Optimal Decision Rules Research Articles

Optimal Stopping for Dynamic Recruitment Problem with Probabilistic Loss of Candidates

A problem that often arises in the recruitment process is that the recruitment firms face possible loss of candidates. The loss of candidates can induce a loss cost to firms which need to restart the recruitment process. In this article, we model the recruitment process as a discrete-time stochastic optimal stopping problem with a finite planning horizon, where candidates may be hired by other firms during the period of waiting for employment with a loss probability. An optimal decision rule is presented to maximize the benefit of the recruitment firm. This decision rule demonstrates that the threshold of direct employment will be reduced as the loss probability (or the loss cost) is increasing. In addition, we find that new applicants are hardly being directly employed when the remaining time to the deadline is very long. Finally, a numerical example is given to illustrate the effectiveness of the proposed decision rule.

Performance of Biomarker-Based Subgroup Selection Rules in Adaptive Enrichment Designs

In the planning stage of a clinical trial investigating a potentially targeted therapy, there is commonly a high degree of uncertainty whether the treatment is more efficient (or efficient only) in a subgroup compared to the whole population. Recently developed adaptive designs enable to allow for an efficacy assessment both for the whole population and a subgroup and to select the target population mid-course based on interim results (see, e.g., Wang et al., Pharm Stat 6:227–244, 2007, Brannath et al., Stat Med 28:1445–1463, 2009, Wang et al., Biom J 51:358–374, 2009, Jenkins et al., Pharm Stat 10:347–356, 2011, Friede et al., Stat Med 31:4309–4120, 2012). Frequently, predictive biomarkers are used in these trials for identifying patients more likely to benefit from a drug. We consider the situation that the selection of the patient population is based on a biomarker and where the diagnostics that evaluates the biomarker may be perfect, i.e., with 100 % sensitivity and specificity, or not. The performance of the applied subset selection rule is crucial for the overall characteristics of the design. In the setting of an adaptive enrichment design, we evaluate the properties of subgroup selection rules in terms of type I error rate and power by taking into account decision rules with a fixed ad hoc threshold and optimal decision rules developed for the situation of uncertain assumptions. In a simulation study, we demonstrate that designs with optimal decision rules are under certain assumptions more powerful as compared to those with ad hoc decision rules. Throughout the results, a strong impact of sensitivity and specificity of the biomarker on both type I error rate and power is observed.

Lower Cost Arrivals for Airlines: Optimal Policies for Managing Runway Operations under Optimized Profile Descent

Optimized profile descent (OPD) is an operating procedure being used by airlines to improve fuel and environmental efficiency during arrival operations at airports. In this study, we develop a stochastic dynamic programming framework to manage the sequencing and separation of flights during OPD operations. We find that simple calculation based measures can be used as optimal decision rules, and that the expected annual savings can be around $29 million if such implementations are adapted by major airports in the United States. Of these savings, $24 million are direct savings for airlines due to reduced fuel usage, corresponding to a potential savings of 10%–15% in fuel consumption over current practice. We also find that most of these savings will be due to the optimal spacing of OPD flights, as opposed to the optimal sequencing policies which contribute only 14% to the total savings. Hence, optimal spacing of OPD flights is much more important than optimal sequencing of these flights. We also conclude that there is not much difference between the environmental costs of fuel‐optimal and sustainably‐optimal spacing policies. Hence, an airline‐centric approach in improving OPD operations is likely to be not in conflict with objectives that might be prioritized by other stakeholders.

Optimal sample planning for system state analysis with partial data collection

We develop optimal and computationally practical procedures to minimize uncertainty concerning the presence of dangerous levels of a contaminant within a building when neither replication nor complete data collection is feasible. More generally, we address inference about the state of a finite system when the state is related to information collected over components of the system when only partial data collection is feasible. When there is no correlation between sample locations, a simple random sample or maximum a priori trait presence would provide optimal sampling choices. When complicated probability models describe trait manifestation, the need to collect only partial data precludes a full fitting of complicated models, and one must rely heavily on prior information naturally leading to a Bayesian approach. Herein, we introduce a computationally efficient heuristic algorithm to simultaneously find optimal sample locations and decision rule parameterizations and then show that it drastically outperforms both random selection and maximum a priori methods. Copyright © 2015 John Wiley & Sons, Ltd.

Decision Rules Acquisition for Inconsistent Disjunctive Set-Valued Ordered Decision Information Systems

Set-valued information system is an important formal framework for the development of decision support systems. We focus on the decision rules acquisition for the inconsistent disjunctive set-valued ordered decision information system in this paper. In order to derive optimal decision rules for an inconsistent disjunctive set-valued ordered decision information system, we define the concept of reduct of an object. By constructing the dominance discernibility function for an object, we compute reducts of the object via utilizing Boolean reasoning techniques, and then the corresponding optimal decision rules are induced. Finally, we discuss the certain reduct of the inconsistent disjunctive set-valued ordered decision information system, which can be used to simplify all certain decision rules as much as possible.

Assessing Traffic Accident Occurrence of Road Segments through an Optimized Decision Rule

Statistical models for estimating the safety status of transportation facilities have received great attention in the last two decades. These models also perform an important role in transportation safety planning as well as diagnoses of locations with high accident risks. However, the current methods largely rely on regression analyses and therefore they could ignore the multicollinearity characteristics of factors, which may provide additional information for enhancing the performance of forecasting models. This study seeks to develop more precise models for forecasting safety status as well as addressing the issue of multicollinearity of dataset. The proposed mathematical approach is indeed a discriminant analysis with respect to the goal of minimizing Bayes risks given multivariate distributions of factors. Based on this model, numerical analyses also perform with the application of a simulated dataset and an empirically observed dataset of traffic accidents in road segments. These examples essentially illustrate the process of Bayes risk minimization on predicating the safety status of road segments toward the objective of smallest misclassification rate. The paper finally concludes with a discussion of this methodology and several important avenues for future studies are also provided.

Future Costs, Fixed Healthcare Budgets, and the Decision Rules of Cost-Effectiveness Analysis.

Life-saving medical technologies result in additional demand for health care due to increased life expectancy. However, most economic evaluations do not include all medical costs that may result from this additional demand in health care and include only future costs of related illnesses. Although there has been much debate regarding the question to which extent future costs should be included from a societal perspective, the appropriate role of future medical costs in the widely adopted but more narrow healthcare perspective has been neglected. Using a theoretical model, we demonstrate that optimal decision rules for cost-effectiveness analyses assuming fixed healthcare budgets dictate that future costs of both related and unrelated medical care should be included. Practical relevance of including the costs of future unrelated medical care is illustrated using the example of transcatheter aortic valve implantation. Our findings suggest that guidelines should prescribe inclusion of these costs.

When is voting optimal?

We consider a framework where the optimal decision rule determining the collective choice depends in a simple way on the decision makers’ posterior probabilities of a particular state of nature. Nevertheless, voting is generally an inefficient way to make collective choices and this paper sheds light on the relationship between the optimal decision rule and voting mechanisms. The paper derives the conditions under which the optimal decision rule is equivalent to some well-known voting procedure (weighted supermajority, weighted majority, and simple majority) and shows that these are very stringent. The paper also considers more general voting procedures, as for example allowing for abstentions, and shows that the conditions for reaching the optimal collective choice remain very stringent.

Game option models of convertible bonds: Determinants of call policies

The interaction of bondholder's conversion and issuer's call in a convertible bond leads to a game option model between the two counterparties. Like typical pricing models for corporate debts, the fair value of a convertible bond is highly dependent on issuer's credit risk, tax benefits of coupons and other structural features. The convertible bond pricing models in the literature can be categorized into two approaches: (i) structural firm value models that incorporate dilution effect in the issuer firm's corporate structure upon conversion; and (ii) reduced form models that price convertible bonds based on calibration with market liquid instruments. We review and comment on various pricing formulations of convertible bonds and effectiveness of different numerical schemes for solving the associated optimal stopping problems. Empirical studies on issuers' optimal call policies have revealed discrepancies between the optimal decision rule derived from pricing models and actual market practices. The more refined model formulation of a convertible bond should include corporate finance considerations in the determination of the optimal call policies.

A Minimax Framework for Classification with Applications to Images and High Dimensional Data.

This paper introduces a minimax framework for multiclass classification, which is applicable to general data including, in particular, imagery and other types of high-dimensional data. The framework consists of estimating a representation model that minimizes the fitting errors under a class of distortions of interest to an application, and deriving subsequently categorical information based on the estimated model. A variety of commonly used regression models, including lasso, elastic net and ridge regression, can be regarded as special cases that correspond to specific classes of distortions. Optimal decision rules are derived for this classification framework. By using kernel techniques the framework can account for nonlinearity in the input space. To demonstrate the power of the framework we consider a class of signal-dependent distortions and build a new family of classifiers as new special cases. This family of new methods-minimax classification with generalized multiplicative distortions-often outperforms the state-of-the-art classification methods such as the support vector machine in accuracy. Extensive experimental results on images, gene expressions and other types of data verify the effectiveness of the proposed framework.

Asymptotically Optimal Decision Rules for Joint Detection and Source Coding

The problem of joint detection and lossless source coding is considered. We derive asymptotically optimal decision rules for deciding whether or not a sequence of observations has emerged from a desired information source, and to compress it if has. In particular, our decision rules asymptotically minimize the cost of compression in the case that the data have been classified as desirable, subject to given constraints on the two kinds of the probability of error. In another version of this performance criterion, the constraint on the false alarm probability is replaced by a constraint on the cost of compression in the false alarm event. We then analyze the asymptotic performance of these decision rules. We also derive universal decision rules for the case where the underlying sources (under either hypothesis or both) are unknown, and training sequences from each source may or may not be available. Finally, we discuss how our framework can be extended in several directions.

Optimal Revenue Maximizing Mechanisms in Common-Value Position Auctions

We study the optimal mechanism in position auctions in a common-value setting where only ordinal information about the advertisers is posted and auctioneer revenue depends on consumer belief about ad qualities. We show that when bidder valuations are correlated, existence of a simple non-ironed optimal mechanism requires a stronger condition that the usual increasing virtual valuation assumption. With fixed number of positions, the corresponding optimal decision rule (among all mixed and pure strategies) is to allocate the ad positions to advertisers in decreasing order of quality. More importantly, when the search engine also chooses the number of ads to post, ignoring the consumer belief endogeneity will lead to posting too many ads compared to what maximizes the search engine revenue. We also show that when only one ad position is available, the optimal allocation rule uses a reserve price which is higher than what is implied by Myerson 1981 seminal work. Finally, we characterize the optimal mechanism when cardinal information about advertiser quality is posted, and we provide results on how search engine revenue compares under the two regimes.

Interactive model building for Q-learning.

Evidence-based rules for optimal treatment allocation are key components in the quest for efficient, effective health care delivery. Q-learning, an approximate dynamic programming algorithm, is a popular method for estimating optimal sequential decision rules from data. Q-learning requires the modeling of nonsmooth, nonmonotone transformations of the data, complicating the search for adequately expressive, yet parsimonious, statistical models. The default Q-learning working model is multiple linear regression, which is not only provably misspecified under most data-generating models, but also results in nonregular regression estimators, complicating inference. We propose an alternative strategy for estimating optimal sequential decision rules for which the requisite statistical modeling does not depend on nonsmooth, nonmonotone transformed data, does not result in nonregular regression estimators, is consistent under a broader array of data-generation models than Q-learning, results in estimated sequential decision rules that have better sampling properties, and is amenable to established statistical approaches for exploratory data analysis, model building, and validation. We derive the new method, IQ-learning, via an interchange in the order of certain steps in Q-learning. In simulated experiments IQ-learning improves on Q-learning in terms of integrated mean squared error and power. The method is illustrated using data from a study of major depressive disorder.

Adaptive Digital Equalization in Optical Coherent Receivers With Stokes-Space Update Algorithm

In this paper, we describe a novel update algorithm for the filter coefficients of the adaptive digital equalizer in coherent receivers, which is based on error signals evaluated in Stokes space and is insensitive to both phase-noise and frequency-offset. We also introduce an optimized decision rule in the Stokes space, which takes into account the exact statistics of noise and yields a performance improvement with respect to the minimum distance decision criterion. We compare the performance of the new algorithm to the standard constant-modulus algorithm (CMA) for polarization-multiplexed 16QAM modulation, achieving similar performance in the absence of phase noise, with comparable complexity. Differently from CMA, the proposed Stokes-space algorithm allows us to remove the phase offset between polarizations, thus enabling the use of a joint carrier-phase estimation algorithm on both polarizations, which in turns yields a nearly doubled phase noise tolerance.

Optimal Information-Theoretic Wireless Location Verification

We develop a new location verification system (LVS) focused on network-based intelligent transport systems (ITSs) and vehicular ad hoc networks (VANETs). The system that we develop is based on an information-theoretic framework in which the mutual information between the system's input and output data is maximized. Our system takes as inputs a user's claimed location and base station (BS) received signal strength (RSS) measurements to form an optimal decision rule on the legitimacy of the claimed location. The scenario that we consider is where a noncolluding malicious user alters his transmit power in an attempt to fool the LVS. We develop a practical threat model for this attack scenario and investigate the performance of the LVS in terms of its input/output mutual information. We show how our LVS decision rule can be straightforwardly implemented with a performance that delivers near optimality under realistic threat conditions. The practical advantages that our new information-theoretic scheme delivers, relative to more traditional Bayesian verification frameworks, are discussed.

Analysis of a training sample and classification in one recognition model

A problem of classification by precedents in partial precedence models is considered. An algorithm is presented for searching for maximum logical regularities of a class (LRCs) for consistent training tables. A two-level solution scheme of a problem is proposed for finding an optimal decision rule. First, LRCs are obtained by training data, and a mapping of the initial feature descriptions of objects into a space of points of a discrete unit cube is constructed. The objects of the training sample can be divided by a hyperplane in the latter space. It is suggested that a linear decision rule in the latter space that provides the maximum gap, similar to the support vector method, should be used as the decision rule.

Optimal Sequential Channel Estimation and Probing for Multiband Cognitive Radio Systems

In this paper, we propose a novel sequential channel estimation approach for multiband cognitive radio (CR) systems. We introduce a general model and test two scenarios of practical interest. The two scenarios are as follows: 1) CR users optimally estimate all the available bands; and 2) CR users find one good channel with a large gain. In particular, we use a sequential search in which the CR users estimate the available channels one by one. During the search, the CR users determine whether to terminate the current channel estimation process and switch to the next channel based on the training symbols received so far. Our objective is to design a switch function, an estimator, and a stopping rule that minimize a combination of estimation time and error. For the multiband estimation scenario, we show that the optimal rule is to find the optimal number of symbols required for each channel in a joint optimization problem. For the good channel search problem, we show that the optimal decision rules that minimize a properly chosen cost function have a simple structure. In particular, both the termination and switching rules are threshold based. Numerical results are provided to illustrate the effectiveness of the proposed algorithms.

An Iterative Decision Rule to minimize cost of Acceptance Sampling Plan in Machine Replacement Problem

In this paper, an optimal iterative decision rule for minimizing total cost in designing a sampling plan for machine replacement problem is presented using the approach of dynamic programming and Bayesian inferences. Cost of replacing the machine and cost of produced defectives have been considered in model. Concept of control threshold policy has been applied for decision making. If the probability of producing a defective was more than a control threshold then the machine is replaced otherwise its performenace will be accepted and continues its production. A numerical example along with sensitivity analysis is performed to show the application of proposed methodology.

Energy Storage and Renewable Energy

I consider an economy with fossil fuel and renewable energy and energy storage, and search for the conditions that lead to welfare improvements when energy is stored. I then solve for the optimal decision rule and analyze the long-run tendencies of the economy-energy variables. The findings are threefold. First, energy storage is fostered by the convexity of the marginal utility (prudence), the marginal cost function for fossil fuel energy, and the degree of intermittency. Second, considering a low penetration of renewable energy to the power grid, energy storage is not welfare improving if the fossil fuel energy cost function is linear. Third, energy storage creates an added value to renewable energy investments when actively used. By showing the in uence that energy storage can have on energy generation and investment decisions, I hope that the current work can be in uential in a more generous treatment of energy supply in future energy-economy-climate models.

Erratum to: Risk-averse dynamic programming for Markov decision processes

The Original publication of the article suffers from a technical inaccuracy associated with verification of measurability of the optimal decision rules. This erratum corrects the gap, by introducing additional conditions of joint continuity and measurability of the functions and multifunctions involved. We use the terminology and notation of [4]. A controlled kernel Q is setwise (strongly) continuous, if for all bounded measurable functions v on X , and all convergent sequences {(xk, uk)}, k = 1, 2, . . . , one has