scholarly journals Strong Algorithms for the Ordinal Matroid Secretary Problem

2021 ◽  
Author(s):  
José A. Soto ◽  
Abner Turkieltaub ◽  
Victor Verdugo
Keyword(s):  
Decision Maker ◽  
Secretary Problem ◽  
Asymptotically Optimal ◽  
Competitive Algorithm ◽  
Optimal Probability ◽  
Design Algorithms ◽  
Better Than

In the ordinal matroid secretary problem (MSP), candidates do not reveal numerical weights, but the decision maker can still discern if a candidate is better than another. An algorithm [Formula: see text] is probability-competitive if every element from the optimum appears with probability [Formula: see text] in the output. This measure is stronger than the standard utility competitiveness. Our main result is the introduction of a technique based on forbidden sets to design algorithms with strong probability-competitive ratios on many matroid classes. We improve upon the guarantees for almost every matroid class considered in the MSP literature. In particular, we achieve probability-competitive ratios of 4 for graphic matroids and of [Formula: see text] for laminar matroids. Additionally, we modify Kleinberg’s utility-competitive algorithm for uniform matroids in order to obtain an asymptotically optimal probability-competitive algorithm. We also contribute algorithms for the ordinal MSP on arbitrary matroids.

A Note on a Lower Bound for the Multiplicative Odds Theorem of Optimal Stopping

2014 ◽  
Vol 51 (03) ◽  
pp. 885-889 ◽  
Author(s):  
Tomomi Matsui ◽  
Katsunori Ano
Keyword(s):  
Lower Bound ◽  
Optimal Stopping ◽  
Secretary Problem ◽  
Bernoulli Trials ◽  
Optimal Stopping Problem ◽  
Maximum Probability ◽  
Optimal Stopping Rule ◽  
Optimal Probability ◽  
Optimal Stopping Theory ◽  
Special Case

In this note we present a bound of the optimal maximum probability for the multiplicative odds theorem of optimal stopping theory. We deal with an optimal stopping problem that maximizes the probability of stopping on any of the last m successes of a sequence of independent Bernoulli trials of length N, where m and N are predetermined integers satisfying 1 ≤ m < N. This problem is an extension of Bruss' (2000) odds problem. In a previous work, Tamaki (2010) derived an optimal stopping rule. We present a lower bound of the optimal probability. Interestingly, our lower bound is attained using a variation of the well-known secretary problem, which is a special case of the odds problem.

Research on the Satisficing Policy of the Secretary Problem

2013 ◽  
Vol 427-429 ◽  
pp. 1924-1927
Author(s):  
Xin Lin Wu ◽  
Yong Zhao
Keyword(s):  
Bounded Rationality ◽  
Decision Maker ◽  
Choice Behavior ◽  
Decision Makers ◽  
Secretary Problem ◽  
Possibility Degree ◽  
Optimal Policies ◽  
Experimental Researches

The methods for determining optimal policies are core problems in the standard secretary problem. The optimal policies are based on the hypothesis of complete rationality. However, some experimental researches showed that decision makers in reality often stopped searching earlier. In this paper, some assumptions of the standard secretary problem are weakened and a satisficing policy based on the hypothesis of bounded rationality is proposed to describe the choice behavior of a decision maker. Moreover, the possibility degree of the decision-maker to choose the satisfactory item is calculated.

scholarly journals Asymptotic Optimality of Estimating Function Estimator for CHARN Model

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Tomoyuki Amano
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Financial Time Series ◽  
Asymptotic Optimality ◽  
Time Series Models ◽  
Estimating Function ◽  
Asymptotically Optimal ◽  
Financial Time ◽  
Conditional Least Squares ◽  
Better Than

CHARN model is a famous and important model in the finance, which includes many financial time series models and can be assumed as the return processes of assets. One of the most fundamental estimators for financial time series models is the conditional least squares (CL) estimator. However, recently, it was shown that the optimal estimating function estimator (G estimator) is better than CL estimator for some time series models in the sense of efficiency. In this paper, we examine efficiencies of CL and G estimators for CHARN model and derive the condition that G estimator is asymptotically optimal.

Minimizing expected makespan in stochastic open shops

1982 ◽  
Vol 14 (4) ◽  
pp. 898-911 ◽  
Author(s):  
Michael L. Pinedo ◽  
Sheldon M. Ross
Keyword(s):  
Exponential Distribution ◽  
Decision Maker ◽  
Optimal Policy ◽  
Processing Time ◽  
Open Shop ◽  
Random Time ◽  
Two Machines ◽  
New Better Than Used ◽  
Expected Makespan ◽  
Better Than

Suppose that two machines are available to process n tasks. Each task has to be processed on both machines; the order in which this happens is immaterial. Task j has to be processed on machine 1 (2) for random time Xj (Yj) with distribution Fj (Gj). This kind of model is usually called an open shop. The time that it takes to process all tasks is normally called the makespan. Every time a machine finishes processing a task the decision-maker has to decide which task to process next. Assuming that Xj and Yj have the same exponential distribution we show that the optimal policy instructs the decision-maker, whenever a machine is freed, to start processing the task with longest expected processing time among the tasks still to be processed on both machines. If all tasks have been processed at least once, it does not matter what the decision-maker does, as long as he keeps the machines busy. We then consider the case of n identical tasks and two machines with different speeds. The time it takes machine 1 (2) to process a task has distribution F (G). Both distributions F and G are assumed to be new better than used (NBU) and we show that the decision-maker stochastically minimizes the makespan when he always gives priority to those tasks which have not yet received processing on either machine.

Minimizing the expected rank with full information

1993 ◽  
Vol 30 (03) ◽  
pp. 616-626 ◽  
Author(s):  
F. Thomas Bruss ◽  
Thomas S. Ferguson
Keyword(s):  
Finite Number ◽  
Optimal Stopping ◽  
Secretary Problem ◽  
Full Information ◽  
Asymptotically Optimal ◽  
A Value ◽  
Optimal Stopping Rule ◽  
Optimal Value ◽  
History Of ◽  
Threshold Rule

The full-information secretary problem in which the objective is to minimize the expected rank is seen to have a value smaller than 7/3 for all n (the number of options). This can be achieved by a simple memoryless threshold rule. The asymptotically optimal value for the class of such rules is about 2.3266. For a large finite number of options, the optimal stopping rule depends on the whole sequence of observations and seems to be intractable. This raises the question whether the influence of the history of all observations may asymptotically fade. We have not solved this problem, but we show that the values for finite n are non-decreasing in n and exhibit a sequence of lower bounds that converges to the asymptotic value which is not smaller than 1.908.

Imperialist Competitive Algorithm with Updated Assimilation for the Solution of Real Valued Optimization Problems

2018 ◽  
Vol 27 (02) ◽  
pp. 1850005
Author(s):  
Zhavat Sherinov ◽  
Ahmet Ünveren ◽  
Adnan Acan
Keyword(s):  
Euclidean Distance ◽  
Optimization Problems ◽  
State Of The Art ◽  
Pearson Correlation ◽  
Imperialist Competitive Algorithm ◽  
Benchmark Problems ◽  
Pearson Correlation Coefficient ◽  
Competitive Algorithm ◽  
Imperialistic Competitive Algorithm ◽  
Better Than

In this paper, an improved imperialistic competitive algorithm is presented for real-valued optimization problems. A new method is introduced for the movement of colonies towards their imperialist, which is called assimilation. The proposed method uses Euclidean distance along with Pearson correlation coefficient as an operator for assimilating colonies with respect to their imperialists. Applications of the proposed algorithm to classical and recently published hard benchmark problems, and statistical analysis associated with the corresponding experimental results illustrated that the achieved success is significantly better than a number of state-of-the art methods.

scholarly journals ON DOMINANCE AND CONTEXT-DEPENDENCE IN DECISIONS INVOLVING MULTIPLE ATTRIBUTES

2012 ◽  
Vol 28 (2) ◽  
pp. 117-132 ◽  
Author(s):  
Prasanta K. Pattanaik ◽  
Yongsheng Xu
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Welfare Economics ◽  
Multiple Criteria ◽  
Context Dependence ◽  
Weak Continuity ◽  
Relative Importance ◽  
Group Decisions ◽  
Dominance Principle ◽  
Better Than

In decision-making involving multiple criteria or attributes, a decision maker first identifies all relevant evaluative attributes in making decisions. Then, a dominance principle is often invoked whenever applicable: whenever an option x is better than an option y in terms of some attribute and no worse than y in terms of any other attributes, x is judged to be better than y. If, however, this dominance principle is not applicable, then the decision maker determines the relative importance between the identified evaluative attributes, consults with contextual features of the options under consideration, and makes a decision. It is shown that the combination of these principles runs into problems in the presence of rationality properties, such as transitivity, and a weak continuity requirement on decisions. The paper gives examples from welfare economics, and theories of individual and group decisions.

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