The core tenet of Bayesian modeling is that subjects represent beliefs as distributions over possible hypotheses. Such models have fruitfully been applied to the study of learning in the context of animal conditioning experiments (and analogously designed human learning tasks), where they explain phenomena such as retrospective revaluation that seem to demonstrate that subjects entertain multiple hypotheses simultaneously. However, a recent quantitative analysis of individual subject records by Gallistel and colleagues cast doubt on a very broad family of conditioning models by showing that all of the key features the models capture about even simple learning curves are artifacts of averaging over subjects. Rather than smooth learning curves (which Bayesian models interpret as revealing the gradual tradeoff from prior to posterior as data accumulate), subjects acquire suddenly, and their predictions continue to fluctuate abruptly. These data demand revisiting the model of the individual versus the ensemble, and also raise the worry that more sophisticated behaviors thought to support Bayesian models might also emerge artifactually from averaging over the simpler behavior of individuals. We suggest that the suddenness of changes in subjects ’ beliefs (as expressed in conditioned behavior) can be modeled by assuming they are conducting inference using sequential Monte Carlo sampling with a small number of samples — one, in our simulations. Ensemble behavior resembles exact Bayesian models since, as in particle filters, it averages over many samples. Further, the model is capable of exhibiting sophisticated behaviors like retrospective revaluation at the ensemble level, even given minimally sophisticated individuals that do not track uncertainty from trial to trial. These results point to the need for more sophisticated experimental analysis to test Bayesian models, and refocus theorizing on the individual, while at the same time clarifying why the ensemble may be of interest. 1

A scheme is described for locally Bayesian parameter updating in models structured as successions of component functions. The essential idea is to back-propagate the target data to interior modules, such that an interior component’s target is the input to the next component that maximizes the probability of the next component’s target. Each layer then does locally Bayesian learning. The approach assumes online trial-by-trial learning. The resulting parameter updating is not globally Bayesian but can better capture human behavior. The approach is implemented for an associative learning model that first maps inputs to attentionally filtered inputs and then maps attentionally filtered inputs to outputs. The Bayesian updating allows the associative model to exhibit retrospective revaluation effects such as backward blocking and unovershadowing, which have been challenging for associative learning models. The back-propagation of target values to attention allows the model to show trial-order effects, including highlighting and differences in magnitude of forward and backward blocking, which have been challenging for Bayesian learning models.

We develop a framework based on Bayesian model averaging to explain how animals cope with uncertainty about contingencies in classical conditioning experiments. Traditional accounts of conditioning fit parameters within a fixed generative model of reinforcer delivery; uncertainty over the model structure is not considered. We apply the theory to explain the puzzling relationship between second-order conditioning and conditioned inhibition, two similar conditioning regimes that nonetheless result in strongly divergent behavioral outcomes. According to the theory, second-order conditioning results when limited experience leads animals to prefer a simpler world model that produces spurious correlations; conditioned inhibition results when a more complex model is justified by additional experience. 1

The authors present their primary value learned value (PVLV) model for understanding the rewardpredictive firing properties of dopamine (DA) neurons as an alternative to the temporal-differences (TD) algorithm. PVLV is more directly related to underlying biology and is also more robust to variability in the environment. The primary value (PV) system controls performance and learning during primary rewards, whereas the learned value (LV) system learns about conditioned stimuli. The PV system is essentially the Rescorla–Wagner/delta-rule and comprises the neurons in the ventral striatum/nucleus accumbens that inhibit DA cells. The LV system comprises the neurons in the central nucleus of the amygdala that excite DA cells. The authors show that the PVLV model can account for critical aspects of the DA firing data, making a number of clear predictions about lesion effects, several of which are consistent with existing data. For example, first- and second-order conditioning can be anatomically dissociated, which is consistent with PVLV and not TD. Overall, the model provides a biologically plausible framework for understanding the neural basis of reward learning.

Bayesian treatments of animal conditioning start from a generative model that specifies precisely a set of assumptions about the structure of the learning task. Optimal rules for learning are direct mathematical consequences of these assumptions. In terms of Marr’s (1982) levels of analyses, the main task at the computational level

This article is concerned with trial-by-trial, online learning of cue-outcome mappings. In models structured as successions of component functions, an external target can be backpropagated such that the lower layer’s target is the input to the higher layer that maximizes the probability of the higher layer’s target. Each layer then does locally Bayesian learning. The resulting parameter updating is not globally Bayesian, but can better capture human behavior. The approach is implemented for an associative learning model that first maps inputs to attentionally filtered inputs, and then maps attentionally filtered inputs to outputs. The model is applied to the humanlearning phenomenon called highlighting, which is challenging to other extant Bayesian models, including the rational model of Anderson, the Kalman filter model of Dayan and

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A. Redish et al. (2007) proposed a reinforcement learning model of context-dependent learning and extinction in conditioning experiments, using the idea of “state classification ” to categorize new observations into states. In the current article, the authors propose an interpretation of this idea in terms of normative statistical inference. They focus on renewal and latent inhibition, 2 conditioning paradigms in which contextual manipulations have been studied extensively, and show that online Bayesian inference within a model that assumes an unbounded number of latent causes can characterize a diverse set of behavioral results from such manipulations, some of which pose problems for the model of Redish et al. Moreover, in both paradigms, context dependence is absent in younger animals, or if hippocampal lesions are made prior to training. The authors suggest an explanation in terms of a restricted capacity to infer new causes.

In numerous and high-profile studies, researchers have recently begun to integrate computational models

Multiple cue probability learning studies have typically focused on stationary environments. We present three experiments investigating learning in changing environments. A fine-grained analysis of the learning dynamics shows that participants were responsive to both abrupt and gradual changes in cue-outcome relations. We found no evidence that participants adapted to these types of change in qualitatively different ways. Also, in contrast to earlier claims that these tasks are learned implicitly, participants showed good insight into what they learned. By fitting formal learning models, we investigated whether participants learned global functional relationships or made localized predictions from similar experienced exemplars. Both a local (the Associative Learning Model) and a global learning model (the novel Bayesian Linear Filter) fitted the data of the first two experiments. However, the results of Experiment 3, which was specifically designed to discriminate between local and global learning models, provided more support for global learning models. Finally, we present a novel model to account for the cue competition effects found in previous research and displayed by some of our participants.