Optimal Rule Research Articles

A fixed point approach for computing actuarially fair Pareto optimal risk-sharing rules

A fixed point approach for computing actuarially fair Pareto optimal risk-sharing rules

Breaking the Metric Voting Distortion Barrier

We consider the following well-studied problem of metric distortion in social choice. Suppose that we have an election with n voters and m candidates located in a shared metric space. We would like to design a voting rule that chooses a candidate whose average distance to the voters is small. However, instead of having direct access to the distances in the metric space, the voting rule obtains, from each voter, a ranked list of the candidates in order of distance. Can we design a rule that, regardless of the election instance and underlying metric space, chooses a candidate whose cost differs from the true optimum by only a small factor (known as the distortion )? A long line of work culminated in finding optimal deterministic voting rules with metric distortion 3. However, for randomized voting rules, there is still a significant gap in our understanding: even though the best lower bound is substantially lower at 2.112, the best upper bound is still 3, which is attained even by simple rules such as Random Dictatorship. Finding a randomized rule that guarantees distortion 3 - ɛ for some constant ɛ has been a major challenge in computational social choice, as prevalent approaches to designing voting rules are known to be insufficient. In particular, such a voting rule must use information beyond aggregate comparisons between pairs of candidates, and cannot only assign positive probability to candidates that are voters’ top choices. In this work, we give a rule that guarantees distortion less than 2.753. To do so, we study a handful of voting rules that are new to the problem. One is Maximal Lotteries , a rule based on the Nash equilibrium of a natural zero-sum game that dates back to the 1960s. The others are novel rules that can be thought of as hybrids of Random Dictatorship and the Copeland rule. None of these rules can beat distortion 3 alone; however, a careful randomization between Maximal Lotteries and any of the novel rules can.

A Dynare toolbox for social learning expectations

Social learning (SL) is a behavioral model in which expectations and the resulting aggregate dynamics stem from the interactions of a large number of heterogeneous agents. Nonetheless, this framework has so far lacked a parsimonious development with a general-solution method. This paper bridges this gap and introduces a Dynare toolbox to solve any linear state-space model with SL expectations, opening up a wide range of potential applications. As an illustration, optimal monetary policy rules are studied in a microfounded New Keynesian (NK) model under SL and rational expectations (RE).

New error estimates for the conjugate gradient method

The conjugate gradient method is the default iterative method for the solution of linear systems of equations with a large symmetric positive definite matrix A. The development of techniques for estimating the norm of the error in iterates computed by this method has received considerable attention. Available methods for bracketing the A-norm of the error evaluate pairs of Gauss and Gauss-Radau quadrature rules to determine lower and upper bounds. The latter methods require a user to allocate a node (the Radau node) between the origin and the smallest eigenvalue of the system matrix. The determination of such a node generally demands further computations to estimate the location of the smallest eigenvalue. An approach that avoids the need for a lower bound of the smallest eigenvalue is to replace the Gauss-Radau quadrature rule by an anti-Gauss rule; see, e.g., Golub and Meurant (1997), Golub and Meurant (2010), Golub and Strakoš (1994), Meurant (1997), Meurant (1999). However, this approach may sometimes yield inaccurate error norm estimates. This paper proposes the use of pairs of Gauss and associated optimal averaged Gauss quadrature rules to estimate the A-norm of the error in iterates determined by the conjugate gradient method.

Adaptive rewiring: a general principle for neural network development.

The nervous system, especially the human brain, is characterized by its highly complex network topology. The neurodevelopment of some of its features has been described in terms of dynamic optimization rules. We discuss the principle of adaptive rewiring, i.e., the dynamic reorganization of a network according to the intensity of internal signal communication as measured by synchronization or diffusion, and its recent generalization for applications in directed networks. These have extended the principle of adaptive rewiring from highly oversimplified networks to more neurally plausible ones. Adaptive rewiring captures all the key features of the complex brain topology: it transforms initially random or regular networks into networks with a modular small-world structure and a rich-club core. This effect is specific in the sense that it can be tailored to computational needs, robust in the sense that it does not depend on a critical regime, and flexible in the sense that parametric variation generates a range of variant network configurations. Extreme variant networks can be associated at macroscopic level with disorders such as schizophrenia, autism, and dyslexia, and suggest a relationship between dyslexia and creativity. Adaptive rewiring cooperates with network growth and interacts constructively with spatial organization principles in the formation of topographically distinct modules and structures such as ganglia and chains. At the mesoscopic level, adaptive rewiring enables the development of functional architectures, such as convergent-divergent units, and sheds light on the early development of divergence and convergence in, for example, the visual system. Finally, we discuss future prospects for the principle of adaptive rewiring.

Optimizing Allocation to Telehealth and In-Person Prolonged Exposure for Women Veterans with Military Sexual Trauma: A Precision Medicine Approach

Military sexual trauma-related post-traumatic stress disorder (PTSD) is highly prevalent and costly among women veterans, making the need for effective and accessible treatment of critical importance. Access to care is a key mechanism of mental health disparities and might affect differential response to treatment. The goal of this study was to estimate an individualized treatment rule based on readily available individual characteristics related to access to care to optimize allocation to in-person vs. telehealth delivery of prolonged exposure for PTSD in military sexual trauma survivors. The following variables were used as prescriptive factors: age, race, disability status, socioeconomic status, rural vs. urban status, and baseline PTSD level. The rule was estimated using a machine-learning approach, Outcome Weighted Learning. The estimated optimal rule outperformed a one-size-fits-all rule where everyone is universally assigned to telehealth; it led to markedly lower mean PTSD levels following 6 months from treatment (Vdopt − VTelehealth = −14.55, 95% CI: −27.24, −1.86). However, the rule did not significantly discriminate for in-person therapy (Vdopt − VIn-person = −11.86, 95% CI: −25.83, 2.12). Upon further validation with larger and more diverse samples, such a rule may be applied in practice settings to aid clinical decision-making and personalization of treatment assignment.

Discounted fully probabilistic design of decision rules

Axiomatic fully probabilistic design (FPD) of optimal decision rules strictly extends the decision making (DM) theory represented by Markov decision processes (MDP). This means that any MDP task can be approximated by an explicitly found FPD task whereas many FPD tasks have no MDP equivalent. MDP and FPD model the closed loop — the coupling of an agent and its environment — via a joint probability density (pd) relating the involved random variables, referred to as behaviour. Unlike MDP, FPD quantifies agent's aims and constraints by an ideal pd. The ideal pd is high on the desired behaviours, small on undesired behaviours and zero on forbidden ones. FPD selects the optimal decision rules as the minimiser of Kullback-Leibler's divergence of the closed-loop-modelling pd to its ideal twin. The proximity measure choice follows from the FPD axiomatics.MDP minimises the expected total loss, which is usually the sum of discounted partial losses. The discounting reflects the decreasing importance of future losses. It also diminishes the influence of errors caused by:▪ the imperfection of the employed environment model;▪ roughly-expressed aims;▪ the approximate learning and decision-rules design.The established FPD cannot currently account for these important features. The paper elaborates the missing discounted version of FPD. This non-trivial filling of the gap in FPD also employs an extension of dynamic programming, which is of an independent interest.

In-situ Reconstruction of Catalyst in Electrocatalysis.

Reconstruction of catalysts is now well recognized as a common phenomenon in electrocatalysis. As the reconstructed structure may promote or hamper the electrochemical performance, how to achieve the designed active surface for highly enhanced catalytic activity through the reconstruction needs to be carefully investigated. In this review, the genesis and electrochemical effects of reconstruction in various electrochemical catalytic processes, such as hydrogen evolution reaction (HER), oxygen evolution reaction (OER), carbon dioxide reduction reaction (CO2RR), and nitrate reduction reaction (NO3RR) are first described. Then, the strategies for optimizing the reconstruction, such as valence states control, active phase retention, phase evolution engineering, and surface poisoning prevention are comprehensively discussed. Finally, the general rules of reconstruction optimization are summarized and give perspectives for future study. It is believed that the review shall provide deep insights into electrocatalytic mechanisms and guide the design of pre-catalysts with highly improved activity.

A model predictive control algorithm for double-hormone artificial pancreas based on optimal three-branch decision switching rules

At present, double-hormone artificial pancreas is a hotspot in the research of regulating blood glucose level; however, there are few studies on switching mechanism of the subsystems for double-hormone artificial pancreas, and most of the existing studies rely on the prior knowledge of application fields. A model predictive control algorithm for double-hormone artificial pancreas based on optimal three-branch decision switching rules is proposed to solve this problem. The blood glucose controllers of insulin subsystems, zero infusion subsystems, and glucagon subsystems are constructed using model predictive control algorithms. Then, using the three-branch decision theory, switching rules between the three subsystems are designed, and the optimal switching threshold value can be solved by the mixed fruit fly algorithm. The algorithm can realize automatic acquisition of the threshold in the three-branch decision switching rules and gets rid of the dependence on the prior knowledge in the field of diabetes research. By the end, the UVa simulation platform is used to conduct experiments on 33 virtual patients and the simulation results verify that the proposed algorithm can control blood glucose effectively within the normal range and can achieve satisfactory performabce in error of tracking set point, safety, operation efficiency, group control quality, and system stability.

Development and validation of a relatively accurate gastric cancer high-risk group screening scoring system in urban residents.

Our study aimed to develop a relatively accurate gastric cancer (GC) screening score system for urban residents and to validate the screening efficacy. The present study included a derivation cohort (n = 3406) and a validation cohort (n = 868) of urban residents. Applying the full-stack engineering intelligent system platform of Hualian Health Big Data of Shandong University, the clinical physical examination data of subjects were collected. Univariate and multivariate analyses were used to identify risk factors for GC, and subsequently, an optimal prediction rule was established to create three distinct scoring systems. In the GC-risk scoring system I, age, plateletocrit (PCT), carcinoembryonic antigen (CEA), glucose, albumin, creatinine were independent risk factors of GC, with scores ranging from 0 to 28 and optimal cut-off was 15.5. The second scoring system consisted of age, PCT, RDW-CV, CEA, glucose, albumin, and creatinine, with scores ranging from 0 to 31. The optimal cut-off point was determined to be 15.5. The scoring system III comprise of age, sex, PCT, RDW CV, CEA, glucose, with scores ranging from 0 to 21 and optimal cut-off was 10.5. All three scoring systems demonstrated excellent discrimination for GC, achieving an AUC of 0.884, 0.89, and 0.876, respectively. In external validation, the AUC values were 0.654, 0.658, and 0.714. Notably, the GC-risk scoring system III exhibited the highest screening efficiency. Urban residents benefited from the effective and verified GC-risk scoring systems, which demonstrated excellent performance in identifying individuals with an elevated risk of GC.

Lost jobs, new jobs and optimal tax-transfer reforms

AbstractAutomation and globalisation imply deep changes in the labour market. An important policy issue is whether and how the tax-transfer rules should be reformed to help coping with those changes. While the prevailing response has consisted of more sophisticated designs of mean-testing and targeting, we also witness an increasing interest in policies inspired by simplicity. Using a combination of behavioural microsimulation and numerical optimization, we look for a (social welfare) optimal tax-transfer rule within a flexible class where total household disposable income is a 4th-degree polynomial in total household taxable income plus a constant. We use a model of household labour supply that makes it possible to account for equilibrium constraints and evaluate the effects of changes of the labour demand scenario. Beside the (observed) Status quo scenario, we consider two alternative stylized cases: the “Jobless” scenario and the “Polarised” scenario. We simulate and compare the social welfare attained by the current tax-transfer rules under the three scenarios and the social welfare attained by the different polynomial optimal tax-transfer rules identified in each scenario. We present results using the 2015 EU-SILC data sets for France, Germany, Italy and Luxembourg. The polynomial optimal rules are social welfare superior to the current ones in all the countries and under all the scenarios and—with the exception of Luxembourg—are close to a Universal Basic Income (or a Negative Income Tax) plus a not-too progressive tax rule (close to a Flat Tax).

Aggregation-Decomposition Coupling Drawdown Rule and Progressive Optimal Algorithm for Optimization of Large-Scale Reservoirs

Aggregation-Decomposition Coupling Drawdown Rule and Progressive Optimal Algorithm for Optimization of Large-Scale Reservoirs

Towards data auctions with externalities

The design of data markets has gained importance as firms increasingly use machine learning models fueled by externally acquired training data. A key consideration is the externalities firms face when data, though inherently freely replicable, is allocated to competing firms. In this setting, we demonstrate that a data seller's optimal revenue increases as firms can pay to prevent allocations to others. To do so, we first reduce the combinatorial problem of allocating and pricing multiple datasets to the auction of a single digital good by modeling utility for data through the increase in prediction accuracy it provides. We then derive welfare and revenue maximizing mechanisms, highlighting how the form of firms' private information – whether the externalities one exerts on others is known, or vice-versa – affects the resulting structures. In all cases, under appropriate assumptions, the optimal allocation rule is a single threshold per firm, where either all data is allocated or none is.

Heat pump and thermal energy storage: Influences of photovoltaic, the control strategy, and price assumptions on the optimal design

Combining heat pump, thermal energy storage, and photovoltaic is a common option to increase renewable energy usage in building energy systems. While research finds that optimal system design depends on the control, design guidelines neglect an influence of (1) photovoltaic, (2) the supervisory control, and (3) prices assumptions on the design of heat pump and thermal energy storage. We analyze how these influences may impact the optimal design. To analyze possible impacts, a pre-screening approach is used to identify relevant model input combinations with a potentially high influence on the optimal design. Applying a simulation-based design optimization with a detailed building energy system model, we optimize three cases: no photovoltaic, no supervisory control, and a state-of-the-art supervisory control. Results indicate that cost optimal design does not change with photovoltaic or the supervisory control, but heat pump size increases with higher electricity prices. For the storage, maximizing the size achieves high self-sufficiency degrees, but cost optimal design changes only for selected price assumptions. Overall, we find that neglecting photovoltaic and surplus control in the system design is a valid assumption. However, price assumptions should be included to allow simple but optimal design rules in current guidelines.

Assessing the Recreational Fishers and their Catches based on Social Media Platforms: Privacy and Ethical Data Analysis Considerations

Social Media (SM) can offer insights to track recreational Fishing (Rf); Many Limitations Hinder Its Practical Application. The proportion and characteristics of RFs that share their catches remain unidentified. The objective was to enhance the surveillance abilities of RF by utilizing SM information. This study focuses on the sharing economy information transmission, network optimization of SM platforms, and privacy protection issues during data transmission. The study starts with the data transmission characteristics in SM platforms, analyzes the data ethics in SM information transmission from the perspectives of natural and economic data attributes, and then focuses on the privacy protection principles in network information transmission. Then, a privacy protection scheme based on a locally sensitive hash algorithm is constructed, and finally, an information transmission scheme and method optimization based on a network optimization module are proposed. The research gathered data using physical (face-to-face) surveys and digital (email) surveys to define marine RF that post catches on online platforms (“sharers”), together with additional demographic and fishing data. A comparative analysis was conducted on the computational convergence and accuracy of different privacy protection methods, and the optimal rule framework for data privacy protection was discussed. The observation results show that the efficiency of information transmission using the Minhash-SSNR method is slightly inferior to that using the OSNR-SSNR method. Minhash technology is based on a similarity comparison of dimensionality-reduced data. This leads to data causing the initially highly similar two sets of lists to be misjudged as not having enough similarity, thereby reducing some potential information dissemination opportunities and affecting the efficacy of information transmission. It can be seen that the Minhash-SSNR strategy can effectively send information to nodes with high similarity, preventing excessive information duplication within the system. Although the Minhash-SSNR strategy has a certain degree of decline in information transmission efficiency, it accounts for only about 5% compared to the OSNR-SSNR strategy, ensuring the essential operational stability of SM opportunity networks without significant impact. With few learning and training times, the network information transmission optimization module proposed in this study quickly achieved a lower exponential error. As the number of training sessions gradually increases, the exponential error of the network information transmission optimization module in this study is small, and the prediction accuracy of the method is high. RFs who captured a prize, iconic, or symbolic species tended to discuss their catches more. This research signifies significant progress in incorporating SM information to oversee RFs.

Nominal GDP growth targeting vs. Taylor rules in a model with financial frictions

Nominal GDP growth targeting has gained favor over the last few decades in monetary policy literature (e.g., Ireland 2020; Garín et al. 2016; Beckworth and Hendrickson 2020). Calibrated, small-scale New Keynesian DSGE models have supported the proposition that nominal GDP growth (NGDP growth) rate targeting will improve welfare as compared with alternative strategies such as inflation targeting and Taylor rules with standard parameter settings. This paper examines that proposition in the context of a medium-scale New Keynesian model having a financial sector with frictions. In that model, NGDP growth rate targeting does poorly as compared with the Optimal Taylor rule and a wide range of Taylor rule settings leading up to the Optimal (representative agent utility maximizing) Taylor rule. The presence of the financial sector reveals that not only is NGDP growth rate targeting the least successful among the alternative targets and rules in creating welfare in this model; NGDP growth rate targeting also creates dramatically higher volatility of the policy rate and most financial variables.

Pandemic shocks and macroprudential policy

Abstract We introduce an extended borrower–saver DSGE (Dynamic Stochastic General Equilibrium) model, where classifications of occupations are split further into two subcategories, according to whether their occupation is directly “affected” by a pandemic shock. We find that, contrary to the standard literature, during a pandemic shock an increase in the Loan-to-Value (LTV) ratio can increase social welfare and make all four agent types (borrowers affected, borrowers non-affected, savers affected, and savers non-affected) better off. Countercyclical optimal LTV rules are shown to increase social welfare, with savers gaining at the expense of borrowers, including those mostly affected by the pandemic. An interest rate mortgage subsidy to those worst affected (“affected” mortgage borrowers), in coordination with stricter monetary and LTV policy, are shown to increase both social welfare and the welfare of borrowers and savers affected by the pandemic.

Stochastic Resource Allocation Problems: Minmax and Maxmin Solutions

Problem definition: Min-max or max-min objective criteria naturally arise in many resource allocation applications, especially when the attendant goal involves distribution of a limited resource across multiple subsystems, locations, or activities. Each has a different consumption rate of the resource. In this setting, the decision maker is interested in optimizing the system performance, which can be measured in terms of the smallest or largest order statistic across subsystems. Examples include the allocation of health resources to maximize the first runout time or to minimize the maximum delay. Methodology/results: In the literature, there are no unified theoretical and computational results on the optimal allocations for these problems. Thus, in this paper, we develop key theoretical properties of the attendant stochastic resource allocation problems, providing a technical condition for the objective functions to have favorable properties, upon which we derive novel optimal allocation rules with clear interpretation. Managerial implications: The proportional allocation rule can be interpreted as a robust solution when the full distribution of the interarrival time is unknown. It generally has poor performance, especially when the resource consumption rates vary across locations, which happens regularly in practice. Our allocation rule is exact and should be used for the allocation of scarce resources—that is, when the number of resources per location is limited, which is often encountered in healthcare settings.

Adaptive Operating Rules for Flood Control of a Multi-Purpose Reservoir

Almost all multipurpose reservoirs in Romania were put into operation 30–50 years ago or even earlier. Meanwhile, a large volume of hydrologic data has been collected, and the initial design flood should be reconsidered. Consequently, the operating rules of flow control structures (bottom gates and weir gates) should be re-examined, mainly for medium and low-frequency floods. The design flood is not unique, being characterized by different shapes and time to peak, which has consequences for flood mitigation rules. Identifying the critical design flood is an important preliminary step, although it is usually neglected in flood management. Simulating the operation of the Stânca–Costești reservoir on the Prut River, it was found that the design flood corresponding to the maximum value of the compactness coefficient is the most difficult to mitigate considering the specific conditions of the dam and the reservoir: the prescribed conservation level in the reservoir, and the design flood volume of medium and rare floods that far exceeds the flood control volume. These conditions can jeopardize both dam safety and downstream flood protection. The main steps of the proposed approach are as follows: (1) developing the hydraulic model; (2) statistical processing of the registered floods and defining critical design floods for different AEPs (Annual Exceedance Probabilities); (3) deriving optimal operation rules based on a simulation-optimization model; (4) implementing real-time adaptive operation of the mechanical outlets; and (5) critically assessing the operating rules after the event. Based on the hydrological forecast, if necessary, new outlets are put into operation while keeping the ones already activated. Based on the hydrological forecast and properly operated, the safety of the Stânca–Costești dam is guaranteed even in the event of a 0.1% CC (Climate Change) flood. However, for floods greater than 1% magnitude, the carrying capacity of the downstream riverbed is exceeded. The main gaps addressed in this paper are the following: (1) the establishment of critical design floods, and (2) the adaptive operating rules of outlet devices aimed at optimizing flood control results, using short-term flood forecasts.

Unconventional policies in state-dependent liquidity traps

We characterize optimal unconventional monetary and fiscal-financial policies against supply- and demand-driven liquidity traps within a tractable New Keynesian model featuring a cash-in-advance constraint and a monetary policy cost channel. Deposit subsidies circumvent the inflation-output trade-off arising from stagflationary shocks and supply-driven liquidity traps by enabling negative nominal interest rates. Additionally, deposit taxes facilitate modest interest rate hikes to escape demand-driven deflationary traps. Notably, discretionary and commitment policies with deposit taxes / subsidies deliver virtually equivalent welfare gains, rendering time-inconsistent forward guidance schedules unnecessary. We also derive robust and implementable optimal policy rules when the sources of shocks are unknown.