Median Predictive Cost of Error with an Asymmetric Cost Function

This paper presents a Bayesian approach for the optimal control of a machine that can experience setup errors assuming an asymmetric off-target cost function. It is assumed that the setup error cannot be observed directly due to presence of measurement and part-to-part errors, and it is further assumed that the variance of this error is not known a priori. The setup error can be compensated by performing sequential adjustments of the process mean based on observations of the parts produced. It is shown how the proposed method converges to the optimal (known variance) trajectory, recovering from a possibly biased initial variance estimate. Simulations results are presented to show the small sample behavior of the proposed method under two types of asymmetric off-target cost functions: a constant asymmetric and a quadratic asymmetric cost function.

Probabilistic retrieval models usually rank documents based on a scalar quantity. However, such models lack any estimate for the uncertainty associated with a document’s rank. Further, such models seldom have an explicit utility (or cost) that is optimized when ranking documents. To address these issues, we take a Bayesian perspective that explicitly considers the uncertainty associated with the estimation of the probability of relevance, and propose an asymmetric cost function for document ranking. Our cost function has the advantage of adjusting the risk in document retrieval via a single parameter for any probabilistic retrieval model. We use the logit model to transform the document posterior distribution with probability space [0,1] into a normal distribution with variable space ( − ∞ , + ∞ ). We apply our risk adjustment approach to a language modelling framework for risk adjustable document ranking. Our experimental results show that our risk-aware model can significantly improve the performance of language models, both with and without background smoothing. When our method is applied to a language model without background smoothing, it can perform as well as the Dirichlet smoothing approach.

The high time needed to reconfigure cloud resources in Network Function Virtualization network environments has led to the proposal of solutions in which a prediction based-resource allocation is performed. All of them are based on traffic or needed resource prediction with the minimization of symmetric loss functions like Mean Squared Error. When inevitable prediction errors are made, the prediction methodologies are not able to differently weigh positive and negative prediction errors that could impact the total network cost. In fact if the predicted traffic is higher than the real one then an over allocation cost, referred to as over-provisioning cost, will be paid by the network operator; conversely, in the opposite case, Quality of Service degradation cost, referred to as under-provisioning cost, will be due to compensate the users because of the resource under allocation. In this paper we propose and investigate a resource allocation strategy based on a Long Short Term Memory algorithm in which the training operation is based on the minimization of an asymmetric cost function that differently weighs the positive and negative prediction errors and the corresponding over-provisioning and under-provisioning costs. In a typical traffic and network scenario, the proposed solution allows for a cost saving by 30% with respect to the case of solution with symmetric cost function.

Feedforward–feedback multiple predictive controllers for glucose regulation in type 1 diabetes

The evolutionary game dynamics of social tolerance among heterogeneous economic agents have been discussed in an economic interaction model with asymmetric social cost functions, where the individual cost depends only on the share of intolerant people in the opposite group. We show that, very different from the symmetric function case studied previously , economic interactions between individuals in a society with asymmetric social cost functions can be exactly solved in phase plane, and rich behaviours can be revealed by using algebraic approach. Our contribution consists in offering the explicit formula of evolutionary trajectories in the phase plane for the first time. The property of equilibrium is shown to be closely related to the group populations. Based on the explicit formula in the phase plane, the equilibriums of the evolutionary dynamics can be easily identified, and the evolutionary trajectory can be exactly analysed. We also show that the explicit solutions obtained would be especially suited to effective control of the evolutionary dynamics of social tolerance. The necessary and sufficient conditions of the full tolerance equilibrium under asymmetric social cost function are also discussed, which provides guidance and reference to set policies and development strategy of social tolerance.

Label embedding (LE) is an important family of multi-label classification algorithms that digest the label information jointly for better performance. Different real-world applications evaluate performance by different cost functions of interest. Current LE algorithms often aim to optimize one specific cost function, but they can suffer from bad performance with respect to other cost functions. In this paper, we resolve the performance issue by proposing a novel cost-sensitive LE algorithm that takes the cost function of interest into account. The proposed algorithm, cost-sensitive label embedding with multidimensional scaling (CLEMS), approximates the cost information with the distances of the embedded vectors by using the classic multidimensional scaling approach for manifold learning. CLEMS is able to deal with both symmetric and asymmetric cost functions, and effectively makes cost-sensitive decisions by nearest-neighbor decoding within the embedded vectors. We derive theoretical results that justify how CLEMS achieves the desired cost-sensitivity. Furthermore, extensive experimental results demonstrate that CLEMS is significantly better than a wide spectrum of existing LE algorithms and state-of-the-art cost-sensitive algorithms across different cost functions.

By deriving an upper bound of the so-called 'price of anarchy', this paper analyses the efficiency of oligopolistic games in networks with non-separable and asymmetric cost functions, splittable flows and fixed demands. The new bound is determined by the optimal objective function values of some optimisation problems. In particular, for some special cases, the bound turns out to be explicit in the sense that it is representable explicitly by the number of players, and the constants measuring the degree of asymmetry and non-linearity of the cost function. Copyright © 2010 Inderscience Enterprises Ltd.

This study investigates game-based PIMFY models for analyzing the interactions among grant-seeking local governments and the central government. From these models we could find the following. The effective prize dissipation ratio in each local government multiplied by its population is the same in two competing local governments – in the first case, of equal valuation and equal cost functions, and in the second case, of equal valuation and asymmetric cost functions. If the central government uses a policy to strengthen cost advantage in favor of the low cost local government, then economic inefficiency in terms of aggregate outlays will decrease. If there a binding constraint on outlay by local government 1 is assigned by the central government, then at the binding level of outlay, local government 2’s new equilibrium level needs to be calculated and it will be smaller than the equilibrium level without the binding constraint.

Optimal feedback stabilization policy with asymmetric loss functions

Many CSPs contain a combination of symmetrical and asymmetrical constraints. We present a global approach that allows to apply any usual methods for breaking symmetries on the symmetrical part of a CSP and then to search for a global solution by integrating afterwards the asymmetrical constraints. Then, we focus on optimization problems where only the cost function is asymmetrical

Application of a Long Short Term Memory neural predictor with asymmetric loss function for the resource allocation in NFV network architectures

A modelling approach for solving quite general network equilibrium problems (with fixed trip productions and attractions) intrinsic to the urban transport planning process is presented. The framework can consider a variety of demand models and route choice behaviours within the same implementation, including multiple user classes and combined travel modes that interact on the same physical network. The demand choices are assumed to have a hierarchical structure. When trip distribution is variable, a doubly constrained entropy‐maximizing model is considered at the first level of choice and a hierarchical logit model is used for the remaining demand choices (time of departure, travel mode, transfer point for combined modes, etc.). If trip distribution is considered to be exogenous, the demand choices are modelled as a hierarchical logit. One of the main features of the model is that it considers the effects of congestion on the road network as well as congestion and capacity constraints effects in each public transport service network. The problem is formulated mathematically as a variational inequality, with asymmetric cost functions, and solved following the diagonalization procedure. Each iteration of the aforementioned procedure solves an optimization problem using the Evans algorithm. Sufficient conditions for the existence and uniqueness of the solution to the diagonalized problem are obtained. The main results of a simple example (solved with an academic version of the proposed algorithm) are presented to show the consistency of the equilibrium flows and levels of services obtained using the model. Finally, a real scale implementation of the model is briefly described to show the feasibility of its application.

Individuals continuously have to balance the error costs of alternative decisions. A wealth of research has studied how single individuals navigate this, showing that individuals develop response biases to avoid the more costly error. We, however, know little about the dynamics in groups facing asymmetrical error costs and when social influence amplifies either safe or risky behavior. Here, we investigate this by modeling the decision process and information flow with a drift–diffusion model extended to the social domain. In the model individuals first gather independent personal information; they then enter a social phase in which they can either decide early based on personal information, or wait for additional social information. We combined the model with an evolutionary algorithm to derive adaptive behavior. We find that under asymmetric costs, individuals in large cooperative groups do not develop response biases because such biases amplify at the collective level, triggering false information cascades. Selfish individuals, however, undermine the group’s performance for their own benefit by developing higher response biases and waiting for more information. Our results have implications for our understanding of the social dynamics in groups facing asymmetrical errors costs, such as animal groups evading predation or police officers holding a suspect at gunpoint.

Stochastic ridesharing equilibrium problem with compensation optimization

This paper extends the framework of “rational behavior adjustment process” (RBAP) to incorporating the “boundedly rational user equilibrium” (BRUE). The proportional-switch adjustment process (PSAP) and the network tatonnement process (NTP) are extended to the BRUE case, and their dynamical equations are shown to be Lipschitz continuous, which guarantees the global uniqueness of the classical solutions. A special group of the BRUE-RBAP is proposed, for which the path flows would increase if the paths are in an acceptable path set, and would decrease otherwise. Classical solutions to this special group of models may not exist. Stability of the BRUE-RBAP with classical solutions is proved with separable link travel cost functions. For nonseparable link travel cost functions, the stability of the BRUE-PSAP is proved. Numerical examples are presented to demonstrate the evolution processes of BRUE-PSAP and BRUE-NTP under various bounded rationality thresholds and different initial states. The applicability of BRUE-PSAP in larger networks with asymmetric link travel cost functions is also illustrated.