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Tracking time-varying properties using quasi time-invariant models with bayesian dynamic programming

MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2025年 223卷

作者： Yang, Yanping Zhu, Zuo Au, Siu-Kui Nanyang Technol Univ Sch Civil & Environm Engn Singapore Singapore Univ Exeter Coll Engn Math & Phys Sci Vibrat Engn Sect Exeter England

Tracking the temporal variation of the properties of a system is relevant in different settings when data of extended duration is available, e.g., anomaly detection, condition monitoring, and trend identification. One simple approach is to divide the data into non-overlapping segments and then identify the model properties of each segment individually using a time-invariant model within the segment. The potential change of the system is then investigated by tracking the variations of model properties from one segment to another. In this context, a dynamic programming approach has been developed recently that determines the 'best partitioning' of data segments, between which a change of model parameters takes place in the sense of bayesian model selection. As a change can result when any one of the parameters has changed in a statistically significant manner, a basic question is concerned with what constitutes a suitable model that meets specific monitoring objectives. E.g., should all or only some of the parameters be allowed to change? Motivated by this, a quasi time-invariant (QTI) modeling methodology is proposed in this work where only some (rather than all) parameters are allowed to change across data segments. Computational issues associated with this new class of models are addressed, e.g., the efficient calculation of posterior most probable value and covariance matrix, and bayesian evidence in the context of dynamic programming. Focusing on modal property (natural frequencies, damping ratios, etc.) tracking with ambient data, the proposed methodology with QTI model is investigated with synthetic and laboratory data;and applied to field data of a tall building during a typhoon event. The results from field data are compared with those from existing methods.

关键词： Quasi time-invariant model QTI model Model property tracking bayesian dynamic programming BAYOMA Structural health monitoring

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Sequential bayesian Replacement With Unknown Transition Probabilities

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NAVAL RESEARCH LOGISTICS 2025年第0期

作者： Chuang, Ya-Tang Natl Cheng Kung Univ Dept Ind & Informat Management Tainan Taiwan

We investigate a class of sequential replacement optimization problems where transition probabilities of states are not known a priori but need to be learned over time via information acquisition. The goal of the decision-maker is to determine the optimal time to replace a system before it fails, while simultaneously learning the unknown transition probabilities to minimize the expected total discounted costs over the finite time horizon. Specifically, in each period, the decision-maker needs to choose between do-nothing and replacement actions. On the one hand, from the perspective of learning, the do-nothing action is favorable since state transitions can be observed, providing informative insights for learning. On the other hand, from the viewpoint of cost optimization, the decision-maker may prefer immediate system replacement to avoid potential failure. We formulate the sequential replacement problem as a bayesian dynamic program (BDP). The primary focus of our analysis is on establishing structural properties that hold in the presence of model uncertainty. In particular, we prove that (i) the optimal policy follows a threshold policy with respect to the system's health state, and (ii) the optimal value function maintains concavity with respect to the posterior distribution. Lastly, we develop two heuristics based on the approximation of the optimal value function and demonstrate that the proposed heuristics are near-optimal.

关键词： bayesian dynamic programming bayesian learning exploration vs exploitation trade-off replacement optimization

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A bayesian model for multicriteria sorting problems

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IISE TRANSACTIONS 2024年第7期56卷 777-791页

作者： Ulu, Canan Shively, Thomas S. Georgetown Univ McDonough Sch Business Washington DC 20057 USA Univ Texas Austin McCombs Sch Business Austin TX USA

Decision makers are often interested in assigning alternatives to preference classes under multiple criteria instead of choosing the best alternative or ranking all the alternatives. Firms need to categorize suppliers based on performance, credit agencies need to classify customers according to their risks, and graduate programs need to decide who to admit. In this article, we develop an interactive bayesian algorithm to aid a decision maker (DM) with a multicriteria sorting problem by learning about her preferences and using that knowledge to sort alternatives. We assume the DM has a linear value function and value thresholds for preference classes. Our method specifies an informative prior distribution on the uncertain parameters. At each stage of the process, we compare the expected cost of stopping with the expected cost of continuing to consult the DM. If it is optimal to continue, we select an alternative to present to the DM and, given the DM's response, we update the prior distribution using Bayes' Theorem. The goal of the algorithm is to minimize expected total cost. We develop lower bounds on the optimal cost and study the performance of a heuristic policy that presents the DM alternatives with the highest expected cost of misplacement.

关键词： Multiple criteria sorting bayesian dynamic programming

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Learning Manipulation Through Information Dissemination

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OPERATIONS RESEARCH 2022年第6期70卷 3490-3510页

作者： Keppo, Jussi Kim, Michael Jong Zhang, Xinyuan Natl Univ Singapore NUS Business Sch Singapore 119245 Singapore Natl Univ Singapore Inst Operat Res & Analyt Singapore 119245 Singapore Univ British Columbia Sauder Sch Business Vancouver BC V6T IZ2 Canada

We study optimal manipulation of a bayesian learner through adaptive provisioning of information. The problem is motivated by settings in which a firm can disseminate possibly biased information at a cost, to influence the public's belief about a hidden parameter related to the firm's payoffs. For example, firms advertise to sell products. We study a sequential optimizationmodel in which the firmdynamically decides on the quantity and content of information sent to the public, aiming to maximize its expected total discounted profits over an infinite horizon. We solve the associated bayesian dynamic programming equation and explicitly characterize the optimal manipulation policy in closed form. The explicit solution allows us to further characterize the evolution of the public's posterior belief under suchmanipulation over time. We also extend our analysis to consider the public as partially bayesian social learners who rely on public reviews to resist manipulation. We show that the public asymptotically learns the truth in this extended setting.

关键词： bayesian dynamic programming information design dynamic learning information disclosure deceptive advertising exponential tilting social learning relative entropy

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Variance Regularization in Sequential bayesian Optimization

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MATHEMATICS OF OPERATIONS RESEARCH 2020年第3期45卷 966-992页

作者： Kim, Michael Jong Univ British Columbia Sauder Sch Business Vancouver BC V6T 1Z2 Canada

Sequential bayesian optimization constitutes an important and broad class of problems where model parameters are not known a priori but need to be learned over time using bayesian updating. It is known that the solution to these problems can in principle be obtained by solving the bayesian dynamic programming (BDP) equation. Although the BDP equation can be solved in certain special cases (for example, when posteriors have low-dimensional representations), solving this equation in general is computationally intractable and remains an open problem. A second unresolved issue with the BDP equation lies in its (rather generic) interpretation. Beyond the standard narrative of balancing immediate versus future costs-an interpretation common to all dynamic programs with or without learning-the BDP equation does not provide much insight into the underlying mechanism by which sequential bayesian optimization trades off between learning (exploration) and optimization (exploitation), the distinguishing feature of this problem class. The goal of this paper is to develop good approximations (with error bounds) to the BDP equation that help address the issues of computation and interpretation. To this end, we show how the BDP equation can be represented as a tractable single-stage optimization problem that trades off between a myopic term and a "variance regularization" term that measures the total solution variability over the remaining planning horizon. Intuitively, the myopic term can be regarded as a pure exploitation objective that ignores the impact of future learning, whereas the variance regularization term captures a pure exploration objective that only puts value on solutions that resolve statistical uncertainty. We develop quantitative error bounds for this representation and prove that the error tends to zero like o(n(-1)) almost surely in the number of stages n, which as a corollary, establishes strong consistency of the approximate solution.

关键词： bayesian dynamic programming variance regularization exploration-exploitation trade-off approximation error bounds strong consistency

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A bayesian model for multicriteria sorting problems

A I I E Transactions

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A I I E Transactions 2024年第7期56卷

作者： Canan Ulu Thomas S. Shively a McDonough School of Business Georgetown University Washington DC USA b McCombs School of Business University of Texas at Austin Austin TX USA

Decision makers are often interested in assigning alternatives to preference classes under multiple criteria instead of choosing the best alternative or ranking all the alternatives. Firms need to categorize suppliers based on performance, credit agencies need to classify customers according to their risks, and graduate programs need to decide who to admit. In this article, we develop an interactive bayesian algorithm to aid a decision maker (DM) with a multicriteria sorting problem by learning about her preferences and using that knowledge to sort alternatives. We assume the DM has a linear value function and value thresholds for preference classes. Our method specifies an informative prior distribution on the uncertain parameters. At each stage of the process, we compare the expected cost of stopping with the expected cost of continuing to consult the DM. If it is optimal to continue, we select an alternative to present to the DM and, given the DM’s response, we update the prior distribution using Bayes’ Theorem. The goal of the algorithm is to minimize expected total cost. We develop lower bounds on the optimal cost and study the performance of a heuristic policy that presents the DM alternatives with the highest expected cost of misplacement.

关键词： Multiple criteria sorting bayesian dynamic programming

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dynamic Inventory Optimization with Learning and Model Ambiguity

Dynamic Inventory Optimization with Learning and Model Ambig...

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作者： Ya-Tang Chuang University of Toronto

学位级别：博士

Classic inventory control problems typically assume that the demand distribution is known a priori. In reality, this assumption is not always satisfied. Motivated by this concern, the joint optimization of learn- ing and control is studied. We first consider the situation where parameters of the demand distribution are not known a priori, but need to be learned using right-censored sales data. A bayesian framework is adopted for demand learning and the corresponding control problem is analyzed via bayesian dynamic programming (BDP). Structural results of the optimal policy are established. In particular, we show that the BDP-optimal decisions can be expressed as the sum of a myopic-optimal decision plus a non- negative exploration boost which is proportional to the posterior index of dispersion of the unknown mean demand. This structure clearly articulates the manner in which the statistical learning and inven- tory control are jointly optimized. Next, we study an optimal inventory control problem in the presence of model miss-specification. In this problem, decision makers account for the miss-specification via solv- ing a worst-case problem against an adversary, "nature", who has the ability to alter the underlying demand distribution so as to minimize the decision maker's expected reward. We show that the decision maker's robust-optimal decisions are bounded above by the optimal solutions of the nominal model. This structural result clearly explains the trade-off between optimization and risk aversion. In the last chapter, we attempt to incorporate the elements of the bayesian and robust approaches, namely robust bayesian optimization. In particular, we are interested in how decision makers can remain robust to model uncertainty while also learning at the same time. We establish an analytical upper bound of the decision maker's optimal decisions, which can be expressed as the sum of a myopic-optimal decision plus an exploration boost and minus a risk aversion adj

关键词： bayesian dynamic programming bayesian learning inventory management

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Intelligent Model Learning Based on Variance for bayesian Reinforcement Learning 27

Intelligent Model Learning Based on Variance for Bayesian Re...

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27th IEEE International Conference on Tools with Artificial Intelligence (ICTAI)

作者： You, Shuhua Liu, Quan Zhang, Zongzhang Wang, Hui Zhang, Xiaofang Soochow Univ Sch Comp Sci & Technol Suzhou Peoples R China Minist Educ Key Lab Symbol Computat & Knowledge Engn Seoul South Korea

ISBN: (纸本)9781509001637

We consider a modular method to reinforcement learning that represents uncertainty of model parameters by maintaining probability distributions over them. The algorithm we call MBDP (model-based bayesian dynamic programming) can be decomposed into two parallel types of inference: model learning and policy learning. During learning a model, we update posterior distributions of a model over observations after taking an action in each state. During learning a policy, we solve MDPs by dynamic programming with greedy approximation to make an agent choose behaviors which maximize return under the estimated model. Furthermore, we propose a principled method which utilizes the variance of Dirichlet distributions for determining when to learn and relearn the model. We demonstrate that MBDP can find near optimal policies with high probability by sufficient model learning and experimental results show that MBDP performs better compared with current state-of-the-art methods in reinforcement learning.

关键词： reinforcement learning bayesian dynamic programming model learning policy learning Dirichlet distributions

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Intelligent Model Learning Based on Variance for bayesian Reinforcement Learning

Intelligent Model Learning Based on Variance for Bayesian Re...

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International Conference on Tools with Artificial Intelligence

作者： Shuhua You Quan Liu Zongzhang Zhang Hui Wang Xiaofang Zhang School of Computer Science and Technology Soochow University Suzhou China Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education

ISBN: (纸本)9781509001644

关键词： reinforcement learning bayesian dynamic programming model learning policy learning Dirichlet distributions

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dynamic traffic splitting to parallel wireless networks with partial information: A bayesian approach

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PERFORMANCE EVALUATION 2012年第1期69卷 41-52页

作者： Bhulai, S. Hoekstra, G. J. Bosman, J. W. van der Mei, R. D. Vrije Univ Amsterdam Dept Math Amsterdam Netherlands CWI Probabil & Stochast Networks NL-1009 AB Amsterdam Netherlands Thales Innovat Res & Technol Huizen Netherlands

Contemporary wireless networks are based on a wide range of different technologies providing overlapping coverage. This offers users a seamless integration of connectivity by allowing to switch between networks, and opens up a promising area for boosting the performance of wireless networks. Motivated by this, we consider a networking environment in which users are able to select between the available wireless networks to minimize the mean processing times for file downloads in the presence of background traffic. The information available to the user is only the total number of jobs in each network, rather than the per-network numbers of foreground and background jobs. This leads to a complex partial information decision problem which is the focus of this paper. We develop and evaluate a bayesian learning algorithm that optimally splits a stream of jobs that minimizes the expected sojourn time. The algorithm learns as the system operates and provides information at each decision and departure epoch. We evaluate the optimality of the partial information algorithm by comparing the performance of the algorithm with the "ideal" performance obtained by solving a Markov decision problem with full state information. To this end, we have conducted extensive experiments both numerically and in a simulation testbed with the full wireless protocol stack. The results show that the bayesian algorithm has close to optimal performance over a wide range of parameter values. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Traffic splitting Processor sharing Concurrent access Flow-level performance bayesian dynamic programming Partial information model

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