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## Section: New Results

### Curiosity-Driven Learning in Humans

#### Computational Models Of Information-Seeking and Curiosity-Driven Learning in Human Adults

Participants : Pierre-Yves Oudeyer [correspondant] , Sébastien Forestier, Alexandr Ten.

This project involves a collaboration between the Flowers team and the Cognitive Neuroscience Lab of J. Gottlieb at Columbia Univ. (NY, US), on the understanding and computational modeling of mechanisms of curiosity, attention and active intrinsically motivated exploration in humans.

It is organized around the study of the hypothesis that subjective meta-cognitive evaluation of information gain (or control gain or learning progress) could generate intrinsic reward in the brain (living or artificial), driving attention and exploration independently from material rewards, and allowing for autonomous lifelong acquisition of open repertoires of skills. The project combines expertise about attention and exploration in the brain and a strong methodological framework for conducting experimentations with monkeys, human adults and children together with computational modeling of curiosity/intrinsic motivation and learning.

Such a collaboration paves the way towards a central objective, which is now a central strategic objective of the Flowers team: designing and conducting experiments in animals and humans informed by computational/mathematical theories of information seeking, and allowing to test the predictions of these computational theories.

##### Context

Curiosity can be understood as a family of mechanisms that evolved to allow agents to maximize their knowledge (or their control) of the useful properties of the world - i.e., the regularities that exist in the world - using active, targeted investigations. In other words, we view curiosity as a decision process that maximizes learning/competence progress (rather than minimizing uncertainty) and assigns value ("interest") to competing tasks based on their epistemic qualities - i.e., their estimated potential allow discovery and learning about the structure of the world.

Because a curiosity-based system acts in conditions of extreme uncertainty (when the distributions of events may be entirely unknown) there is in general no optimal solution to the question of which exploratory action to take [108], [130], [141]. Therefore we hypothesize that, rather than using a single optimization process as it has been the case in most previous theoretical work [86], curiosity is comprised of a family of mechanisms that include simple heuristics related to novelty/surprise and measures of learning progress over longer time scales [128] [56], [118]. These different components are related to the subject's epistemic state (knowledge and beliefs) and may be integrated with fluctuating weights that vary according to the task context. Our aim is to quantitatively characterize this dynamic, multi-dimensional system in a computational framework based on models of intrinsically motivated exploration and learning.

Because of its reliance on epistemic currencies, curiosity is also very likely to be sensitive to individual differences in personality and cognitive functions. Humans show well-documented individual differences in curiosity and exploratory drives [106], [140], and rats show individual variation in learning styles and novelty seeking behaviors [80], but the basis of these differences is not understood. We postulate that an important component of this variation is related to differences in working memory capacity and executive control which, by affecting the encoding and retention of information, will impact the individual's assessment of learning, novelty and surprise and ultimately, the value they place on these factors [133], [149], [50], [155]. To start understanding these relationships, about which nothing is known, we will search for correlations between curiosity and measures of working memory and executive control in the population of children we test in our tasks, analyzed from the point of view of a computational models of the underlying mechanisms.

A final premise guiding our research is that essential elements of curiosity are shared by humans and non-human primates. Human beings have a superior capacity for abstract reasoning and building causal models, which is a prerequisite for sophisticated forms of curiosity such as scientific research. However, if the task is adequately simplified, essential elements of curiosity are also found in monkeys [106], [98] and, with adequate characterization, this species can become a useful model system for understanding the neurophysiological mechanisms.

##### Objectives

Our studies have several highly innovative aspects, both with respect to curiosity and to the traditional research field of each member team.

• Linking curiosity with quantitative theories of learning and decision making: While existing investigations examined curiosity in qualitative, descriptive terms, here we propose a novel approach that integrates quantitative behavioral and neuronal measures with computationally defined theories of learning and decision making.

• Linking curiosity in children and monkeys: While existing investigations examined curiosity in humans, here we propose a novel line of research that coordinates its study in humans and non-human primates. This will address key open questions about differences in curiosity between species, and allow access to its cellular mechanisms.

• Neurophysiology of intrinsic motivation: Whereas virtually all the animal studies of learning and decision making focus on operant tasks (where behavior is shaped by experimenter-determined primary rewards) our studies are among the very first to examine behaviors that are intrinsically motivated by the animals' own learning, beliefs or expectations.

• Neurophysiology of learning and attention: While multiple experiments have explored the single-neuron basis of visual attention in monkeys, all of these studies focused on vision and eye movement control. Our studies are the first to examine the links between attention and learning, which are recognized in psychophysical studies but have been neglected in physiological investigations.

• Computer science: biological basis for artificial exploration: While computer science has proposed and tested many algorithms that can guide intrinsically motivated exploration, our studies are the first to test the biological plausibility of these algorithms.

• Developmental psychology: linking curiosity with development: While it has long been appreciated that children learn selectively from some sources but not others, there has been no systematic investigation of the factors that engender curiosity, or how they depend on cognitive traits.

##### Current results: experiments in Active Categorization

Figure 5. Proportion of trials on each task (1D, I1D, 2D, and R). The group with an externally prescribed learning maximization goal is referred to as “Strategic”, and the unconstrained group is referred to as “Free”. 1D was the task were categorization was determined by a single variable dimension. In I1D (ignore 1D), the stimuli varied across 2 dimensions, but only one determined the stimulus category. In 2D, there were 2 variable dimensions and both jointly determined the category. Finally in R, there were 2 variable dimensions, but none of them could reliably predict the stimulus class. The top plot shows data aggregated across experimental groups, shown separately in the bottom plot. In hte figure, task difficulty increases from left to right.
Figure 6. Learning outcomes by group. The group with an externally prescribed learning maximization goal is referred to as “Strategic”, and the unconstrained group is referred to as “Free”. Number of people in the groups are given in parentheses. The figure shows that some people seem to set and pursue learning maximization goals in the absence of external rewards and instructions. Additionally, learning goals have to be matched with appropriate behavioral strategies in order to be reached, which explains the failure to learn all 3 tasks by some people in the Strategic group.

Assuming that task choice decisions are based on a subjective evaluative process that assigns value to choice candidates, we considered a simple choice model of task selection. In a classic conditional logit model [116], choices are made probabilistically and the choice probabilities are proportional to choice utilities (the inherent subjective value of a choice; also see ref [159]). We elaborated on the utility component of the basic choice model to consider two utility aspects of interest: a relative measure of learning progress (LP) and an absolute measure of proportion correct (PC). Although both measures are based on empirical feedback (correct / incorrect), the LP measure is considered relative, because it captures how performance changes over time by comparing performance estimates across different time scales, while PC is absolute in a sense that it only characterizes performance at a given instance. While PC alone does not differentiate between an unfamiliar (but potentially easy) task on which the performance might be low and a familiar but very hard task, the former can have markedly LP (due to the gradual improvement on that task) than the latter. Only the tasks characterized by high LP are then worthy of time and effort if the goal is to master tasks. The utility component in our model thus includes two principal quantities:

${u}_{i,t}=\alpha L{P}_{i,t}+\beta P{C}_{i,t}$

where $\alpha$ and $\beta$ are free parameters indexing the model's sensitivity to LP and PC, respectively. Index $i$ designates the task, while $t$ indexes time. Thus, in our model, utility is seen as a dual-component linear computation of both relative and absolute competence quantities. Task utilities enter the decision-making process that assigns relative preference to each task:

$p\left(tas{k}_{i}\right)=\frac{{e}^{{u}_{i}/\tau }}{{\sum }_{j}{e}^{{u}_{j}/\tau }}$

where $\tau$ is another free parameter (known as temperature) that controls the stochasticity of utility-based decision. The sum over $j$ elements, ${\sum }_{j}$ constitutes the total exponentiated utility of each task in the task space, thus normalizing each individual exponentiated task utility ${u}_{i}$.

The computation of the utility components is important for the model, because it ultimately determines how well the model can fit to choice data. We started exploring the model with a simple definition for both LP and PC. Both components are based on averaging binary feedback over multiple trials in the past. Since the familiarization stage of our experiment was 15-trials-long, the first free choice was made based on feedback data from 15 trials on each task. Accordingly, we defined PC to be the proportion of correct guesses in 15 trials. LP was defined as the absolute difference between the first 9 and the last 6 trials of the recent most 15 trials in the past. While a participant was engaged with one of the tasks, LP and PC for that task changed according to her dynamic performance, while LPs and PCs for other tasks remained unchanged. We acknowledge that there are probably multiple other components at play when it comes to utility computation, some of which may have little to do with task competence. We also submit that there are multiple ways of defining the PC and LP components that are more biologically rooted and plausible given what we know of memory and metacognition. Finally, we do not rule out the possibility of dynamic changes of free parameters themselves, corresponding to changes in motivation during the learning process. All of these considerations are worthy directions of future research, but in this study we focused on finding some necessary evidence for the sensitivity to learning progress.

We fitted the model to each individual's choice data using maximum likelihood estimation. Assuming that choice probabilities on each trial come from a categorical distribution (also called a generalized Bernoulli distribution), where the probability of choosing item $i$ is given by:

$P\left(𝐱\mid 𝐩\right)=\prod _{i=1}^{k}{p}_{i}^{{x}_{i}}$

where p is a vector of probabilities associated with $k$ events, and p is a one-hot encoded vector representing discrete items ${x}_{i}$. We add a time index to indicate the dynamic quality of choice probabilities, so that:

${P}_{t}\left(𝐱\mid {𝐩}_{t}\right)=\prod _{i=1}^{k}{p}_{i,t}^{{x}_{i}}$

Then, the likelihood of the choice model ($p\left(tas{k}_{i}\mid \alpha ,\beta ,\tau \right)$) at time $t$ is equal to the product of choice probabilities given by that model for that time step:

${L}_{t}\left(\alpha ,\beta ,\tau \mid 𝐱\right)=\prod _{i}^{k}{p}_{i,t}^{{x}_{i}}$

and since the empirical choice data can be represented in a one-hot format, the likelihood of the model for a given time point boils down to the predicted probability of the actualy choice:

${L}_{t}\left(\alpha ,\beta ,\tau \mid choice=i\right)={p}_{i,t}=\frac{{e}^{{u}_{i,t}/\tau }}{{\sum }_{j}{e}^{{u}_{j,t}/\tau }}$

The likelihood of the model across all $m$ trials is obtained by applying the product rule of probability:

${L}_{overall}\left(\alpha ,\beta ,\tau \mid choice=i\right)=\prod _{t}^{m}{p}_{i,t}=\frac{{e}^{{u}_{i,t}/\tau }}{{\sum }_{j}{e}^{{u}_{j,t}/\tau }}$

For convenience, we use the negative log transformation to avoid computational precision problems and convert a likelihood maximization objective into negative likelihood minimization problem solvable by publicly accessible optimization tools:

$-log{L}_{overall}\left(\alpha ,\beta ,\tau \mid choice=i\right)=-\sum _{t}^{m}log{p}_{i,t}$

Having formulated the likelihood function, we optimized the free parameters to obtain a model that fits the individual data best. We thus fit an individual-level model to each participant's choice data. The fitted parameters can be interpreted as relative sensitivity to the competence quantities of interest (LP and PC), since these quantities share the same range of values (0 to 1). Finally, we performed some group-level analyses on these individual-level parameter estimates to evaluate certain group-level effects that might influence them (e.g. effect of instruction or learning proficiency).

The group with a learning maximization goal devalued tasks with higher positive feedback expectation. Qualitatively, this matched our prior observations showing their strong preference for harder tasks. However, the best learners (3-task learners) across both instruction groups showed a slight preference for learning progress and a relatively strong aversion to positive feedback. It appears that what separated better and worse learners among the learning maximizers was whether they followed learning progress, and not just the feedback heuristic. On the other hand, while less successful learners in the unconstrained group seemed to choose tasks according to learning progress, they valued positive feedback over it, which prevented them from exploring more challenging learnable tasks. This is reflected in group mean values of the fitted parameters summarized in table 1

We also looked at the relative importance of the utility model parameters by performing model comparisons. We compared 4 models based on combinations of 2 factors: PC and LP. According to the AIC scores (see Table 2), the best model was the one which included both LP and PC factors, followed by the PC-only model, and then by the LP-only model. The random-choice model came in last with the highest AIC score. The results of this model comparison show that both learning progress and positive feedback expectation factors provide substantive improvement to model likelihood compared to when these factors are included alone, or when neither of them is present. This is potentially important, as it provides some evidence for the role of relative competence kind of measure in autonomous exploration. We are planning to submit the work described about to a high impact peer-reviewed journal focusing on computational modeling of human behavior.

#### Experimental study of the role of intrinsic motivation in developmental psychology experiments and in the development of tool use

Participants : Pierre-Yves Oudeyer, Sébastien Forestier [correspondant] , Laurianne Rat-Fisher.

Children are so curious to explore their environment that it can be hard to focus their attention on one given activity. Many experiments in developmental psychology evaluate particular skills of children by setting up a task that the child is encouraged to solve. However, children may sometimes be following their own motivation to explore the experimental setup or other things in the environment. We suggest that considering the intrinsic motivations of children in those experiments could help understanding their role in the learning of related skills and on long-term child development. To illustrate this idea, we reanalyzed and reinterpretd a typical experiment aiming to evaluate particular skills in infants. In this experiment run by Lauriane Rat-Fischer et al, 32 21-month old infants have to retrieve a toy stuck inside a tube, by inserting several blocks in sequence into the tube. In order to understand the mechanisms of the motivations of babies, we studied in detail their behaviors, goals and strategies in this experiment. We showed that their motivations are diverse and do not always coincide with the target goal expected and made salient by the experimenter. Intrinsically motivated exploration seems to play an important role in the observed behaviors and to interfere with the measured success rates. This new interpretation provides a motivation for studying curiosity and intrinsic motivations in robotic models.