Reinforcement learning and the power law of practice: some analytical results

Erev and Roth (1998) among others provide a comprehensive analysis of experimental evidence on learning in games, based on a stochastic model of learning that accounts for two main elements: the Law of Effect (positive reinforcement of actions that perform well) and the Power Law of Practice (learning curves tend to be steeper initially). This note complements this literature by providing an analytical study of the properties of such learning models. Specifically, the paper shows that: (a) up to an error term, the stochastic process is driven by a system of discrete time difference equations of the replicator type. This carries an analogy with Börgers and Sarin (1997), where reinforcement learning accounts only for the Law of Effect. (b) if the trajectories of the system of replicator equations converge sufficiently fast, then the probability that all realizations of the learning process over a possibly infinite spell of time lie within a given small distance of the solution path of the replicator dynamics becomes, from some time on, arbitrarily close to one. Fast convergence, in the form of exponential convergence, is shown to hold for any strict Nash equilibrium of the underlying game.

The dynamics of public opinion under majority rules

This note explains the process of public opinion formation via a locally interactive, space-time analysis. The model we use is a special case of the general framework for modelling social interaction proposed in Blume and Durlauf (2001). In the reduced form of the model we study how each individual, when faced with the choice of one, out of two, opinions, tends to conform to the opinion held by the majority of her neighbours. We consider different, symmetric and asymmetric, majority rules. Depending on the specific behavioral rule, the aggregate process of opinion formation may display contagion on one specific opinion, or consensus among all individuals in the population, or co-existence of both opinions. Whenever consensus obtains, we observe the formation of homogeneous areas (clusters) that seem almost stationary along the dynamics

Test of non-standard neutrino properties with the BOREXINO source experiments

We calculate the event rates induced by high-intensity radioactive sources of nu_e (51Cr) and of anti-nu_e (90Sr), to be located near the BOREXINO detector. Calculations are performed both in the standard case and assuming non-standard properties of neutrinos, including flavor oscillations, neutrino electromagnetic interactions, and deviations from the standard vector and axial couplings in the nu_e-e interaction. It is shown that, in some cases, the current limits on non-standard neutrino properties can be significantly improved.Comment: 15 pages (RevTeX) + 4 figures (postscript) included with epsfig.sty. Minor changes and corrections, 3 references added. Final version to be published in Europ. Phys. Jour.

Gran Sasso laboratory: Present and prospects

Research activities carried out at the underground Gran Sasso laboratory are reviewed

An estimate of theta_14 independent of the reactor antineutrino flux determinations

In a previous paper [Phys. Rev. D 83, 113013 (2011)] we have shown that the solar sector data (solar and KamLAND) are sensitive to the parameter theta_14, encoding the admixture of the electron neutrino with a fourth (essentially) sterile mass eigenstate. In that work we evidenced that such data prefer a non-zero value of theta_14 and that such a preference is completely degenerate with that of non-zero theta_13. In this report we show how the evidence of theta_13 > 0, recently emerged from global neutrino data analyses, lifts such a degeneracy and disfavors the case of sterile neutrino mixing. By excluding from our analysis the total rate information coming from the reactor experiments we untie our results from any assumption on their flux normalization. In this way, we establish the robust upper bound sin^2 (theta_14) < 0.04 at the 90% C.L.Comment: 4 pages, 1 figure, minor changes, matches version accepted by PR

Optimism - Is the Conceptual Glass Half-Empty (or Half-Full)

Optimism has been a favourite topic of research in positive psychology. Optimism, defined as a generalized positive expectancy for the future, is generally regarded as a positive trait. However, despite positive findings for optimism, some researchers have suggested that optimism is not beneficial in all contexts. Alternatives to optimism have been proposed, including flexible optimism (Seligman, 1991; Forgeard & Seligman, 2012) and cautious optimism (Wallston, 1994). While such criticism of optimism lacks substantial empirical support, there are a few studies that appear to support these contentions. Previous research suggests that optimism is associated with maladaptive persistence in gambling (Gibson & Sanbonmatsu, 2004) and poorer health (de Ridder, Schreurs, & Bensing, 2000). Furthermore, research on defensive pessimism and unrealistic optimism supports the notion of a “dark side” of optimism. A new construct is proposed to reconcile these divergent findings: expectancy flexibility. Expectancy flexibility is defined as the ability to change one’s expectations of the future in response to contextual cues. It was hypothesized that expectancy flexibility would moderate or mediate the associations between optimism and various outcomes. Four studies were conducted to validate the Expectancy Flexibility Scale (EFS), an instrument developed to measure expectancy flexibility. The first two studies were used to develop a scale with good internal consistency reliability, a low correlation with optimism (to provide discriminant validity), and a moderate correlation with theoretically related constructs (to provide convergent validity). The purpose of the third study was to test whether shifts in expectations actually occur in response to negative feedback, and whether these shifts were predicted by scores on the EFS. The fourth study tested whether the EFS was associated with constructs believed to be outcomes, including preventive health behaviours, academic success, and problem gambling. In all four studies, participants were undergraduate students who were recruited through a participant pool at a Canadian university. The EFS and several other self-report questionnaires were completed by participants via an online platform. The findings of Study 1 and Study 2 supported the reliability and validity of the EFS. Internal consistency reliability was in the acceptable range (α \u3e 0.70). Supporting the scale’s convergent validity, expectancy flexibility was associated with related measures like defensive pessimism and cognitive flexibility. Weak and non-significant correlations were found between expectancy flexibility and optimism, locus of control, and coping flexibility, supporting the scale’s discriminant validity. The findings of Study 3 partially supported the hypothesis that expectancy flexibility is associated with shifts in expectations. In the gambling scenario, losses were generally associated with reduced expectations, while gains were associated with no change or slight increases in gambling expectations. This pattern of findings was not evident in the academic scenario, where disappointing exam results did not produce a negative shift in expectations. In Study 4, expectancy flexibility was positively associated with academic approach coping, social health, general academic skills, and confidence; it was negatively related to substance use and problem gambling. Analysis of the qualitative questions generally supported the hypothesis that expectancy flexibility is associated with shifts in expectations. However, the moderational and mediational models were not supported. Overall, the results provide support for the validity of the flexible optimism construct