A Method for Inferring the Optimization Cost Function of Experimentally Observed Motor Strategies

2005 ◽  
Author(s):  
Carlo L. Bottasso ◽  
Alessandro Croce ◽  
Stefano Sartirana ◽  
Boris I. Prilutsky
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Cost Function ◽  
Motor Task ◽  
Computational Procedure ◽  
Search Space ◽  
Optimality Criteria ◽  
Cost Functions ◽  
The Cost ◽  
Motor Strategies

We propose a computational procedure for inferring the cost functions that, according to the Principle of Optimality, underlie experimentally observed motor strategies. This work tries to overcome the need to hypothesize the cost functions, extracting this non-directly observable information from experimental data. Optimality criteria of observed motor tasks are here indirectly derived using: a) a mathematical model of the bio-system; and b) a parametric mathematical model of the possible cost functions, i.e. a search space constructed in such a way as to presumably contain the unknown function that was used by the bio-system in the given motor task of interest. The cost function that best matches the experimental data is identified within the search space by solving a nested optimization problem. This problem can be recast as a non-linear programming problem and therefore solved using standard techniques. The proposed methodology is tested on representative examples.

scholarly journals Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization

2020 ◽  
Vol 30 (6) ◽  
pp. 1645-1663
Author(s):  
Ömer Deniz Akyildiz ◽  
Dan Crisan ◽  
Joaquín Míguez
Keyword(s):  
Monte Carlo ◽  
Cost Function ◽  
Global Minimum ◽  
Sequential Monte Carlo ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Gradient Based ◽  
Multiple Minima ◽  
The Cost

Abstract We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed scheme is a stochastic zeroth-order optimization algorithm which demands only the capability to evaluate small subsets of components of the cost function. It can be depicted as a bank of samplers that generate particle approximations of several sequences of probability measures. These measures are constructed in such a way that they have associated probability density functions whose global maxima coincide with the global minima of the original cost function. The algorithm selects the best performing sampler and uses it to approximate a global minimum of the cost function. We prove analytically that the resulting estimator converges to a global minimum of the cost function almost surely and provide explicit convergence rates in terms of the number of generated Monte Carlo samples and the dimension of the search space. We show, by way of numerical examples, that the algorithm can tackle cost functions with multiple minima or with broad “flat” regions which are hard to minimize using gradient-based techniques.

scholarly journals New approach to the retrieval of AOD and its uncertainty from MISR observations over dark water

2018 ◽  
Vol 11 (1) ◽  
pp. 429-439 ◽  
Author(s):  
Marcin L. Witek ◽  
Michael J. Garay ◽  
David J. Diner ◽  
Michael A. Bull ◽  
Felix C. Seidel
Keyword(s):  
Statistical Analysis ◽  
Cost Function ◽  
Entire Range ◽  
Cost Functions ◽  
Retrieval Algorithm ◽  
New Approach ◽  
Aerosol Retrieval ◽  
Operational Algorithm ◽  
Confidence Index ◽  
The Cost

Abstract. A new method for retrieving aerosol optical depth (AOD) and its uncertainty from Multi-angle Imaging SpectroRadiometer (MISR) observations over dark water is outlined. MISR's aerosol retrieval algorithm calculates cost functions between observed and pre-simulated radiances for a range of AODs (from 0.0 to 3.0) and a prescribed set of aerosol mixtures. The previous version 22 (V22) operational algorithm considered only the AOD that minimized the cost function for each aerosol mixture and then used a combination of these values to compute the final, “best estimate” AOD and associated uncertainty. The new approach considers the entire range of cost functions associated with each aerosol mixture. The uncertainty of the reported AOD depends on a combination of (a) the absolute values of the cost functions for each aerosol mixture, (b) the widths of the cost function distributions as a function of AOD, and (c) the spread of the cost function distributions among the ensemble of mixtures. A key benefit of the new approach is that, unlike the V22 algorithm, it does not rely on empirical thresholds imposed on the cost function to determine the success or failure of a particular mixture. Furthermore, a new aerosol retrieval confidence index (ARCI) is established that can be used to screen high-AOD retrieval blunders caused by cloud contamination or other factors. Requiring ARCI ≥0.15 as a condition for retrieval success is supported through statistical analysis and outperforms the thresholds used in the V22 algorithm. The described changes to the MISR dark water algorithm will become operational in the new MISR aerosol product (V23), planned for release in 2017.

scholarly journals Assessing worker performance using dynamic cost functions in human robot collaborative tasks

2019 ◽  
Vol 234 (1) ◽  
pp. 289-301 ◽  
Author(s):  
Thomas Smith ◽  
Panorios Benardos ◽  
David Branson
Keyword(s):  
Cost Function ◽  
Completion Time ◽  
Cost Functions ◽  
Initial Development ◽  
Worker Performance ◽  
Manufacturing Assembly ◽  
And Performance ◽  
The Cost ◽  
Assembly Tasks ◽  
Human Robot Collaboration

The aim of this research is to develop a framework to allow efficient human robot collaboration on manufacturing assembly tasks based on cost functions that quantify capabilities and performance of each element in a system and enable their efficient evaluation. A proposed cost function format is developed along with initial development of two example cost function variables, completion time and fatigue, obtained as each worker is completing assembly tasks. The cost function format and example variables were tested with two example tasks utilizing an ABB YuMi Robot in addition to a simulated human worker under various levels of fatigue. The total costs produced clearly identified the best worker to complete each task with these costs also clearly indicating when a human worker is fatigued to a greater or lesser degree than expected.

Delta's New Song: A Case on Cost Estimation in the Airline Industry

2004 ◽  
Vol 19 (3) ◽  
pp. 345-358 ◽  
Author(s):  
Shane S. Dikolli ◽  
Karen L. Sedatole
Keyword(s):  
Cost Function ◽  
Cost Estimation ◽  
Airline Industry ◽  
Low Cost ◽  
Opportunity To Learn ◽  
Cost Functions ◽  
Function Estimation ◽  
Cost Category ◽  
Income Statement ◽  
The Cost

This case provides the opportunity to use various empirical techniques (i.e., high-low method, simple regression, and multiple regression) in the estimation of cost functions. The case uses the airline industry as the setting for this analysis and, in particular, focuses on the ef forts of Delta Airlines to plan for salaries, the cost category that dominates its income statement. The case provides the data and the opportunity to learn the details of cost function estimation, but more importantly, it provides a rich setting in which issues related to the interpretation of these cost functions can be discussed. Finally, the entry of Delta into the low-cost carrier segment with its formation of Song provides a unique opportunity to think about how the cost function of an established full-service airline compares to that of a low-fare startup. Data from successful newcomer JetBlue is used to illustrate these differences. More generally, the case shows how the use of historical costs and cost estimation techniques can facilitate decision making about entry into new product markets.

scholarly journals Inverse KKT: Learning cost functions of manipulation tasks from demonstrations

2017 ◽  
Vol 36 (13-14) ◽  
pp. 1474-1488 ◽  
Author(s):  
Peter Englert ◽  
Ngo Anh Vien ◽  
Marc Toussaint
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Cost Functions ◽  
Quadratic Program ◽  
Relevant Task ◽  
Kernel Hilbert Spaces ◽  
The Cost ◽  
Linear Parameterization

Inverse optimal control (IOC) assumes that demonstrations are the solution to an optimal control problem with unknown underlying costs, and extracts parameters of these underlying costs. We propose the framework of inverse Karush–Kuhn–Tucker (KKT), which assumes that the demonstrations fulfill the KKT conditions of an unknown underlying constrained optimization problem, and extracts parameters of this underlying problem. Using this we can exploit the latter to extract the relevant task spaces and parameters of a cost function for skills that involve contacts. For a typical linear parameterization of cost functions this reduces to a quadratic program, ensuring guaranteed and very efficient convergence, but we can deal also with arbitrary non-linear parameterizations of cost functions. We also present a non-parametric variant of inverse KKT that represents the cost function as a functional in reproducing kernel Hilbert spaces. The aim of our approach is to push learning from demonstration to more complex manipulation scenarios that include the interaction with objects and therefore the realization of contacts/constraints within the motion. We demonstrate the approach on manipulation tasks such as sliding a box, closing a drawer and opening a door.

scholarly journals Arm movement adaptation to concurrent pain constraints

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Johannes Kühn ◽  
Carlo Bagnato ◽  
Etienne Burdet ◽  
Sami Haddadin
Keyword(s):  
Motor Task ◽  
Arm Movement ◽  
Noxious Stimulation ◽  
Joint Movement ◽  
Movement Coordination ◽  
Conservative Strategy ◽  
Subject Specific ◽  
The Cost ◽  
Motor Strategies ◽  
As If

AbstractHow do humans coordinate their movements in order to avoid pain? This paper investigates a motor task in the presence of concurrent potential pain sources: the arm must be withdrawn to avoid a slap on the hand while avoiding an elbow obstacle with an electrical noxious stimulation. The results show that our subjects learned to control the hand retraction movement in order to avoid the potential pain. Subject-specific motor strategies were used to modify the joint movement coordination to avoid hitting the obstacle with the elbow at the cost of increasing the risk of hand slap. Furthermore, they used a conservative strategy as if assuming an obstacle in 100% of the trials.

scholarly journals CONTROL OF A COMPLEX OBJECTS, STATES OF WHICH ARE DESCRIBING BY THE MATRIX RATING MECHANISM

2020 ◽  
pp. 114-139
Author(s):  
Aleksander Alekseev ◽  
Keyword(s):  
Control Problem ◽  
Cost Function ◽  
Algebraic Equation ◽  
Production Function ◽  
Control Object ◽  
Inverse Function ◽  
Second Order ◽  
Cost Functions ◽  
The Cost ◽  
Douglas Production Function

The control problem of a multi-criteria object is considered. Controlled object that has several criteria that are significant for a decision maker. Each criterion characterizes a control object in terms of a particular result of activity or an efficiency indicator. To evaluate the effectiveness of the functioning of the managed facility as a whole, the rating matrix mechanism is used, taking into account all the criteria in the complex. The optimal control problem is formulated as a search for the values ​​of aggregated criteria that provide a given value of a complex indicator with minimal costs for providing values ​​of particular criteria. The generalized cost function was reduced to an equation with one variable. The analytical equation of the level line of the indicator aggregated as a result of the convolution of two criteria is obtained. The line equation is found for an arbitrary binary convolution matrix, including the elements of which are given continuous values. It is shown that the objective function is reduced to a fourth-order polynomial, which can be analytically solved using the Ferrari or Descartes-Euler methods. It is shown that the task of searching for the values of two particular criteria describing the state of the control object for which the complex indicator calculated using the additive-multiplicative approach to complex assessment is equal to the given value and the costs for their provision are minimal, has a solution in general form for arbitrary nondecreasing convolution matrix of two criteria. Particular solutions to the control problem are found using costly functions, which are the inverse function of the Cobb-Douglas production function. It was shown that the cost function of the aggregate indicator has additional terms and is described by an algebraic equation with nonzero coefficients for variables and an additional constant. Based on what it was concluded that the cost functions, which are the inverse function e of the Cobb-Douglas production function, can be applied to control objects that have only two criteria. A similar formulation of the control problem for an arbitrary non-decreasing convolution matrix of two criteria is considered when using the additive-multiplicative approach to aggregation and when using cost functions described by a second-order algebraic equation in general form. As a result of the study, it is shown that the form of the cost function for the aggregated indicator is preserved. Thus, using cost functions in the form of second-order equations, the control problem has a solution in the general form for any number of criteria.

scholarly journals One problem, too many solutions: How costly is honest signalling of need?

2017 ◽  
Author(s):  
Szabolcs Számadó ◽  
Dániel Czégel ◽  
István Zachar
Keyword(s):  
Cost Function ◽  
Specific Model ◽  
Cost Functions ◽  
Unique Equilibrium ◽  
Offspring Quality ◽  
Honest Signalling ◽  
Signalling Theory ◽  
The Cost ◽  
Model Support ◽  
Signalling Games

AbstractThe “cost of begging” is a prominent prediction of costly signalling theory, suggesting that offspring begging has to be costly in order to be honest. More specifically, it predicts that there is a single cost function for the offspring (depending on e.g. offspring quality) that maintains honesty and it must be proportional to parent’s fitness loss. Here we show another interpretation of the cost. We demonstrate that cost, proportional to the fitness gain of the offspring, also results in honest signalling. Since the loss of the parent does not necessarily coincide with the gain of the offspring, it is provable that any linear combination of the two cost functions (one proportional to parent’s loss, one to offspring’s gain) also leads to honest signalling. Our results, applied for a specific model, support the previous general conclusion that signalling games have different cost functions for different equilibria. Consequently, costly signalling theory cannot predict a unique equilibrium cost in signalling games especially in case of parent-offspring conflicts. As an important consequence, any measured equilibrium cost in real cases has to be compared both to the parent’s fitness loss and to the offspring’s fitness gain in order to provide meaningfully interpretation.

scholarly journals New approach to the retrieval of AOD and its uncertainty from MISR observations over dark water

2017 ◽  
Author(s):  
Marcin L. Witek ◽  
Michael J. Garay ◽  
David J. Diner ◽  
Michael A. Bull ◽  
Felix C. Seidel
Keyword(s):  
Statistical Analysis ◽  
Cost Function ◽  
Entire Range ◽  
Cost Functions ◽  
Retrieval Algorithm ◽  
New Approach ◽  
Aerosol Retrieval ◽  
Operational Algorithm ◽  
Confidence Index ◽  
The Cost

Abstract. A new method for retrieving aerosol optical depth (AOD) and its uncertainty from Multi-angle Imaging SpectroRadiometer (MISR) observations over dark water is outlined. MISR’s aerosol retrieval algorithm calculates cost functions between observed and pre-simulated radiances for a range of AODs (from 0.0 to 3.0) and a prescribed set of aerosol mixtures. The previous Version 22 (V22) operational algorithm considered only the AOD that minimized the cost function for each aerosol mixture, then used a combination of these values to compute the final, best estimate AOD and associated uncertainty. The new approach considers the entire range of cost functions associated with each aerosol mixture. The uncertainty of the reported AOD depends on a combination of a) the absolute values of the cost functions for each aerosol mixture, b) the widths of the cost function distributions as a function of AOD, and c) the spread of the cost function distributions among the ensemble of mixtures. A key benefit of the new approach is that, unlike the V22 algorithm, it does not rely on arbitrary thresholds imposed on the cost function to determine the success or failure of a particular mixture. Furthermore, a new Aerosol Retrieval Confidence Index (ARCI) is established that can be used to screen high-AOD retrieval blunders caused by cloud contamination or other factors. Requiring ARCI ≥ 0.15 as a condition for retrieval success is supported through statistical analysis and outperforms the thresholds used in the V22 algorithm. The described changes to the MISR dark water algorithm will become operational in the new MISR aerosol product (V23), planned for release in 2017.

Triple Bottom Line-Focused Optimization of Oblique Turning Processes Based on Hybrid Modeling

2021 ◽  
pp. 215-241
Author(s):  
Ramón Quiza ◽  
Iván La Fé-Perdomo ◽  
Marcelino Rivas ◽  
Veena Ramtahalsing
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide Emissions ◽  
Hybrid Approach ◽  
Triple Bottom Line ◽  
Search Space ◽  
The Other ◽  
Wide Sense ◽  
Bottom Line ◽  
Conflicting Objectives ◽  
The Cost

This chapter proposes a hybrid approach for modelling and optimizing the oblique turning processes. Analytical modelling and statistical regressions are combined for predicting the values of the most important parameters involved in the oblique cutting process. The predictions of the model were validated by using experimental data, showing coincidence for a 95% confidence level. Then, an a posteriori multi-objective optimization is carried out by using a genetic algorithm. Three conflicting objectives, which represent the three pillars of the sustainability as defined in the triple bottom line, are simultaneously considered: the carbon dioxide emissions, the cost, and the cutting time. The outcome of the optimization process is a set of non-nominate solutions, which are optimal in the wide sense that no other solution in the search space can improve one objective without worsening the other one. Finally, the decision-maker chooses the most convenient solution depending on the actual workshop conditions.

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