Risk, Unexpected Uncertainty, and Estimation Uncertainty: Bayesian Learning in Unstable Settings

Recently, evidence has emerged that humans approach learning using Bayesian updating rather than (model-free) reinforcement algorithms in a six-arm restless bandit problem. Here, we investigate what this implies for human appreciation of uncertainty. In our task, a Bayesian learner distinguishes three equally salient levels of uncertainty. First, the Bayesian perceives irreducible uncertainty or risk: even knowing the payoff probabilities of a given arm, the outcome remains uncertain. Second, there is (parameter) estimation uncertainty or ambiguity: payoff probabilities are unknown and need to be estimated. Third, the outcome probabilities of the arms change: the sudden jumps are referred to as unexpected uncertainty. We document how the three levels of uncertainty evolved during the course of our experiment and how it affected the learning rate. We then zoom in on estimation uncertainty, which has been suggested to be a driving force in exploration, in spite of evidence of widespread aversion to ambiguity. Our data corroborate the latter. We discuss neural evidence that foreshadowed the ability of humans to distinguish between the three levels of uncertainty. Finally, we investigate the boundaries of human capacity to implement Bayesian learning. We repeat the experiment with different instructions, reflecting varying levels of structural uncertainty. Under this fourth notion of uncertainty, choices were no better explained by Bayesian updating than by (model-free) reinforcement learning. Exit questionnaires revealed that participants remained unaware of the presence of unexpected uncertainty and failed to acquire the right model with which to implement Bayesian updating

Multisensory causal inference in the brain

At any given moment, our brain processes multiple inputs from its different sensory modalities (vision, hearing, touch, etc.). In deciphering this array of sensory information, the brain has to solve two problems: (1) which of the inputs originate from the same object and should be integrated and (2) for the sensations originating from the same object, how best to integrate them. Recent behavioural studies suggest that the human brain solves these problems using optimal probabilistic inference, known as Bayesian causal inference. However, how and where the underlying computations are carried out in the brain have remained unknown. By combining neuroimaging-based decoding techniques and computational modelling of behavioural data, a new study now sheds light on how multisensory causal inference maps onto specific brain areas. The results suggest that the complexity of neural computations increases along the visual hierarchy and link specific components of the causal inference process with specific visual and parietal regions

Computations of uncertainty mediate acute stress responses in humans

The effects of stress are frequently studied, yet its proximal causes remain unclear. Here we demonstrate that subjective estimates of uncertainty predict the dynamics of subjective and physiological stress responses. Subjects learned a probabilistic mapping between visual stimuli and electric shocks. Salivary cortisol confirmed that our stressor elicited changes in endocrine activity. Using a hierarchical Bayesian learning model, we quantified the relationship between the different forms of subjective task uncertainty and acute stress responses. Subjective stress, pupil diameter and skin conductance all tracked the evolution of irreducible uncertainty. We observed a coupling between emotional and somatic state, with subjective and physiological tuning to uncertainty tightly correlated. Furthermore, the uncertainty tuning of subjective and physiological stress predicted individual task performance, consistent with an adaptive role for stress in learning under uncertain threat. Our finding that stress responses are tuned to environmental uncertainty provides new insight into their generation and likely adaptive function. Copyright The Authors

Uncertainty in perception and the Hierarchical Gaussian Filter

In its full sense, perception rests on an agent's model of how its sensory input comes about and the inferences it draws based on this model. These inferences are necessarily uncertain. Here, we illustrate how the Hierarchical Gaussian Filter (HGF) offers a principled and generic way to deal with the several forms that uncertainty in perception takes. The HGF is a recent derivation of one-step update equations from Bayesian principles that rests on a hierarchical generative model of the environment and its (in)stability. It is computationally highly efficient, allows for online estimates of hidden states, and has found numerous applications to experimental data from human subjects. In this paper, we generalize previous descriptions of the HGF and its account of perceptual uncertainty. First, we explicitly formulate the extension of the HGF's hierarchy to any number of levels; second, we discuss how various forms of uncertainty are accommodated by the minimization of variational free energy as encoded in the update equations; third, we combine the HGF with decision models and demonstrate the inversion of this combination; finally, we report a simulation study that compared four optimization methods for inverting the HGF/decision model combination at different noise levels. These four methods (Nelder-Mead simplex algorithm, Gaussian process-based global optimization, variational Bayes and Markov chain Monte Carlo sampling) all performed well even under considerable noise, with variational Bayes offering the best combination of efficiency and informativeness of inference. Our results demonstrate that the HGF provides a principled, flexible, and efficient-but at the same time intuitive-framework for the resolution of perceptual uncertainty in behaving agents

Sensitivity and Bias in Decision-Making under Risk: Evaluating the Perception of Reward, Its Probability and Value

BACKGROUND: There are few clinical tools that assess decision-making under risk. Tests that characterize sensitivity and bias in decisions between prospects varying in magnitude and probability of gain may provide insights in conditions with anomalous reward-related behaviour. OBJECTIVE: We designed a simple test of how subjects integrate information about the magnitude and the probability of reward, which can determine discriminative thresholds and choice bias in decisions under risk. DESIGN/METHODS: Twenty subjects were required to choose between two explicitly described prospects, one with higher probability but lower magnitude of reward than the other, with the difference in expected value between the two prospects varying from 3 to 23%. RESULTS: Subjects showed a mean threshold sensitivity of 43% difference in expected value. Regarding choice bias, there was a 'risk premium' of 38%, indicating a tendency to choose higher probability over higher reward. An analysis using prospect theory showed that this risk premium is the predicted outcome of hypothesized non-linearities in the subjective perception of reward value and probability. CONCLUSIONS: This simple test provides a robust measure of discriminative value thresholds and biases in decisions under risk. Prospect theory can also make predictions about decisions when subjective perception of reward or probability is anomalous, as may occur in populations with dopaminergic or striatal dysfunction, such as Parkinson's disease and schizophrenia

Pharmacological Fingerprints of Contextual Uncertainty

Successful interaction with the environment requires flexible updating of our beliefs about the world. By estimating the likelihood of future events, it is possible to prepare appropriate actions in advance and execute fast, accurate motor responses. According to theoretical proposals, agents track the variability arising from changing environments by computing various forms of uncertainty. Several neuromodulators have been linked to uncertainty signalling, but comprehensive empirical characterisation of their relative contributions to perceptual belief updating, and to the selection of motor responses, is lacking. Here we assess the roles of noradrenaline, acetylcholine, and dopamine within a single, unified computational framework of uncertainty. Using pharmacological interventions in a sample of 128 healthy human volunteers and a hierarchical Bayesian learning model, we characterise the influences of noradrenergic, cholinergic, and dopaminergic receptor antagonism on individual computations of uncertainty during a probabilistic serial reaction time task. We propose that noradrenaline influences learning of uncertain events arising from unexpected changes in the environment. In contrast, acetylcholine balances attribution of uncertainty to chance fluctuations within an environmental context, defined by a stable set of probabilistic associations, or to gross environmental violations following a contextual switch. Dopamine supports the use of uncertainty representations to engender fast, adaptive responses. \ua9 2016 Marshall et al

Market Imitation and Win-Stay Lose-Shift Strategies Emerge as Unintended Patterns in Market Direction Guesses.

Decisions made in our everyday lives are based on a wide variety of information so it is generally very difficult to assess what are the strategies that guide us. Stock market provides a rich environment to study how people make decisions since responding to market uncertainty needs a constant update of these strategies. For this purpose, we run a lab-in-the-field experiment where volunteers are given a controlled set of financial information -based on real data from worldwide financial indices- and they are required to guess whether the market price would go "up" or "down" in each situation. From the data collected we explore basic statistical traits, behavioural biases and emerging strategies. In particular, we detect unintended patterns of behavior through consistent actions, which can be interpreted as Market Imitation and Win-Stay Lose-Shift emerging strategies, with Market Imitation being the most dominant. We also observe that these strategies are affected by external factors: the expert advice, the lack of information or an information overload reinforce the use of these intuitive strategies, while the probability to follow them significantly decreases when subjects spends more time to make a decision. The cohort analysis shows that women and children are more prone to use such strategies although their performance is not undermined. Our results are of interest for better handling clients expectations of trading companies, to avoid behavioural anomalies in financial analysts decisions and to improve not only the design of markets but also the trading digital interfaces where information is set down. Strategies and behavioural biases observed can also be translated into new agent based modelling or stochastic price dynamics to better understand financial bubbles or the effects of asymmetric risk perception to price drops

Activity in Inferior Parietal and Medial Prefrontal Cortex Signals the Accumulation of Evidence in a Probability Learning Task

In an uncertain environment, probabilities are key to predicting future events and making adaptive choices. However, little is known about how humans learn such probabilities and where and how they are encoded in the brain, especially when they concern more than two outcomes. During functional magnetic resonance imaging (fMRI), young adults learned the probabilities of uncertain stimuli through repetitive sampling. Stimuli represented payoffs and participants had to predict their occurrence to maximize their earnings. Choices indicated loss and risk aversion but unbiased estimation of probabilities. BOLD response in medial prefrontal cortex and angular gyri increased linearly with the probability of the currently observed stimulus, untainted by its value. Connectivity analyses during rest and task revealed that these regions belonged to the default mode network. The activation of past outcomes in memory is evoked as a possible mechanism to explain the engagement of the default mode network in probability learning. A BOLD response relating to value was detected only at decision time, mainly in striatum. It is concluded that activity in inferior parietal and medial prefrontal cortex reflects the amount of evidence accumulated in favor of competing and uncertain outcomes

Two spatiotemporally distinct value systems shape reward-based learning in the human brain

Avoiding repeated mistakes and learning to reinforce rewarding decisions is critical for human survival and adaptive actions. Yet, the neural underpinnings of the value systems that encode different decision-outcomes remain elusive. Here coupling single-trial electroencephalography with simultaneously acquired functional magnetic resonance imaging, we uncover the spatiotemporal dynamics of two separate but interacting value systems encoding decision-outcomes. Consistent with a role in regulating alertness and switching behaviours, an early system is activated only by negative outcomes and engages arousal-related and motor-preparatory brain structures. Consistent with a role in reward-based learning, a later system differentially suppresses or activates regions of the human reward network in response to negative and positive outcomes, respectively. Following negative outcomes, the early system interacts and downregulates the late system, through a thalamic interaction with the ventral striatum. Critically, the strength of this coupling predicts participants’ switching behaviour and avoidance learning, directly implicating the thalamostriatal pathway in reward-based learning

Confidence and psychosis: a neuro-computational account of contingency learning disruption by NMDA blockade.

A state of pathological uncertainty about environmental regularities might represent a key step in the pathway to psychotic illness. Early psychosis can be investigated in healthy volunteers under ketamine, an NMDA receptor antagonist. Here, we explored the effects of ketamine on contingency learning using a placebo-controlled, double-blind, crossover design. During functional magnetic resonance imaging, participants performed an instrumental learning task, in which cue-outcome contingencies were probabilistic and reversed between blocks. Bayesian model comparison indicated that in such an unstable environment, reinforcement learning parameters are downregulated depending on confidence level, an adaptive mechanism that was specifically disrupted by ketamine administration. Drug effects were underpinned by altered neural activity in a fronto-parietal network, which reflected the confidence-based shift to exploitation of learned contingencies. Our findings suggest that an early characteristic of psychosis lies in a persistent doubt that undermines the stabilization of behavioral policy resulting in a failure to exploit regularities in the environment.FV was supported by the Groupe Pasteur Mutualité. RG was supported by the Fondation pour la Recherche Médicale and the Fondation Bettencourt Schueller. SP is supported by a Marie Curie Intra-European fellowship (FP7-PEOPLE-2012-IEF). AF was supported by National Health and Medical Research Council grants (IDs : 1050504 and 1066779) and an Australian Research Council Future Fellowship (ID: FT130100589). This work was supported by the Wellcome Trust and the Bernard Wolfe Health Neuroscience Fund.This is the final version of the article. It first appeared from the Nature Publishing Group via http://dx.doi.org/10.1038/mp.2015.7