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This paper investigates a modelfree algorithm of broad interest in reinforcement learning, namely, Qlearning. Whereas substantial progress had been made toward understanding the sample efficiency of Qlearning in recent years, it remained largely unclear whether Qlearning is sampleoptimal and how to sharpen the sample complexity analysis of Qlearning. In this paper, we settle these questions: (1) When there is only a single action, we show that Qlearning (or, equivalently, TD learning) is provably minimax optimal. (2) When there are at least two actions, our theory unveils the strict suboptimality of Qlearning and rigorizes the negative impact of overestimation in Qlearning. Our theory accommodates both the synchronous case (i.e., the case in which independent samples are drawn) and the asynchronous case (i.e., the case in which one only has access to a single Markovian trajectory).
more » « less NSFPAR ID:
 10501626
 Publisher / Repository:
 INFORMS
 Date Published:
 Journal Name:
 Operations Research
 Volume:
 72
 Issue:
 1
 ISSN:
 0030364X
 Page Range / eLocation ID:
 222 to 236
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract Expert testimony varies in scientific quality and jurors have a difficult time evaluating evidence quality (McAuliff et al., 2009). In the current study, we apply Fuzzy Trace Theory principles, examining whether visual and gist aids help jurors calibrate to the strength of scientific evidence. Additionally we were interested in the role of jurors’ individual differences in scientific reasoning skills in their understanding of case evidence. Contrary to our preregistered hypotheses, there was no effect of evidence condition or gist aid on evidence understanding. However, individual differences between jurors’ numeracy skills predicted evidence understanding. Summary Poorquality expert evidence is sometimes admitted into court (Smithburn, 2004). Jurors’ calibration to evidence strength varies widely and is not robustly understood. For instance, previous research has established jurors lack understanding of the role of control groups, confounds, and sample sizes in scientific research (McAuliff, Kovera, & Nunez, 2009; Mill, Gray, & Mandel, 1994). Still others have found that jurors can distinguish weak from strong evidence when the evidence is presented alone, yet not when simultaneously presented with case details (Smith, Bull, & Holliday, 2011). This research highlights the need to present evidence to jurors in a way they can understand. Fuzzy Trace Theory purports that people encode information in exact, verbatim representations and through “gist” representations, which represent summary of meaning (Reyna & Brainerd, 1995). It is possible that the presenting complex scientific evidence to people with verbatim content or appealing to the gist, or bottomline meaning of the information may influence juror understanding of that evidence. Application of Fuzzy Trace Theory in the medical field has shown that gist representations are beneficial for helping laypeople better understand risk and benefits of medical treatment (BrustRenck, Reyna, Wilhelms, & Lazar, 2016). Yet, little research has applied Fuzzy Trace Theory to information comprehension and application within the context of a jury (c.f. Reyna et. al., 2015). Additionally, it is likely that jurors’ individual characteristics, such as scientific reasoning abilities and cognitive tendencies, influence their ability to understand and apply complex scientific information (Coutinho, 2006). Methods The purpose of this study was to examine how jurors calibrate to the strength of scientific information, and whether individual difference variables and gist aids inspired by Fuzzy Trace Theory help jurors better understand complicated science of differing quality. 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Two experts presented opposing opinions about the scientific evidence related to the mtDNA match estimate for the defendant’s identification. The quality and content of this mtDNA evidence differed based on the two conditions. The high quality evidence condition used a larger database than the low quality evidence to compare to the mtDNA sample and could exclude a larger percentage of people. In the decision aid condition, experts in the gist information group presented gist aid inspired visuals and examples to help explain the proportion of people that could not be excluded as a match. Those in the no gist information group were not given any aid to help them understand the mtDNA evidence presented. After viewing the trial, participants filled out a questionnaire on how well they understood the mtDNA evidence and their overall judgments of the case (e.g. verdict, witness credibility, scientific evidence strength). 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