the optimal decentralized controller based upon the OSDIS Pattern and the solution to a static team problem is found to be affine. A unifying approach to determine controllers based upon these three Information Patterns is obtained by noting that the value of a quadratic exponent of an exponential function is independent of the Information structure. Both necessary and sufficient conditions for the controllers to be minimizing are obtained regardless of the exponential form. The negative exponential form is included which is unimodal but not convex. >
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Decentralized solutions of the linear-exponential-Gaussian problem
[1992] Proceedings of the 31st IEEE Conference on Decision and Control, 1Co-Authors: C.-h. Fan, Jason L. Speyer, C.r. JaenschAbstract:The authors consider stochastic control problems with an exponential cost criterion. Necessary and sufficient conditions and the control law of the decentralized linear-exponential-Gaussian (LEG) team problem with a one-step delayed Information sharing Pattern are given. The one-step delayed Information Pattern is that only the past observations are available and the current observations are not available. It is shown that the optimal control law of the ith member is an affine function of its own observation at the current time and the state estimate based on a one-step delayed Information Pattern. >
W. Bruce Croft - One of the best experts on this subject based on the ideXlab platform.
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An Information-Pattern-based approach to novelty detection
Information Processing & Management, 2008Co-Authors: W. Bruce CroftAbstract:In this paper, a new novelty detection approach based on the identification of sentence level Information Patterns is proposed. First, ''novelty'' is redefined based on the proposed Information Patterns, and several different types of Information Patterns are given corresponding to different types of users' Information needs. Second, a thorough analysis of sentence level Information Patterns is elaborated using data from the TREC novelty tracks, including sentence lengths, named entities (NEs), and sentence level opinion Patterns. Finally, a unified Information-Pattern-based approach to novelty detection (ip-BAND) is presented for both specific NE topics and more general topics. Experiments on novelty detection on data from the TREC 2002, 2003 and 2004 novelty tracks show that the proposed approach significantly improves the performance of novelty detection in terms of precision at top ranks. Future research directions are suggested.
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CIKM - Improving novelty detection for general topics using sentence level Information Patterns
Proceedings of the 15th ACM international conference on Information and knowledge management - CIKM '06, 2006Co-Authors: W. Bruce CroftAbstract:The detection of new Information in a document stream is an important component of many potential applications. In this work, a new novelty detection approach based on the identification of sentence level Information Patterns is proposed. First, the Information-Pattern concept for novelty detection is presented with the emphasis on new Information Patterns for general topics (queries) that cannot be simply turned into specific questions whose answers are specific named entities (NEs). Then we elaborate a thorough analysis of sentence level Information Patterns on data from the TREC novelty tracks, including sentence lengths, named entities, sentence level opinion Patterns. This analysis provides guidelines in applying those Patterns in novelty detection particularly for the general topics. Finally, a unified Pattern-based approach is presented to novelty detection for both general and specific topics. The new method for dealing with general topics will be the focus. Experimental results show that the proposed approach significantly improves the performance of novelty detection for general topics as well as the overall performance for all topics from the 2002-2004 TREC novelty tracks.
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Sentence level Information Patterns for novelty detection
2006Co-Authors: W. Bruce CroftAbstract:The detection of new Information in a document stream is an important component of many potential applications. In this thesis, a new novelty detection approach based on the identification of sentence level Information Patterns is proposed. Given a user's Information need, some Information Patterns in sentences such as combinations of query words, sentence lengths, named entities and phrases, and other sentence Patterns, may contain more important and relevant Information than single words. The work of the thesis includes three parts. First, we redefine "what is novelty detection" in the lights of the proposed Information Patterns. Examples of several different types of Information Patterns are given corresponding to different types of uses' Information need. Second, we analyze why the proposed Information Pattern concept has a significant impact in novelty detection. A thorough analysis of sentence level Information Patterns is elaborated on data from the TREC novelty tracks, including sentence lengths, named entities (NEs), and sentence level opinion Patterns. Finally, we present how we perform novelty detection based on Information Patterns, which focuses on the identification of previously unseen query-related Patterns in sentences. A unified Pattern-based approach is presented to novelty detection for both specific NE topics and more general topics. Experiments on novelty detection were carried out on data from the TREC 2002, 2003 and 2004 novelty tracks. Experimental results show that the proposed approach significantly improves the performance of novelty detection for both specific and general topics, therefore the overall performance for all topics, in terms of precision at top ranks. Future research directions are suggested.
Serdar Yüksel - One of the best experts on this subject based on the ideXlab platform.
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stochastic nestedness and the belief sharing Information Pattern in decentralized control
American Control Conference, 2009Co-Authors: Serdar YükselAbstract:In a dynamic decentralized control problem, a common Information state supplied to each of the Decision Makers leads to a tractable dynamic programming recursion. However, communication requirements for such conditions require exchange of very large data noiselessly, hence these assumptions are generally impractical. We present a weaker notion of nestedness, which we term as stochastic nestedness, which is characterized by a sequence of Markov chain conditions. It is shown that if the Information structure is stochastically nested, then an optimization problem is tractable, and in particular for LQG problems, the team optimal solution is linear, despite the lack of deterministic nestedness or partial nestedness. One other contribution of this paper is that, by regarding the multiple decision makers as a single decision maker and using Witsenhausen's equivalent model for discrete-stochastic control, it is shown that the common state required need not consist of observations and it suffices to share beliefs on the state and control actions; a Pattern we refer to as k-stage belief sharing Pattern. We evaluate a precise expression for the minimum amount of Information required to achieve such an Information Pattern for k = 1. The Information exchange needed is generally strictly less than the Information exchange needed for deterministic nestedness and is zero whenever stochastic nestedness applies.
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Stochastic Nestedness and the Belief Sharing Information Pattern
IEEE Transactions on Automatic Control, 2009Co-Authors: Serdar YükselAbstract:Solutions to decentralized stochastic optimization problems lead to recursions in which the state space enlarges with the time-horizon, thus leading to non-tractability of classical dynamic programming. A common joint Information state supplied to each of the agents leads to a tractable recursion, as is evident in the one-step-delayed Information sharing structure case or when deterministic nestedness in Information holds when there is a causality relationship as in the case of partially nested Information structure. However, communication requirements for such conditions require exchange of very large data noiselessly, hence these assumptions are generally impractical. In this paper, we present a weaker notion of nestedness, which we term as stochastic nestedness, which is characterized by a sequence of Markov chain conditions. It is shown that if the Information structure is stochastically nested, then an optimization problem is tractable, and in particular for LQG problems, the team optimal solution is linear, despite the lack of deterministic nestedness or partial nestedness. One other contribution of this paper is that, by regarding the multiple decision makers as a single decision maker and using Witsenhausen's equivalent model for discrete-stochastic control, it is shown that the common state required need not consist of observations and it suffices to share beliefs on the state and control actions; a Pattern we refer to as k-stage belief sharing Pattern. We discuss the minimum amount of Information exchange required to achieve such an Information Pattern for k =1. The Information exchange needed is generally strictly less than what is needed for deterministic nestedness and is zero whenever stochastic nestedness applies. In view of nestedness, we present a discussion on the monotone values of Information channels.
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ACC - Stochastic nestedness and the belief sharing Information Pattern in decentralized control
2009 American Control Conference, 2009Co-Authors: Serdar YükselAbstract:In a dynamic decentralized control problem, a common Information state supplied to each of the Decision Makers leads to a tractable dynamic programming recursion. However, communication requirements for such conditions require exchange of very large data noiselessly, hence these assumptions are generally impractical. We present a weaker notion of nestedness, which we term as stochastic nestedness, which is characterized by a sequence of Markov chain conditions. It is shown that if the Information structure is stochastically nested, then an optimization problem is tractable, and in particular for LQG problems, the team optimal solution is linear, despite the lack of deterministic nestedness or partial nestedness. One other contribution of this paper is that, by regarding the multiple decision makers as a single decision maker and using Witsenhausen's equivalent model for discrete-stochastic control, it is shown that the common state required need not consist of observations and it suffices to share beliefs on the state and control actions; a Pattern we refer to as k-stage belief sharing Pattern. We evaluate a precise expression for the minimum amount of Information required to achieve such an Information Pattern for k = 1. The Information exchange needed is generally strictly less than the Information exchange needed for deterministic nestedness and is zero whenever stochastic nestedness applies.
Joshua W. Clemens - One of the best experts on this subject based on the ideXlab platform.
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On the LQG Game With Nonclassical Information Pattern Using a Direct Solution Method
IEEE Transactions on Automatic Control, 2020Co-Authors: Joshua W. Clemens, Jason L. SpeyerAbstract:A two-sided (simultaneous) optimization technique is presented for the two-player linear quadratic Gaussian multistage game. This direct solution method naturally decomposes the solution into separate deterministic and stochastic terms, which provides insight into the optimal control strategies. We use the optimal governing equations to derive a compact expression for the optimal performance index value. We prove that this two-sided linear solution is indeed optimal out of all possible strategies (linear and nonlinear) by way of a saddle point proof. In addition, we provide some numerical results to show how system noises affect the optimal control strategies and optimal performance index value.
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ACC - The LQG game with nonclassical Information Pattern using a direct solution method
2017 American Control Conference (ACC), 2017Co-Authors: Joshua W. Clemens, Jason L. SpeyerAbstract:A two-sided (simultaneous) optimization technique is presented for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of results as compared to previously used formal solution methods. For example, this direct solution method naturally decomposes the problem into separate deterministic and stochastic terms. This decomposition provides insight into the resulting optimal control strategies. In addition to the optimal control strategies, we derive a Lagrange multiplier (influence) sequence and an expression for the performance index differential, as well as an expression for the optimal performance index value.
Reinhard Neck - One of the best experts on this subject based on the ideXlab platform.
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Optimal Macroeconomic Policies in a Monetary Union: A Dynamic Game Analysis
IFAC-PapersOnLine, 2015Co-Authors: Dimitri Blueschke, Reinhard NeckAbstract:Abstract In this paper we present an application of the dynamic tracking games framework to a monetary union. We use a small stylized nonlinear two-country macroeconomic model of a monetary union (MUMOD1) to analyse the interactions between fiscal (governments) and monetary (common central bank) policy makers, assuming different objective functions of these decision makers. Using the OPTGAME algorithm we calculate solutions for four game strategies: one cooperative (Pareto optimal) and three non-cooperative games: the Nash game for the open-loop Information Pattern, the Nash game for the feedback Information Pattern, and the Stackelberg game for the feedback Information Pattern. Applying the OPTGAME algorithm to the MUMOD1 model we show how the policy makers react to demand and supply shocks according to different solution concepts. Some comments are given on possible applications to the recent sovereign debt crisis in Europe.
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Policy Interactions in a Monetary Union: An Application of the OPTGAME Algorithm
Dynamic Games in Economics, 2014Co-Authors: Dimitri Blueschke, Reinhard NeckAbstract:In this chapter we present an application of the dynamic tracking games framework to a monetary union. We use a small stylized nonlinear two-country macroeconomic model (MUMOD1) of a monetary union to analyse the interactions between fiscal (governments) and monetary (common central bank) policy makers, assuming different objective functions of these decision makers. Using the OPTGAME algorithm we calculate equilibrium solutions for four game strategies: one cooperative (Pareto optimal) and three non-cooperative games: the Nash game for the open-loop Information Pattern, the Nash game for the feedback Information Pattern, and the Stackelberg game for the feedback Information Pattern. Applying the OPTGAME algorithm to the MUMOD1 model we show how the policy makers react to demand and supply shocks according to different solution concepts. Some comments are given on possible applications to the recent sovereign debt crisis in Europe.
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An Algorithmic Equilibrium Solution for n -Person Dynamic Stackelberg Difference Games with Open-Loop Information Pattern
Dynamic Modeling and Econometrics in Economics and Finance, 2011Co-Authors: Philipp Hungerländer, Reinhard NeckAbstract:In this paper, extensions are presented for the open-loop Stackelberg equilibrium solution of n-person discrete-time affine-quadratic dynamic games of prespecified fixed duration to allow for an arbitrary number of followers and the possibility of algorithmic implementation. First we prove a general result about the existence of a Stackelberg equilibrium solution with one leader and arbitrarily many followers in n-person discrete-time deterministic infinite dynamic games of prespecified fixed duration with open-loop Information Pattern. Then this result is applied to affine-quadratic games. Thereby we get a system of equilibrium equations that can easily be used for an algorithmic solution of the given Stackelberg game.
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Commitment and coordination in a dynamic game model of international economic policy-making
Open Economies Review, 1995Co-Authors: Reinhard Neck, Engelbert J. DocknerAbstract:In this paper, we consider a dynamic game model of two identical countries. Policy-makers of both countries have quadratic intertemporal objective functions and want to stabilize domestic output, domestic inflation, and the real rate of exchange. We present different analytical and numerical solutions for this policy game. Noncooperative open-loop equilibria are interpreted as requiring unilateral commitment and policy-makers' credibility. Potential gains from cooperation are present, as the noncooperative equilibrium solutions are not Pareto-optimal. Under an Information Pattern that admits memory strategies, the possibility of obtaining “cooperative” results without coordination and commitment arises.