The interpretation of computational model parameters depends on the context
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Evaluation Summary:
Eckstein and colleagues take a within-participant approach to answer two critical questions in the field of human reinforcement learning: to what extent do estimated computational model parameters generalize across different tasks and can their meaning be interpreted in the same way in different task contexts? The authors find that inferred parameters show moderate to little generalizability across tasks, and that their interpretation strongly depends on task context. Support for these claims could be further strengthened through additional simulations and by providing greater methodological detail.
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Abstract
Reinforcement Learning (RL) models have revolutionized the cognitive and brain sciences, promising to explain behavior from simple conditioning to complex problem solving, to shed light on developmental and individual differences, and to anchor cognitive processes in specific brain mechanisms. However, the RL literature increasingly reveals contradictory results, which might cast doubt on these claims. We hypothesized that many contradictions arise from two commonly-held assumptions about computational model parameters that are actually often invalid: That parameters generalize between contexts (e.g. tasks, models) and that they capture interpretable (i.e. unique, distinctive) neurocognitive processes. To test this, we asked 291 participants aged 8–30 years to complete three learning tasks in one experimental session, and fitted RL models to each. We found that some parameters (exploration / decision noise) showed significant generalization: they followed similar developmental trajectories, and were reciprocally predictive between tasks. Still, generalization was significantly below the methodological ceiling. Furthermore, other parameters (learning rates, forgetting) did not show evidence of generalization, and sometimes even opposite developmental trajectories. Interpretability was low for all parameters. We conclude that the systematic study of context factors (e.g. reward stochasticity; task volatility) will be necessary to enhance the generalizability and interpretability of computational cognitive models.
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Author Response
Reviewer #1 (Public Review):
In computational modeling studies of behavioral data using reinforcement learning models, it has been implicitly assumed that parameter estimates generalize across tasks (generalizability) and that each parameter reflects a single cognitive function (interpretability). In this study, the authors examined the validity of these assumptions through a detailed analysis of experimental data across multiple tasks and age groups. The results showed that some parameters generalize across tasks, while others do not, and that interpretability is not sufficient for some parameters, suggesting that the interpretation of parameters needs to take into account the context of the task. Some researchers may have doubted the validity of these assumptions, but to my knowledge, no study has explicitly …
Author Response
Reviewer #1 (Public Review):
In computational modeling studies of behavioral data using reinforcement learning models, it has been implicitly assumed that parameter estimates generalize across tasks (generalizability) and that each parameter reflects a single cognitive function (interpretability). In this study, the authors examined the validity of these assumptions through a detailed analysis of experimental data across multiple tasks and age groups. The results showed that some parameters generalize across tasks, while others do not, and that interpretability is not sufficient for some parameters, suggesting that the interpretation of parameters needs to take into account the context of the task. Some researchers may have doubted the validity of these assumptions, but to my knowledge, no study has explicitly examined their validity. Therefore, I believe this research will make an important contribution to researchers who use computational modeling. In order to clarify the significance of this research, I would like the authors to consider the following points.
- Effects of model misspecification
In general, model parameter estimates are influenced by model misspecification. Specifically, if components of the true process are not included in the model, the estimates of other parameters may be biased. The authors mentioned a little about model misspecification in the Discussion section, but they do not mention the possibility that the results of this study itself may be affected by it. I think this point should be discussed carefully.
The authors stated that they used state-of-the-art RL models, but this does not necessarily mean that the models are correctly specified. For example, it is known that if there is history dependence in the choice itself and it is not modeled properly, the learning rates depending on valence of outcomes (alpha+, alpha-) are subject to biases (Katahira, 2018, J Math Pscyhol). In the authors' study, the effect of one previous choice was included in the model as choice persistence, p. However, it has been pointed out that not including the effect of a choice made more than two trials ago in the model can also cause bias (Katahira, 2018). The authors showed taht the learning rate for positive RPE, alpha+ was inconsistent across tasks. But since choice persistence was included only in Task B, it is possible that the bias of alpha+ was different between tasks due to individual differences in choice persistence, and thus did not generalize.
However, I do not believe that it is necessary to perform a new analysis using the model described above. As for extending the model, I don't think it is possible to include all combinations of possible components. As is often said, every model is wrong, and only to varying degrees. What I would like to encourage the authors to do is to discuss such issues and then consider their position on the use of the present model. Even if the estimation results of this model are affected by misspecification, it is a fact that such a model is used in practice, and I think it is worthwhile to discuss the nature of the parameter estimates.
We thank the reviewer for this thoughtful question, and have added the following paragraph to the discussion section that is aims to address it:
“Another concern relates to potential model misspecification and its effects on model parameter estimates: If components of the true data-generating process are not included in a model (i.e., a model is misspecified), estimates of existing model parameters may be biased. For example, if choices have an outcome-independent history dependence that is not modeled properly, learning rate parameters have shown to be biased [63]. Indeed, we found that learning rate parameters were inconsistent across the tasks in our study, and two of our models (A and C) did not model history dependence in choice, while the third (model B) only included the effect of one previous choice (persistence parameter), but no multi-trial dependencies. It is hence possible that the differences in learning rate parameters between tasks were caused by differences in the bias induced by misspecification of history dependence, rather than a lack of generalization. Though pressing, however, this issue is difficult to resolve in practicality, because it is impossible to include all combinations of possible parameters in all computational models, i.e., to exhaustively search the space of possible models ("Every model is wrong, but to varying degrees"). Furthermore, even though our models were likely affected by some degree of misspecification, the research community is currently using models of this kind. Our study therefore sheds light on generalizability and interpretability in a realistic setting, which likely includes models with varying degrees of misspecification. Lastly, our models were fitted using robust computational tools and achieved good behavioral recovery (Fig. D.7), which also reduces the likelihood of model misspecification.“
- Issue of reliability of parameter estimates
I think it is important to consider not only the bias in the parameter estimates, but also the issue of reliability, i.e., how stable the estimates will be when the same task is repeated with the same individual. For the task used in this study, has test-retest reliability been examined in previous studies? I think that parameters with low reliability will inevitably have low generalizability to other tasks. In this study, the use of three tasks seems to have addressed this issue without explicitly considering the reliability, but I would like the author to discuss this issue explicitly.
We thank the reviewer for this useful comment, and have added the following paragraph to the discussion section to address it:
“Furthermore, parameter generalizability is naturally bounded by parameter reliability, i.e., the stability of parameter estimates when participants perform the same task twice (test-retest reliability) or when estimating parameters from different subsets of the same dataset (split-half reliability). The reliability of RL models has recently become the focus of several parallel investigations [...], some employing very similar tasks to ours [...]. The investigations collectively suggest that excellent reliability can often be achieved with the right methods, most notably by using hierarchical model fitting. Reliability might still differ between tasks or models, potentially being lower for learning rates than other RL parameters [...], and differing between tasks (e.g., compare [...] to [...]). In this study, we used hierarchical fitting for tasks A and B and assessed a range of qualitative and quantitative measures of model fit for each task [...], boosting our confidence in high reliability of our parameter estimates, and the conclusion that the lack of between-task parameter correlations was not due to a lack of parameter reliability, but a lack of generalizability. This conclusion is further supported by the fact that larger between-task parameter correlations (r>0.5) than those observed in humans were attainable---using the same methods---in a simulated dataset with perfect generalization.“
- About PCA
In this paper, principal component analysis (PCA) is used to extract common components from the parameter estimates and behavioral features across tasks. When performing PCA, were each parameter estimate and behavioral feature standardized so that the variance would be 1? There was no mention about this. It seems that otherwise the principal components would be loaded toward the features with larger variance. In addition, Moutoussis et al. (Neuron, 2021, 109 (12), 2025-2040) conducted a similar analysis of behavioral parameters of various decision-making tasks, but they used factor analysis instead of PCA. Although the authors briefly mentioned factor analysis, it would be better if they also mentioned the reason why they used PCA instead of factor analysis, which can consider unique variances.
To answer the reviewer's first question: We indeed standardized all features before performing the PCA. Apologies for missing to include this information - we have now added a corresponding sentence to the methods sections.
We also thank the reviewer for the mentioned reference, which is very relevant to our findings and can help explain the roles of different PCs. Like in our study, Moutoussis et al. found a first PC that captured variability in task performance, and subsequent PCs that captured task contrasts. We added the following paragraph to our manuscript:
“PC1 therefore captured a range of "good", task-engaged behaviors, likely related to the construct of "decision acuity" [...]. Like our PC1, decision acuity was the first component of a factor analysis (variant of PCA) conducted on 32 decision-making measures on 830 young people, and separated good and bad performance indices. Decision acuity reflects generic decision-making ability, and predicted mental health factors, was reflected in resting-state functional connectivity, but was distinct from IQ [...].”
To answer the reviewer's question about PCA versus FA, both approaches are relatively similar conceptually, and oftentimes share the majority of the analysis pipeline in practice. The main difference is that PCA breaks up the existing variance in a dataset in a new way (based on PCs rather than the original data features), whereas FA aims to identify an underlying model of latent factors that explain the observable features. This means that PCs are linear combinations of the original data features, whereas Factors are latent factors that give rise to the observable features of the dataset with some noise, i.e., including an additional error term.
However, in practice, both methods share the majority of computation in the way they are implemented in most standard statistical packages: FA is usually performed by conducting a PCA and then rotating the resulting solution, most commonly using the Varimax rotation, which maximizes the variance between features loadings on each factor in order to make the result more interpretable, and thereby foregoing the optimal solution that has been achieved by the PCA (which lack the error term). Maximum variance in feature loadings means that as many features as possible will have loadings close to 0 and 1 on each factor, reducing the number of features that need to be taken into account when interpreting this factor. Most relevant in our situation is that PCA is usually a special case of FA, with the only difference that the solution is not rotated for maximum interpretability. (Note that this rotation can be minor if feature loadings already show large variance in the PCA solution.)
To determine how much our results would change in practice if we used FA instead of PCA, we repeated the analysis using FA. Both are shown side-by-side below, and the results are quite similar:
We therefore conclude that our specific results are robust to the choice of method used, and that there is reason to believe that our PC1 is related to Moutoussis et al.’s F1 despite the differences in method.
Reviewer #2 (Public Review):
I am enthusiastic about the comprehensive approach, the thorough analysis, and the intriguing findings. This work makes a timely contribution to the field and warrants a wider discussion in the community about how computational methods are deployed and interpreted. The paper is also a great and rare example of how much can be learned from going beyond a meta-analytic approach to systematically collect data that assess commonly held assumptions in the field, in this case in a large data-driven study across multiple tasks. My only criticism is that at times, the paper misses opportunities to be more constructive in pinning down exactly why authors observe inconsistencies in parameter fits and interpretation. And the somewhat pessimistic outlook relies on some results that are, in my view at least, somewhat expected based on what we know about human RL. Below I summarize the major ways in which the paper's conclusions could be strengthened.
One key point the authors make concerns the generalizability of absolute vs. relative parameter values. It seems that at least in the parameter space defined by +LRs and exploration/noise (which are known to be mathematically coupled), subjects clustered similarly for tasks A and C. In other words, as the authors state, "both learning rate and inverse temperature generalized in terms of the relationships they captured between participants". This struck me as a more positive and important result than it was made out to be in the paper, for several reasons:
- As authors point out in the discussion, a large literature on variable LRs has shown that people adapt their learning rates trial-by-trial to the reward function of the environment; given this, and given that all models tested in this work have fixed learning rates, while the three tasks vary on the reward function, the comparison of absolute values seems a bit like a red-herring.
We thank the reviewers for this recommendation and have reworked the paper substantially to address the issue. We have modified the highlights, abstract, introduction, discussion, conclusion, and relevant parts of the results section to provide equal weight to the successes and failures of generalization.
Highlights:
● “RL decision noise/exploration parameters generalize in terms of between-participant variation, showing similar age trajectories across tasks.”
● “These findings are in accordance with previous claims about the developmental trajectory of decision noise/exploration parameters.”
Abstract:
● “We found that some parameters (exploration / decision noise) showed significant generalization: they followed similar developmental trajectories, and were reciprocally predictive between tasks.“
The introduction now introduces different potential outcomes of our study with more equal weight:
“Computational modeling enables researchers to condense rich behavioral datasets into simple, falsifiable models (e.g., RL) and fitted model parameters (e.g., learning rate, decision temperature) [...]. These models and parameters are often interpreted as a reflection of ("window into") cognitive and/or neural processes, with the ability to dissect these processes into specific, unique components, and to measure participants' inherent characteristics along these components.
For example, RL models have been praised for their ability to separate the decision making process into value updating and choice selection stages, allowing for the separate investigation of each dimension. Crucially, many current research practices are firmly based on these (often implicit) assumptions, which give rise to the expectation that parameters have a task- and model-independent interpretation and will seamlessly generalize between studies. However, there is growing---though indirect---evidence that these assumptions might not (or not always) be valid.
The following section lays out existing evidence in favor and in opposition of model generalizability and interpretability. Building on our previous opinion piece, which---based on a review of published studies---argued that there is less evidence for model generalizability and interpretability than expected based on current research practices [...], this study seeks to directly address the matter empirically.”
We now also provide more even evidence for both potential outcomes:
“Many current research practices are implicitly based on the interpretability and generalizability of computational model parameters (despite the fact that many researchers explicitly distance themselves from these assumptions). For our purposes, we define a model variable (e.g., fitted parameter, reward-prediction error) as generalizable if it is consistent across uses, such that a person would be characterized with the same values independent of the specific model or task used to estimate the variable. Generalizability is a consequence of the assumption that parameters are intrinsic to participants rather than task dependent (e.g., a high learning rate is a personal characteristic that might reflect an individual's unique brain structure). One example of our implicit assumptions about generalizability is the fact that we often directly compare model parameters between studies---e.g., comparing our findings related to learning-rate parameters to a previous study's findings related to learning-rate parameters. Note that such a comparison is only valid if parameters capture the same underlying constructs across studies, tasks, and model variations, i.e., if parameters generalize. The literature has implicitly equated parameters in this way in review articles [...], meta-analyses [...], and also most empirical papers, by relating parameter-specific findings across studies. We also implicitly evoke parameter generalizability when we study task-independent empirical parameter priors [...], or task-independent parameter relationships (e.g., interplay between different kinds of learning rates [...]), because we presuppose that parameter settings are inherent to participants, rather than task specific.
We define a model variable as interpretable if it isolates specific and unique cognitive elements, and/or is implemented in separable and unique neural substrates. Interpretability follows from the assumption that the decomposition of behavior into model parameters "carves cognition at its joints", and provides fundamental, meaningful, and factual components (e.g., separating value updating from decision making). We implicitly invoke interpretability when we tie model variables to neural substrates in a task-general way (e.g., reward prediction errors to dopamine function [...]), or when we use parameters as markers of psychiatric conditions (e.g., working-memory parameter and schizophrenia [...]). Interpretability is also required when we relate abstract parameters to aspects of real-world decision making [...], and generally, when we assume that model variables are particularly "theoretically meaningful" [...].
However, in midst the growing recognition of computational modeling, the focus has also shifted toward inconsistencies and apparent contradictions in the emerging literature, which are becoming apparent in cognitive [...], developmental [...], clinical [...], and neuroscience studies [...], and have recently become the focus of targeted investigations [...]. For example, some developmental studies have shown that learning rates increased with age [...], whereas others have shown that they decrease [...]. Yet others have reported U-shaped trajectories with either peaks [...] or troughs [...] during adolescence, or stability within this age range [...] (for a comprehensive review, see [...]; for specific examples, see [...]). This is just one striking example of inconsistencies in the cognitive modeling literature, and many more exist [...]. These inconsistencies could signify that computational modeling is fundamentally flawed or inappropriate to answer our research questions. Alternatively, inconsistencies could signify that the method is valid, but our current implementations are inappropriate [...]. However, we hypothesize that inconsistencies can also arise for a third reason: Even if both method and implementation are appropriate, inconsistencies like the ones above are expected---and not a sign of failure---if implicit assumptions of generalizability and interpretability are not always valid. For example, model parameters might be more context-dependent and less person-specific that we often appreciate [...]“
In the results section, we now highlight findings more that are compatible with generalization: “For α+, adding task as a predictor did not improve model fit, suggesting that α+ showed similar age trajectories across tasks (Table 2). Indeed, α+ showed a linear increase that tapered off with age in all tasks (linear increase: task A: β = 0.33, p < 0.001; task B: β = 0.052, p < 0.001; task C: β = 0.28, p < 0.001; quadratic modulation: task A: β = −0.007, p < 0.001; task B: β = −0.001, p < 0.001; task C: β = −0.006, p < 0.001). For noise/exploration and Forgetting parameters, adding task as a predictor also did not improve model fit (Table 2), suggesting similar age trajectories across tasks.”
“For both α+ and noise/exploration parameters, task A predicted tasks B and C, and tasks B and C predicted task A, but tasks B and C did not predict each other (Table 4; Fig. 2D), reminiscent of the correlation results that suggested successful generalization (section 2.1.2).”
“Noise/exploration and α+ showed similar age trajectories (Fig. 2C) in tasks that were sufficiently similar (Fig. 2D).” And with respect to our simulation analysis (for details, see next section):
“These results show that our method reliably detected parameter generalization in a dataset that exhibited generalization. ”
We also now provide more nuance in our discussion of the findings:
“Both generalizability [...] and interpretability (i.e., the inherent "meaningfulness" of parameters) [...] have been explicitly stated as advantages of computational modeling, and many implicit research practices (e.g., comparing parameter-specific findings between studies) showcase our conviction in them [...]. However, RL model generalizability and interpretability has so far eluded investigation, and growing inconsistencies in the literature potentially cast doubt on these assumptions. It is hence unclear whether, to what degree, and under which circumstances we should assume generalizability and interpretability. Our developmental, within-participant study revealed a nuanced picture: Generalizability and interpretability differed from each other, between parameters, and between tasks.”
“Exploration/noise parameters showed considerable generalizability in the form of correlated variance and age trajectories. Furthermore, the decline in exploration/noise we observed between ages 8-17 was consistent with previous studies [13, 66, 67], revealing consistency across tasks, models, and research groups that supports the generalizability of exploration / noise parameters. However, for 2/3 pairs of tasks, the degree of generalization was significantly below the level of generalization expected for perfect generalization. Interpretability of exploration / noise parameters was mixed: Despite evidence for specificity in some cases (overlap in parameter variance between tasks), it was missing in others (lack of overlap), and crucially, parameters lacked distinctiveness (substantial overlap in variance with other parameters).”
“Taken together, our study confirms the patterns of generalizable exploration/noise parameters and task-specific learning rate parameters that are emerging from the literature [13].”
- Regarding the relative inferred values, it's unclear how high we really expect correlations between the same parameter across tasks to be. E.g., if we take Task A and make a second, hypothetical, Task B by varying one feature at a time (say, stochasticity in reward function), how correlated are the fitted LRs going to be? Given the different sources of noise in the generative model of each task and in participant behavior, it is hard to know whether a correlation coefficient of 0.2 is "good enough" generalizability.
We thank the reviewer for this excellent suggestion, which we think helped answer a central question that our previous analyses had failed to address, and also provided answers to several other concerns raised by both reviewers in other section. We have conducted these additional analyses as suggested, simulating artificial behavioral data for each task, fitting these data using the models used in humans, repeating the analyses performed on humans on the new fitted parameters, and using bootstrapping to statistically compare humans to the hence obtained ceiling of generalization. We have added the following section to our paper, which describes the results in detail:
“Our analyses so far suggest that some parameters did not generalize between tasks, given differences in age trajectories (section 2.1.3) and a lack of mutual prediction (section 2.1.4). However, the lack of correspondence could also arise due to other factors, including behavioral noise, noise in parameter fitting, and parameter trade-offs within tasks. To rule these out, we next established the ceiling of generalizability attainable using our method.
We established the ceiling in the following way: We first created a dataset with perfect generalizability, simulating behavior from agents that use the same parameters across all tasks (suppl. Appendix E). We then fitted this dataset in the same way as the human dataset (e.g., using the same models), and performed the same analyses on the fitted parameters, including an assessment of age trajectories (suppl. Table E.8) and prediction between tasks (suppl. Tables E.9, E.10, and E.11). These results provide the practical ceiling of generalizability. We then compared the human results to this ceiling to ensure that the apparent lack of generalization was valid (significant difference between humans and ceiling), and not in accordance with generalization (lack of difference between humans and ceiling).
Whereas humans had shown divergent trajectories for parameter alpha- (Fig. 2B; Table 1), the simulated agents did not show task differences for alpha- or any other parameter (suppl. Fig E.8B; suppl. Table E.8, even when controlling for age (suppl. Tables E.9 and E.10), as expected from a dataset of generalizing agents. Furthermore, the same parameters were predictive between tasks in all cases (suppl. Table E.11). These results show that our method reliably detected parameter generalization in a dataset that exhibited generalization.
Lastly, we established whether the degree of generalization in humans was significantly different from agents. To this aim, we calculated the Spearman correlations between each pair of tasks for each parameter, for both humans (section 2.1.2; suppl. Fig. H.9) and agents, and compared both using bootstrapped confidence intervals (suppl. Appendix E). Human parameter correlations were significantly below the ceiling for all parameters except alpha+ (A vs B) and epsilon / 1/beta (A vs C; suppl. Fig. E.8C). This suggests that humans were within the range of maximally detectable generalization in two cases, but showed less-than-perfect generalization between other task combinations and for parameters Forgetting and alpha-.”
- The +LR/inverse temp relationship seems to generalize best between tasks A/C, but not B/C, a common theme in the paper. This does not seem surprising given that in A and C there is a key additional task feature over the bandit task in B -- which is the need to retain state-action associations. Whether captured via F (forgetting) or K (WM capacity), the cognitive processes involved in this learning might interact with LR/exploration in a different way than in a task where this may not be necessary.
We thank the reviewer for this comment, which raises an important issue. We are adding the specific pairwise correlations and scatter plots for the pairs of parameters the reviewer asked about below (“bf_alpha” = LR task A; “bf_forget” = F task A; “rl_forget” = F task C; “rl_log_alpha” = LR task C; “rl_K” = WM capacity task C):
Within tasks:
Between tasks:
To answer the question in more detail, we have expanded our section about limitations stemming from parameter tradeoffs in the following way:
“One limitation of our results is that regression analyses might be contaminated by parameter cross-correlations (sections 2.1.2, 2.1.3, 2.1.4), which would reflect modeling limitations (non-orthogonal parameters), and not necessarily shared cognitive processes. For example, parameters alpha and beta are mathematically related in the regular RL modeling framework, and we observed significant within-task correlations between these parameters for two of our three tasks (suppl. Fig. H.10, H.11). This indicates that caution is required when interpreting correlation results. However, correlations were also present between tasks (suppl. Fig. H.9, H.11), suggesting that within-model trade-offs were not the only explanation for shared variance, and that shared cognitive processes likely also played a role.
Another issue might arise if such parameter cross-correlations differ between models, due to the differences in model parameterizations across tasks. For example, memory-related parameters (e.g., F, K in models A and C) might interact with learning- and choice-related parameters (e.g., alpha+, alpha-, noise/exploration), but such an interaction is missing in models that do not contain memory-related parameters (e.g., task B). If this indeed the case, i.e., parameters trade off with each other in different ways across tasks, then a lack of correlation between tasks might not reflect a lack of generalization, but just the differences in model parameterizations. Suppl. Fig. \ref{figure:S2AlphaBetaCorrelations} indeed shows significant, medium-sized, positive and negative correlations between several pairs of Forgetting, memory-related, learning-related, and exploration parameters (though with relatively small effect sizes; Spearman correlation: 0.17 < |r| < 0.22).
The existence of these correlations (and differences in correlations between tasks) suggest that memory parameters likely traded off with each other, as well as with other parameters, which potentially affected generalizability across tasks. However, some of the observed correlations might be due to shared causes, such as a common reliance on age, and the regression analyses in the main paper control for these additional sources of variance, and might provide a cleaner picture of how much variance is actually shared between parameters.
Furthermore, correlations between parameters within models are frequent in the existing literature, and do not prevent researchers from interpreting parameters---in this sense, the existence of similar correlations in our study allows us to address the question of generalizability and interpretability in similar circumstances as in the existing literature.”
- More generally, isn't relative generalizability the best we would expect given systematic variation in task context? I agree with the authors' point that the language used in the literature sometimes implies an assumption of absolute generalizability (e.g. same LR across any task). But parameter fits, interactions, and group differences are usually interpreted in light of a single task+model paradigm, precisely b/c tasks vary widely across critical features that will dictate whether different algorithms are optimal or not and whether cognitive functions such as WM or attention may compensate for ways in which humans are not optimal. Maybe a more constructive approach would be to decompose tasks along theoretically meaningful features of the underlying Markov Decision Process (which gives a generative model), and be precise about (1) which features we expect will engage additional cognitive mechanisms, and (2) how these mechanisms are reflected in model parameters.
We thank the reviewer for this comment, and will address both points in turn:
(1) We agree with the reviewer's sentiment about relative generalizability: If we all interpreted our models exclusively with respect to our specific task design, and never expected our results to generalize to other tasks or models, there would not be a problem. However, the current literature shows a different pattern: Literature reviews, meta-analyses, and discussion sections of empirical papers regularly compare specific findings between studies. We compare specific parameter values (e.g., empirical parameter priors), parameter trajectories over age, relationships between different parameters (e.g., balance between LR+ and LR-), associations between parameters and clinical symptoms, and between model variables and neural measures on a regular basis. The goal of this paper was really to see if and to what degree this practice is warranted. And the reviewer rightfully alerted us to the fact that our data imply that these assumptions might be valid in some cases, just not in others.
(2) With regard to providing task descriptions that relate to the MDP framework, we have included the following sentence in the discussion section:
“Our results show that discrepancies are expected even with a consistent methodological pipeline, and using up-to-date modeling techniques, because they are an expected consequence of variations in experimental tasks and computational models (together called "context"). Future research needs to investigate these context factors in more detail. For example, which task characteristics determine which parameters will generalize and which will not, and to what extent? Does context impact whether parameters capture overlapping versus distinct variance? A large-scale study could answer these questions by systematically covering the space of possible tasks, and reporting the relationships between parameter generalizability and distance between tasks. To determine the distance between tasks, the MDP framework might be especially useful because it decomposes tasks along theoretically meaningful features of the underlying Markov Decision Process.“
Another point that merits more attention is that the paper pretty clearly commits to each model as being the best possible model for its respective task. This is a necessary premise, as otherwise, it wouldn't be possible to say with certainty that individual parameters are well estimated. I would find the paper more convincing if the authors include additional information and analysis showing that this is actually the case.
We agree with the sentiment that all models should fit their respective task equally well. However, there is no good quantitative measure of model fit that is comparable across tasks and models - for example, because of the difference in difficulty between the tasks, the number of choices explained would not be a valid measure to compare how well the models are doing across tasks. To address this issue, we have added the new supplemental section (Appendix C) mentioned above that includes information about the set of models compared, and explains why we have reason to believe that all models fit (equally) well. We also created the new supplemental Figure D.7 shown above, which directly compares human and simulated model behavior in each task, and shows a close correspondence for all tasks. Because the quality of all our models was a major concern for us in this research, we also refer the reviewer and other readers to the three original publications that describe all our modeling efforts in much more detail, and hopefully convince the reviewer that our model fitting was performed according to high standards.
I am particularly interested to see whether some of the discrepancies in parameter fits can be explained by the fact that the model for Task A did not account for explicit WM processes, even though (1) Task A is similar to Task C (Task A can be seen as a single condition of Task C with 4 states and 2 possible visible actions, and stochastic rather than deterministic feedback) and (2) prior work has suggested a role for explicit memory of single episodes even in stateless bandit tasks such as Task B.
We appreciate this very thoughtful question, which raises several important issues. (1) As the reviewer said, the models for task A and task C are relatively different even though the underlying tasks are relatively similar (minus the differences the reviewer already mentioned, in terms of visibility of actions, number of actions, and feedback stochasticity). (2) We also agree that the model for task C did not include episodic memory processes even though episodic memory likely played a role in this task, and agree that neither the forgetting parameters in tasks A and C, nor the noise/exploration parameters in tasks A, B, and C are likely specific enough to capture all the memory / exploration processes participants exhibited in these tasks.
However, this problem is difficult to solve: We cannot fit an episodic-memory model to task B because the task lacks an episodic-memory manipulation (such as, e.g., in Bornstein et al., 2017), and we cannot fit a WM model to task A because it lacks the critical set-size manipulation enabling identification of the WM component (modifying set size allows the model to identify individual participants’ WM capacities, so the issue cannot be avoided in tasks with only one set size). Similarly, we cannot model more specific forgetting or exploration processes in our tasks because they were not designed to dissociate these processes. If we tried fitting more complex models that include these processes to these tasks, they would most likely lose in model comparison because the increased complexity would not lead to additional explained behavioral variance, given that the tasks do not elicit the relevant behavioral patterns. Because the models therefore do not specify all the cognitive processes that participants likely employ, the situation described by the reviewer arises, namely that different parameters sometimes capture the same cognitive processes across tasks and models, while the same parameters sometimes capture different processes.
And while the reviewer focussed largely on memory-related processes, the issue of course extends much further: Besides WM, episodic memory, and more specific aspects of forgetting and exploration, our models also did not take into account a range of other processes that participants likely engaged in when performing the tasks, including attention (selectivity, lapses), reasoning / inference, mental models (creation and use), prediction / planning, hypothesis testing, etc., etc. In full agreement with the reviewer’s sentiment, we recently argued that this situation is ubiquitous to computational modeling, and should be considered very carefully by all modelers because it can have a large impact on model interpretation (Eckstein et al., 2021).
If we assume that many more cognitive processes are likely engaged in each task than are modeled, and consider that every computational model includes just a small number of free parameters, parameters then necessarily reflect a multitude of cognitive processes. The situation is additionally exacerbated by the fact that more complex models become increasingly difficult to fit from a methodological perspective, and that current laboratory tasks are designed in a highly controlled and consequently relatively simplistic way that does not lend itself to simultaneously test a variety of cognitive processes.
The best way to deal with this situation, we think, is to recognize that in different contexts (e.g., different tasks, different computational models, different subject populations), the same parameters can capture different behaviors, and different parameters can capture the same behaviors, for the reasons the reviewer lays out. Recognizing this helps to avoid misinterpreting modeling results, for example by focusing our interpretation of model parameters to our specific task and model, rather than aiming to generalize across multiple tasks. We think that recognizing this fact also helps us understand the factors that determine whether parameters will capture the same or different processes across contexts and whether they will generalize. This is why we estimated here whether different parameters generalize to different degrees, which other factors affect generalizability, etc. Knowing the practical consequences of using the kinds of models we currently use will therefore hopefully provide a first step in resolving the issues the reviewer laid out.
It is interesting that one of the parameters that generalizes least is LR-. The authors make a compelling case that this is related to a "lose-stay" behavior that benefits participants in Task B but not in Task C, which makes sense given the probabilistic vs deterministic reward function. I wondered if we can rule out the alternative explanation that in Task C, LR- could reflect a different interpretation of instructions vis. a vis. what rewards indicate - do authors have an instruction check measure in either task that can be correlated with this "lose-stay" behavior and with LR-? And what does the "lose-stay" distribution look like, for Task C at least? I basically wonder if some of these inconsistencies can be explained by participants having diverging interpretations of the deterministic nature of the reward feedback in Task C. The order of tasks might matter here as well -- was task order the same across participants? It could be that due to the within-subject design, some participants may have persisted in global strategies that are optimal in Task B, but sub-optimal in Task C.
The PCA analysis adds an interesting angle and a novel, useful lens through which we can understand divergence in what parameters capture across different tasks. One observation is that loadings for PC2 and PC3 are strikingly consistent for Task C, so it looks more like these PCs encode a pairwise contrast (PC2 is C with B and PC2 is C with A), primarily reflecting variability in performance - e.g. participants who did poorly on Task C but well on Task B (PC2) or Task A (PC3). Is it possible to disentangle this interpretation from the one in the paper? It also is striking that in addition to performance, the PCs recover the difference in terms of LR- on Task B, which again supports the possibility that LR- divergence might be due to how participants handle probabilistic vs. deterministic feedback.
We appreciate this positive evaluation of our PCA and are glad that it could provide a useful lens for understanding parameters. We also agree to the reviewer's observation that PC2 and PC3 reflect task contrasts (PC2: task B vs task C; PC3: task A vs task C), and phrase it in the following way in the paper:
“PC2 contrasted task B to task C (loadings were positive / negative / near-zero for corresponding features of tasks B / C / A; Fig. 3B). PC3 contrasted task A to both B and C (loadings were positive / negative for corresponding features on task A / tasks B and C; Fig. 3C).”
Hence, the only difference between our interpretation and the reviewer’s seems to be whether PC3 contrasts task C to task B as well as task A, or just to task A. Our interpretation is supported by the fact that loadings for tasks A and C are quite similar on PC3; however, both interpretations seem appropriate.
We also appreciate the reviewer's positive evaluation of the fact that the PCA reproduces the differences in LR-, and its relationship to probabilistic/deterministic feedback. The following section reiterates this idea:
“alpha- loaded positively in task C, but negatively in task B, suggesting that performance increased when participants integrated negative feedback faster in task C, but performance decreased when they did the same in task B. As mentioned before, contradictory patterns of alpha- were likely related to task demands: The fact that negative feedback was diagnostic in task C likely favored fast integration of negative feedback, while the fact that negative feedback was not diagnostic in task B likely favored slower integration (Fig. 1E). This interpretation is supported by behavioral findings: "Lose-stay" behavior (repeating choices that produce negative feedback) showed the same contrasting pattern as alpha- on PC1. It loaded positively in task B, showing Lose-stay behavior benefited performance, but it loaded negatively on task C, showing that it hurt performance (Fig. 3A). This supports the claim that lower alpha- was beneficial in task B, while higher alpha- was beneficial in task C, in accordance with participant behavior and developmental differences.“
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Evaluation Summary:
Eckstein and colleagues take a within-participant approach to answer two critical questions in the field of human reinforcement learning: to what extent do estimated computational model parameters generalize across different tasks and can their meaning be interpreted in the same way in different task contexts? The authors find that inferred parameters show moderate to little generalizability across tasks, and that their interpretation strongly depends on task context. Support for these claims could be further strengthened through additional simulations and by providing greater methodological detail.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #2 agreed to share their name …
Evaluation Summary:
Eckstein and colleagues take a within-participant approach to answer two critical questions in the field of human reinforcement learning: to what extent do estimated computational model parameters generalize across different tasks and can their meaning be interpreted in the same way in different task contexts? The authors find that inferred parameters show moderate to little generalizability across tasks, and that their interpretation strongly depends on task context. Support for these claims could be further strengthened through additional simulations and by providing greater methodological detail.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #2 agreed to share their name with the authors.)
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Reviewer #1 (Public Review):
In computational modeling studies of behavioral data using reinforcement learning models, it has been implicitly assumed that parameter estimates generalize across tasks (generalizability) and that each parameter reflects a single cognitive function (interpretability). In this study, the authors examined the validity of these assumptions through a detailed analysis of experimental data across multiple tasks and age groups. The results showed that some parameters generalize across tasks, while others do not, and that interpretability is not sufficient for some parameters, suggesting that the interpretation of parameters needs to take into account the context of the task. Some researchers may have doubted the validity of these assumptions, but to my knowledge, no study has explicitly examined their validity. …
Reviewer #1 (Public Review):
In computational modeling studies of behavioral data using reinforcement learning models, it has been implicitly assumed that parameter estimates generalize across tasks (generalizability) and that each parameter reflects a single cognitive function (interpretability). In this study, the authors examined the validity of these assumptions through a detailed analysis of experimental data across multiple tasks and age groups. The results showed that some parameters generalize across tasks, while others do not, and that interpretability is not sufficient for some parameters, suggesting that the interpretation of parameters needs to take into account the context of the task. Some researchers may have doubted the validity of these assumptions, but to my knowledge, no study has explicitly examined their validity. Therefore, I believe this research will make an important contribution to researchers who use computational modeling. In order to clarify the significance of this research, I would like the authors to consider the following points.
1. Effects of model misspecification
In general, model parameter estimates are influenced by model misspecification. Specifically, if components of the true process are not included in the model, the estimates of other parameters may be biased. The authors mentioned a little about model misspecification in the Discussion section, but they do not mention the possibility that the results of this study itself may be affected by it. I think this point should be discussed carefully.
The authors stated that they used state-of-the-art RL models, but this does not necessarily mean that the models are correctly specified. For example, it is known that if there is history dependence in the choice itself and it is not modeled properly, the learning rates depending on valence of outcomes (alpha+, alpha-) are subject to biases (Katahira, 2018, J Math Pscyhol). In the authors' study, the effect of one previous choice was included in the model as choice persistence, p. However, it has been pointed out that not including the effect of a choice made more than two trials ago in the model can also cause bias (Katahira, 2018). The authors showed taht the learning rate for positive RPE, alpha+ was inconsistent across tasks. But since choice persistence was included only in Task B, it is possible that the bias of alpha+ was different between tasks due to individual differences in choice persistence, and thus did not generalize.
However, I do not believe that it is necessary to perform a new analysis using the model described above. As for extending the model, I don't think it is possible to include all combinations of possible components. As is often said, every model is wrong, and only to varying degrees. What I would like to encourage the authors to do is to discuss such issues and then consider their position on the use of the present model. Even if the estimation results of this model are affected by misspecification, it is a fact that such a model is used in practice, and I think it is worthwhile to discuss the nature of the parameter estimates.
2. Issue of reliability of parameter estimates
I think it is important to consider not only the bias in the parameter estimates, but also the issue of reliability, i.e., how stable the estimates will be when the same task is repeated with the same individual. For the task used in this study, has test-retest reliability been examined in previous studies? I think that parameters with low reliability will inevitably have low generalizability to other tasks. In this study, the use of three tasks seems to have addressed this issue without explicitly considering the reliability, but I would like the author to discuss this issue explicitly.
3. About PCA
In this paper, principal component analysis (PCA) is used to extract common components from the parameter estimates and behavioral features across tasks. When performing PCA, were each parameter estimate and behavioral feature standardized so that the variance would be 1? There was no mention about this. It seems that otherwise the principal components would be loaded toward the features with larger variance. In addition, Moutoussis et al. (Neuron, 2021, 109 (12), 2025-2040) conducted a similar analysis of behavioral parameters of various decision-making tasks, but they used factor analysis instead of PCA. Although the authors briefly mentioned factor analysis, it would be better if they also mentioned the reason why they used PCA instead of factor analysis, which can consider unique variances.
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Reviewer #2 (Public Review):
I am enthusiastic about the comprehensive approach, the thorough analysis, and the intriguing findings. This work makes a timely contribution to the field and warrants a wider discussion in the community about how computational methods are deployed and interpreted. The paper is also a great and rare example of how much can be learned from going beyond a meta-analytic approach to systematically collect data that assess commonly held assumptions in the field, in this case in a large data-driven study across multiple tasks. My only criticism is that at times, the paper misses opportunities to be more constructive in pinning down exactly why authors observe inconsistencies in parameter fits and interpretation. And the somewhat pessimistic outlook relies on some results that are, in my view at least, somewhat …
Reviewer #2 (Public Review):
I am enthusiastic about the comprehensive approach, the thorough analysis, and the intriguing findings. This work makes a timely contribution to the field and warrants a wider discussion in the community about how computational methods are deployed and interpreted. The paper is also a great and rare example of how much can be learned from going beyond a meta-analytic approach to systematically collect data that assess commonly held assumptions in the field, in this case in a large data-driven study across multiple tasks. My only criticism is that at times, the paper misses opportunities to be more constructive in pinning down exactly why authors observe inconsistencies in parameter fits and interpretation. And the somewhat pessimistic outlook relies on some results that are, in my view at least, somewhat expected based on what we know about human RL. Below I summarize the major ways in which the paper's conclusions could be strengthened.
One key point the authors make concerns the generalizability of absolute vs. relative parameter values. It seems that at least in the parameter space defined by +LRs and exploration/noise (which are known to be mathematically coupled), subjects clustered similarly for tasks A and C. In other words, as the authors state, "both learning rate and inverse temperature generalized in terms of the relationships they captured between participants". This struck me as a more positive and important result than it was made out to be in the paper, for several reasons:
- As authors point out in the discussion, a large literature on variable LRs has shown that people adapt their learning rates trial-by-trial to the reward function of the environment; given this, and given that all models tested in this work have fixed learning rates, while the three tasks vary on the reward function, the comparison of absolute values seems a bit like a red-herring.
- Regarding the relative inferred values, it's unclear how high we really expect correlations between the same parameter across tasks to be. E.g., if we take Task A and make a second, hypothetical, Task B by varying one feature at a time (say, stochasticity in reward function), how correlated are the fitted LRs going to be? Given the different sources of noise in the generative model of each task and in participant behavior, it is hard to know whether a correlation coefficient of 0.2 is "good enough" generalizability.
- The +LR/inverse temp relationship seems to generalize best between tasks A/C, but not B/C, a common theme in the paper. This does not seem surprising given that in A and C there is a key additional task feature over the bandit task in B -- which is the need to retain state-action associations. Whether captured via F (forgetting) or K (WM capacity), the cognitive processes involved in this learning might interact with LR/exploration in a different way than in a task where this may not be necessary.
- More generally, isn't relative generalizability the best we would expect given systematic variation in task context? I agree with the authors' point that the language used in the literature sometimes implies an assumption of absolute generalizability (e.g. same LR across *any* task). But parameter fits, interactions, and group differences are usually interpreted in light of a single task+model paradigm, *precisely b/c* tasks vary widely across critical features that will dictate whether different algorithms are optimal or not and whether cognitive functions such as WM or attention may compensate for ways in which humans are not optimal. Maybe a more constructive approach would be to decompose *tasks* along theoretically meaningful features of the underlying Markov Decision Process (which gives a generative model), and be precise about (1) which features we expect will engage additional cognitive mechanisms, and (2) how these mechanisms are reflected in model parameters.
Another point that merits more attention is that the paper pretty clearly commits to each model as being the best possible model *for its respective task*. This is a necessary premise, as otherwise, it wouldn't be possible to say with certainty that individual parameters are well estimated. I would find the paper more convincing if the authors include additional information and analysis showing that this is actually the case. I am particularly interested to see whether some of the discrepancies in parameter fits can be explained by the fact that the model for Task A did not account for explicit WM processes, even though (1) Task A is similar to Task C (Task A can be seen as a single condition of Task C with 4 states and 2 possible visible actions, and stochastic rather than deterministic feedback) and (2) prior work has suggested a role for explicit memory of single episodes even in stateless bandit tasks such as Task B.
It is interesting that one of the parameters that generalizes least is LR-. The authors make a compelling case that this is related to a "lose-stay" behavior that benefits participants in Task B but not in Task C, which makes sense given the probabilistic vs deterministic reward function. I wondered if we can rule out the alternative explanation that in Task C, LR- could reflect a different interpretation of instructions vis. a vis. what rewards indicate - do authors have an instruction check measure in either task that can be correlated with this "lose-stay" behavior and with LR-? And what does the "lose-stay" distribution look like, for Task C at least? I basically wonder if some of these inconsistencies can be explained by participants having diverging interpretations of the deterministic nature of the reward feedback in Task C. The order of tasks might matter here as well -- was task order the same across participants? It could be that due to the within-subject design, some participants may have persisted in global strategies that are optimal in Task B, but sub-optimal in Task C.
The PCA analysis adds an interesting angle and a novel, useful lens through which we can understand divergence in what parameters capture across different tasks. One observation is that loadings for PC2 and PC3 are strikingly consistent for Task C, so it looks more like these PCs encode a pairwise contrast (PC2 is C with B and PC2 is C with A), primarily reflecting variability in performance - e.g. participants who did poorly on Task C but well on Task B (PC2) *or* Task A (PC3). Is it possible to disentangle this interpretation from the one in the paper? It also is striking that in addition to performance, the PCs recover the difference in terms of LR- on Task B, which again supports the possibility that LR- divergence might be due to how participants handle probabilistic vs. deterministic feedback.
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