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### Rigorous computer analysis of the Chow-Robbins game [article]

Olle Häggström, Johan Wästlund
2012 arXiv   pre-print
We establish a simple upper bound on the expected payoff in a given position, allowing efficient and rigorous computer analysis of positions early in the game.  ...  This so-called Chow-Robbins game is amenable to computer analysis, but while simple-minded number crunching can show that it is best to continue in a given position, establishing rigorously that stopping  ...  The Chow-Robbins game The following game was introduced by Yuan-Shih Chow and Herbert Robbins [1] in 1964: We toss a coin repeatedly, and stop whenever we want.  ...

### Rigorous Computer Analysis of the Chow–Robbins Game

Olle Häggström, Johan Wästlund
2013 The American mathematical monthly
We establish a simple upper bound on the expected payoff in a given position, allowing efficient and rigorous computer analysis of positions early in the game.  ...  This so-called Chow-Robbins game is amenable to computer analysis, but while simple-minded number crunching can show that it is best to continue in a given position, establishing rigorously that stopping  ...  The Chow-Robbins game The following game was introduced by Yuan-Shih Chow and Herbert Robbins [1] in 1964: We toss a coin repeatedly, and stop whenever we want.  ...

### On the Sn/n-Problem [article]

Sören Christensen, Simon Fischer
2021 arXiv   pre-print
The Chow-Robbins game is a classical still partly unsolved stopping problem introduced by Chow and Robbins in 1965. You repeatedly toss a fair coin.  ...  For the Chow-Robbins game we as well give a tight lower bound and use these to calculate, on the integers, the complete continuation and the stopping set of the problem for n≤ 10^5.  ...  We use T = 10 6 to calculate V (0, 0) and the integer thresholdsb(n) := b(n) . For 34 values n ≤ 10 6 the exact valueb(n) can not be determined this way, the smallest such value is n = 489.242.  ...

### An Experimental Mathematics Perspective on the Old, and still Open, Question of When To Stop? [article]

Luis A. Medina, Doron Zeilberger
2010 arXiv   pre-print
In a recent article in American Scientist, Theodore Hill described a coin-tossing game whose pay-off is the number of heads over the total number of throws.  ...  In the present article, we explore different strategies to this game from the Experimental Mathematics perspective.  ...  The work of the second author was supported in part by the USA National Science Foundation. July 23, 2009  ...

Mark Rowland, Will Dabney, Rémi Munos
2020 arXiv   pre-print
A great variety of off-policy learning algorithms exist in the literature, and new breakthroughs in this area continue to be made, improving theoretical understanding and yielding state-of-the-art reinforcement  ...  We develop one such algorithm, C-trace, demonstrating that it is able to more efficiently make these trade-offs than existing methods in use, and that it can be scaled to yield state-of-the-art performance  ...  Bilal Piot, Tom Schaul, and Yunhao Tang for interesting conversations during the course of this work.  ...

### Selected Papers

1985 Southern Journal of Agricultural Economics
"Total Factor Productivity and the Elasticity of Scale: An Analysis of U.S. Agriculture." Robbin Shoemaker, ERS, USDA.  ...  "Grain Export Elevators: Economies of Size Analysis." Magid A. Dagher, University of Maryland; and Lynn W. Robbins, University of Kentucky.  ...  Additionally, evaluation of the hypothesis that the 1975 frost in Brazil had resulted in structural changes in the international coffee economy was accepted, based on the Chow test.  ...

### Optimal Stopping Under Ambiguity

Frank Riedel
2006 Social Science Research Network
If, however, the class of priors is time-consistent, we establish a generalization of the classical theory of optimal stopping.  ...  We solve two classes of examples: the so-called independent and indistinguishable case (the parking problem) and the case of American Options (Cox-Ross-Rubinstein model).  ...  Having established these two key theorems, one can proceed as in the classical literature (Chow, Robbins, and Siegmund (1971) , Snell (1952) ).  ...

### The stochastic root-finding problem

Raghu Pasupathy, Sujin Kim
2011 ACM Transactions on Modeling and Computer Simulation
The stochastic root-finding problem (SRFP) is that of finding the zero(s) of a vector function, that is, solving a nonlinear system of equations when the function is expressed implicitly through a stochastic  ...  With a view towards helping the practitioner, we discuss specific variations in their implementable form, and provide references to computer code when easily available.  ...  ACKNOWLEDGMENT We would like to thank the anonymous referees and the area editor for their thorough reviews and suggestions.  ...

### Communication Technology Integration into Social Work Practice

Angela N. Bullock, Alex D. Colvin
As a result of this transformation, the use of technology has evolved in social work practice.  ...  This article will examine a theoretically based direction for the future creation of technologically driven interventions in social work practice and address both the challenges and opportunities communication  ...  Acknowledgements The author wishes to acknowledge the contribution of the participants in this research.  ...

### Interpretable and Personalized Apprenticeship Scheduling: Learning Interpretable Scheduling Policies from Heterogeneous User Demonstrations [article]

Rohan Paleja, Andrew Silva, Letian Chen, Matthew Gombolay
2021 arXiv   pre-print
inferred, personalized embedding non-parametric in the number of demonstrator types.  ...  Due to the large-scale and dynamic nature of resource coordination in hospitals and factories, human domain experts manually plan and adjust schedules on the fly.  ...  Machine learning techniques for analyzing training behavior in serious gaming. IEEE Transactions on Computational Intelligence and AI in Games, 2017. [18] Blake Griffin.  ...

### Apresentação

António Manuel Fonseca
2017 Portugese Journal of Sport Sciences / Revista Portuguesa de Ciências do Desporto
The results also call for the inclusion of "out-of-system" situations in training. KEY-WORDS: Performance Analysis. Social Network Analysis. Eigenvector. Game Complexes.  ...  The system measures the relative position of the pupil and corneal reflection. The record process is done through transferred to a computer and analyzed by running Tobii Glasses Analysis Software.  ...

### Effective Policy Search Method for Robot Reinforcement Learning with Noisy Reward 노이즈 환경에서 효과적인 로봇 강화 학습의 정책 탐색 방법

Young-Ha Yang, Cheol-Soo Lee
2022 The Journal of Korea Robotics Society
We also wish to thank the many people who have read drafts of this book and provided valuable comments, including  ...  , 1992; Doya, 1996) . 3 We use R t+1 instead of R t to denote the reward due to A t because it emphasizes that the next reward and next state, R t+1 and S t+1 , are jointly determined.  ...  2 We restrict attention to discrete time to keep things as simple as possible, even though many of the ideas can be extended to the continuous-time case (e.g., see Bertsekas and Tsitsiklis, 1996; Werbos  ...

### Robot Learning from Randomized Simulations: A Review [article]

Fabio Muratore, Fabio Ramos, Greg Turk, Wenhao Yu, Michael Gienger, Jan Peters
2021 arXiv   pre-print
The rise of deep learning has caused a paradigm shift in robotics research, favoring methods that require large amounts of data.  ...  Therefore, state-of-the-art approaches learn in simulation where data generation is fast as well as inexpensive and subsequently transfer the knowledge to the real robot (sim-to-real).  ...  This question relates to the problems of optimal stopping (Chow and Robbins, 1963) as well as multi-fidelity optimization (Forrester et al., 2007) , and can be seen as a reformulation thereof in the  ...

### Errata and Addenda to Mathematical Constants [article]

Steven Finch
2021 arXiv   pre-print
We wonder if Shepp's constant can be employed to give a high-precision estimate of the Chow-Robbins constant 2(0.7929535064...) − 1 = 0.5859070128...  ...  Lhote [319, 320] developed rigorous techniques for computing H and other constants to high precision.  ...

### The biopsychosocial and "complex" systems approach as a unified framework for addiction

Mark D. Griffiths
2008 Behavioral and Brain Sciences
(5) incorrect search of situation-action-outcome relationships, (6) misclassification of situations, (7) overvaluation in the habit system, (8) a mismatch in the balance of the two decision systems, (  ...  The understanding of decision-making systems has come together in recent years to form a unified theory of decision-making in the mammalian brain as arising from multiple, interacting systems (a planning  ...  To those who believe that science gains rigor as it zooms in on the particular, the integrative activity of the brain is no doubt too nebulous an object for any rigorous analysis.  ...
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