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A micro-genesis account of longer-form reinforcement learning in structured and unstructured environments

Abstract

We explored the possibility that in order for longer-form expressions of reinforcement learning (win-calmness, loss-restlessness) to manifest across tasks, they must first develop because of micro-transactions within tasks. We found no evidence of win-calmness or loss-restlessness when wins could not be maximised (unexploitable opponents), nor when the threat of win minimisation was presented (exploiting opponents), but evidence of win-calmness (but not loss-restlessness) when wins could be maximised (exploitable opponents).

Introduction

Behaviour is dynamically shaped via the reinforcement learning (operant conditioning) principles of win-stay and lose-shift1. The tendency to repeat actions that produce positive outcomes, and, to change actions that produce negative outcomes are fundamentally important associations. First, these close (i.e., trial n-1 on trial n) outcome-action bonds have a stronger effect on performance than any other higher-order bonds (e.g., trial n-2 on trial n; see2,3,4). Second, relatively simple win-stay/lose-shift models can outperform more complex reinforcement learning models in accounting for human performance5,6,7. Third, the ability to explicitly represent outcome-action associations that are close in time and space acknowledges the limitations of our cognitive system8,9,10. Therefore, focusing on the immediate association between current outcome and future action is both robust and plausible, from a human information-processing perspective.

Nevertheless, longer-form reinforcement learning principles have been identified that extend the associative chain between multiple outcomes and actions. Specifically, (ref. 11 p. 1102) identified gain-calmness as the “decreased choice switching following prior tasks producing gains” and loss-restlessness as the “increased tendency to switch choices following prior tasks with losses.” Described in this way, gain-calmness and loss-restlessness represent longer-term effects between tasks whereby the degree of historic success or failure produces shockwaves that determine future performance, with win-stay and lose-shift mechanisms remaining central. Here we explore the possibility that in order for gain-calmness and loss-restlessness to manifest between tasks, these effects must be available at the end of the previous task, and as such, must develop because of micro-transactions within tasks.

Across ten experiments, we used the game Rock, Paper, Scissors (RPS) to test a micro-genesis account of these longer-form reinforcement-learning principles at both a group and individual level. Simple zero-sum games offer a high degree of experimental control, move beyond the restrictions of one-shot responding by allowing for an investigation of repeated decision-making12,13, and, can often be fun to play14. Furthermore, RPS represents an intriguing, non-binary paradigm in terms of its relation with traditionally dominant forces of behavioural modification. Specifically, reward mechanisms tend to shape behaviour to a greater degree than punishment mechanisms12,15, such that win-stay selections are more frequent than lose-shift within certain simple games (see16 in the context of cooperative games, see17 in the context of Matching Pennies). However, RPS can yield an over-use of lose-shift relative to win-stay behaviour18,19,20,21.

Specifically, we operationalise calmness as two stay responses (once between trial n-2 and n-1, and, then again between trial n-1 and n) and restlessness as two shift responses (once between trial n-2 and n-1, and, then again between trial n-1 and n) within a block of trials. Thus, evidence for gain-calmness is observed at the micro-level if the proportion of calmness (stay-stay) is highest when the outcome of trial n-2 is a win. Similarly, evidence for loss-restlessness is observed at a micro-level if the proportion of restlessness (switch-switch) is highest when the outcome of trial n-2 is a loss.

In Experiments 1–4, we created game spaces where a computerised opponent operated in accordance with a variant of mixed-strategy, guaranteeing unexploitability. This represented an initially unstructured learning environment in which the average win rate would centre on the baseline value determined by the game (i.e., Rock, Paper, Scissors = 33.3%). Since this baseline value is expected regardless of how the participant behaves, standard law of effect mechanisms (win-stay, lose-shift;1) should not operate. This further echoes the caveat that participants need to experience reliable gains or losses (i.e., different from baseline) for gain-calmness and loss-restlessness to take effect11. Therefore, we should not see any evidence of longer-form stay or shift behaviour determined by trial n-2 outcome against unexploitable opponents, where win rates cannot reliably deviate from baseline. Importantly, participants never encountered any other form of opponent in these studies. Thus, Experiments 1–4 serve as a benchmark as to the degree to which calmness and / or restlessness is produced by prior outcome when win rates cannot be maximised.

Participants were rejected from analysis if they failed to exhibit all combinations of trial n-2 outcome (win, lose, draw) x trial n-1 behaviour (stay, shift; missing data prevents the use of a within-participants analysis). Of the initial sample of 148, 145 data sets (97.97%) were retained. In accordance with the unexploitable nature of the opponent, the observed win rate across the sample of 33.01% (95% CI [32.39%, 33.62%]) was not significantly different from the expected win rate of 33.33% (t[144] = −1.03, p = 0.304, d = −0.08; one-sample t-test). With respect to the proportion of trials representing calmness (here, x stay – stay), a one-way repeated-measures ANOVA was conducted where x represents wins, losses and draws, a main effect was shown: F(2,288) = 6.76, MSE = 0.024, p = 0.001, ƞp2 = 0.045. Tukey’s HSD (p < 0.05) revealed that calmness was significantly less likely following wins (26.61%) relative to both losses (33.09%) and draws (30.97%; see Fig. 1A). With respect to the proportion of trials representing restlessness (here, x shift-shift) where, again, x represents wins, losses and draws, a main effect was again shown: F(2,288) = 28.47, MSE = 0.002, p < 0.001, ƞp2 = 0.165. Tukey’s HSD (p < 0.05) revealed that restlessness was significantly less likely following losses (34.29%) relative to both wins (38.28%) and draws (36.68%). Therefore, neither win-calmness nor loss-restlessness were apparent under conditions against an unexploitable opponent where win rates could not be maximised.

Fig. 1: Proportion of calmness (stay – stay) and restlessness (shift – shift) behaviour between trial n-2 to n-1, and, trial n-1 to n as a function of outcome at trial n-2 (win, lose, draw), and the nature of opponency.
figure1

Error bars represent standard error. Group performance is represented when participants engaged with A unexploitable opponents only, B unexploitable opponents in the context of other opponents, and C exploitable and exploiting opponents.

Experiment 5–10 consisted of participants completing 2 blocks against an unexploitable opponent (defined as per Experiments 1–4) and either 2 blocks against an exploiting opponent (Experiments 5, 7, 9), or, 2 blocks against an exploitable opponent (Experiments 6, 8, 10). We operationalized an exploiting opponent as one who would take advantage of periodic item biases expressed by the participant, and, an exploitable opponent as one who expressed an item bias themselves. This allowed us to answer two further questions. First, we attempt to replicate the absence of win-calmness and loss-restlessness as a result of unexploitable opponency, but within the larger context of other opponent types. Whether the nature of opponency bled into unexploitable contexts was deemed a critical consideration, given the putative cross-task expression of win-stay and lose-shift mechanics11,14. Second, we assessed the degree of win-calmness and loss-restlessness within structured learning environments where win rates could decrease or increase from baseline via engagement with exploiting (threat of win minimisation) and exploitable (promise of win maximisation) opponency, respectively. If any form of win rate deviation from baseline was sufficient for the expression of calmness or restlessness, then we should see such behaviour in evidence irrespective of whether the opponent is exploiting or exploitable. However, if only deflated (inflated) win rate determines win-calmness and loss-restlessness, then such behaviour should only be observed in the case of exploiting (exploitable) opponents.

A total of 208 participants were initially available for analysis from exploiting (n = 100) and exploitable (n = 108) experiments. From this initial sample, 84.13% (n = 175) were retained for calmness and restless analysis for unexploitable opponents, in accordance with the criteria specified for Experiments 1–4. Observed win rates against unexploitable opponents were not significantly difference between the two contexts (32.94% [95% CI [31.43%, 42.85%]] vs. 32.96% [95% CI [29.66%, 39.66%]]): t[173] = −0.50, p = 0.959, d = 0.006 (two-sided, independent t-test). Once again, in accordance with unexploitable opponency, neither was significantly different from 33.33% (t[81] = −0.98, p = 0.328, d = −0.107, and, t[92] = −1.04, p = 0.300, d = −0.109; one-sampled t-test).

First, we examined unexploitable opponency in the context of other opponents. Calmness (here, x stay – stay) was once again assessed using the within-participant factor of outcome (x: win, lose and draw) and the between-participant factor of context (exploiting, exploitable) using a mixed ANOVA. A significant main effect of context: F(1,173) = 12.94, MSE = 0.084, p < 0.001, ƞp2 = 0.070 revealed increased calmness against unexploitable opponent during exploitable (40.26%) relative to exploiting (31.14%) contexts. This is clear evidence of win-calmness transferring from an exploitable opponent to an unexploitable opponent11. The significant main effect of outcome: F(2,346) = 5.71, MSE = 0.017, p = 0.004, ƞp2 = 0.032, replicated the observation that calmness was significantly less likely following wins (33.35%) relative to both losses(37.69%) and draws (36.91%). There was no significant interaction: F(2,346) = 1.80, MSE = 0.017, p = 0.167, ƞp2 = 0.010 (see Fig. 1B).

Restlessness (here, x shift - shift) was analysed in a similar way, revealing only a main effect of outcome: F(2,348) = 35.67, MSE = 0.002, p < 0.001, ƞp2 = 0.170. Again, restlessness was significantly less likely following losses (32.71%) relative to both wins (36.76%) and draws (35.96%; Tukey’s HSD, p < 0.05). Neither the main effect of context: F(1,174) = 2.64, MSE = 0.010, p = 0.106, ƞp2 = 0.015, nor the interaction: F(2,348) = 1.24, MSE = 0.002, p = 0.291, ƞp2 = 0.007, were significant (see Fig. 1B). Collectively, these data replicate the observations from Experiment 1–4, in that under conditions where win rate minimisation was threatened, neither win-calmness nor loss-restlessness were apparent.

Second, we directly compared performance between exploiting and exploitable opponents. 75.48% (n = 157) of data were retained for subsequent analysis. Win rates were significantly different between exploiting (34.18% [95% CI [33.92%, 46.06%]) and exploitable (43.78% [95% CI [58.82%, 81.72%]) opponents: t[155] = 10.98, p < 0.001, d = 1.321 (two-sided, independent t-test). Exploiting (t[83] = 2.06, p = 0.042, d = 0.226) and exploitable (t[72] = 11.65, p < 0.001, d = 1.527) opponent win rates were different from the expected baseline value of 33.33%. Calmness (stay – stay) behaviour was examined as a function of the within-participants factor outcome (win, lose, draw), and, the between-participants factor opponent (exploiting, exploitable) using a mixed ANOVA. The main effect of opponency was significant: F(1,155) = 60.26, MSE = 0.090, p < 0.001, ƞp2 = 0.280, the main effect of outcome was not significant: F (2,310) = 0.94, MSE = 0.018, p = 0.391, ƞp2 = 0.006, and, there was a significant interaction between opponency x outcome: F(2,310) = 11.86, MSE = 0.018, p < 0.001, ƞp2 = 0.071. Calmness was significantly higher against exploitable (50.71%) versus exploiting (29.16%) opponents. The interaction was caused by calmness being numerically less likely following wins (25.88%) relative to losses (31.67%) and draws (29.94%) against exploiting opponents (Tukey’s HSD, p > 0.05), but significantly more likely following wins (56.05%) relative to both losses (48.30%) and draws (47.78%) against exploitable opponents (Tukey’s HSD, p < 0.05; see Fig. 1C).

A similar analysis using restlessness (shift - shift) showed a significant main effect of opponent: F(1,155) = 9.07, MSE = 0.009, p = 0.003, ƞp2 = 0.055, a significant main effect of outcome: F(2,310) = 58.67, MSE = 0.002, p < 0.001, ƞp2 = 0.275, but no interaction: F(2,310) = 2.42, MSE = 0.002, p = 0.091, ƞp2 = 0.015. Here, restlessness was greater during exploiting opponents (35.62%) relative to exploitable opponents (33.00%). As in all other analyses, restlessness was also significantly less likely following losses (31.44%) relative to both wins (37.32%) and draws (34.43%).

According to11, longer-form reinforcement learning associations may arise where tendencies to repeat responding are facilitated by previous exposure to success (win-calmness), whereas tendencies to change responding are facilitated by previous exposure to failure (loss-restlessness). We tested a micro-genesis account of these longer-form associations by analysing the contingencies between trial triplets (n-2, n-1, n) within blocks and as a function of opponency.

We reliably saw that when individuals worked in unstructured learning environments where win rates could not be maximised, neither win-calmness nor loss-restlessness were in evidence. In fact, the data generated by exclusively unexploitable contexts is best characterised as lose-calmness and win-restlessness. One possibility is that these longer-form reinforcement learning principles are inhibited when standard law-of-effect mechanisms cannot operate (see also unexploitable opponent (exploiting context), exploiting opponent; Fig. 1), resulting in weak expression of the opposite direction. When unexploitable opponents were encountered in the context of other exploiting opponents, the latter did not influence behaviour against the former (see Fig. 1B, solid line). However, when unexploitable opponents were played in the context of other exploitable opponents, the degree of calmness rose (see Fig. 1B, dotted line). This shows that the promise of win maximisation—rather than the threat of win minimisation—allows for cognitive transactions across blocks. Fundamental differences between human cognition as a function of win maximisation (rather than win minimisation) was further manifest in the direct comparison between exploiting and exploitable opponents. Here, exploiting opponents yielded data equivalent to that generated by unexploitable opponents: lose-calmness and win-restlessness (see Fig. 1C, solid line). In stark contrast, when the promise of win maximisation was available via exposure to exploitable opponents, win-calmness was clearly in evidence at the micro-level (see Fig. 1C, dotted line).

To further support win maximisation as the mechanism by which longer-form reinforcement learning expressions were manifest, we examined performance across all 10 experiments (n = 357) at an individual level. Here, the degree of win-calmness and loss-restlessness was correlated with win rate across the five categories of opponency (unexploitable, unexploitable in the context of exploiting, unexploitable in the context of exploitable, exploiting, exploitable; see Fig. 2A–E). Only against exploitable opponents do we observe a positive correlation between win-calmness and win rate (r = 0.631, p < 0.001), and, a negative correlation between loss-restlessness and win rate (r = −0.339, p = 0.003). Moreover, the difference between these correlations was also significantly different (z = 6.48, p < 0.001).

Fig. 2: Scatterplots of win-calmness (stay – stay) and loss-restlessness (shift – shift) behaviour as a function of individual win rate, and the nature of opponency.
figure2

Individual performance is represented when participants engaged with A unexploitable opponents only, B unexploitable opponents in the context of exploiting opponents, C unexploitable opponents in the context of exploitable opponents, D exploiting opponents, and E exploitable opponents. Only correlations with win rate against exploitable opponents were significant win-calmness (r = 0.631, p < 0.001), loss-restlessness (r = −0.339, p = 0.003).

In sum, the expression of longer-form behavioural calmness and restlessness is the result of micro-transactions between trials in accordance with classic reinforcement learning principles of win-stay and lose-shift. That calmness and restlessness manifest under different opponent contexts (see Fig. 1) and are differentially impacted by win rate (see Fig. 2) at both group and individual levels, is consistent with the multiple anatomical22, evolutionary10,23 and behavioural2 observations that win-stay and lose-shift are independent.

Specifically, periods of behavioural inertia because of success (win-calmness) are much more apparent (and more closely tied to individual win rate experience) than periods of behavioural reconfiguration following failure (loss-restlessness). That it should be so. The organism may enjoy the repetition of their opponent’s exploitation during success in structured learning environments that afford success, but must engage in explorative behaviour when the mental model of opponent exploitation is elusive24 or they themselves run the risk of exploitation.

Further research will require identifying which characteristics of the decision-making space allow for (a) violations of win-calmness and loss-restlessness during unsuccessful win maximisation, and (b) provide evidence for win-calmness (but not loss-restlessness) during successful win maximisation. For example25, emphasizes the importance of the kind of structural information participants are provided prior to the game. In contrast16, note that patterns of data regarding win-stay / lose-shift dominance within a cooperative game are largely independent of group size. Similarly, we might speculate whether there is something unique about binary (i.e., 2 response) versus non-binary (i.e., 3+ response) decision-making paradigms. In particular, we need to consider whether win-stay preponderance is more likely within binary response games whereas lose-shift is more likely within non-binary response games, and, the degree to which restricted choice maps onto aspects of real-world decision-making13. Our forthcoming work related to the comparison of structurally isomorphic 3 vs. 5, and, 2 vs. 6 response games should in part help to illuminate game characteristics that play a fundamental role in determining both short- and long-form reinforcement learning principles.

Methods

Experiments 1–4

Data from 148 participants were reanalysed from (18 Experiment 1) (19 Experiment 1), (20 Experiment 1) and21. See Table 1 for demographic information and block x trial structure. All studies were approved by the Life Sciences and Psychology Research Ethics Committee (C-REC) at the University of Sussex (ER/BJD21/3, ER/BJD21/4), or, Research Ethics Board 2 at the University of Alberta (PRO00083768, PRO00086116). Participants from refs. 19,21 provided informed consent from the University of Sussex community, and received either course credit or £20 for participation. Performance-independent compensation was offered as behavioural data were collected in the context of a longer electroencephalographic study. Participants from refs. 18,20 were recruited from the undergraduate community at the University of Alberta as part of the Psychology Research Participation scheme, and received performance-independent course credit.

Table 1 Summary statistics from those individuals who volunteered demographic information across experiments 1–10. Standard deviation in brackets.

The game Rock, Paper, Scissors represents a competitive, two-player game where each player must select one of three possible responses. When played physically, these responses are variations in hand shape: Rock (closed fist), Paper (flat hand), Scissors (index and middle fingers extended and separated). In the current computerised version of the game, participants selected a key that represented one of these three responses. The rules of the game dictate that if both players select the same response, then the round results in a draw. However, players can win or lose following the additional rules that Rock beats Scissors, Scissors beats Paper, and, Paper beats Rock. Thus, if the responses differ between players, one individual will win and one individual will lose.

In all cases, participants played Rock, Paper, Scissors against an unexploitable opponent where wins, losses and draws were assigned the numeric value +1, −1 and 0, respectively. Unexploitability was operationalized by distributing Rock, Paper, Scissors responses equally across the block size (33.3%) but in random order. Pictures of two gloved hands representing the 9 interactions between participant and opponent during Rock, Paper, Scissors were used (approximate on-screen size 10.5 cm x 4 cm). Stimulus presentation and response monitoring was conducted by Presentation software.

Experiment 5–10

Experiment 5–10 consisted of participants completing 2 blocks against an unexploitable opponent (defined as per Experiments 1–4) and either 2 blocks against an exploiting opponent (Experiments 5, 7, 9), or, 2 blocks against an exploitable opponent (Experiments 6, 8, 10). Conditions were presented across participants in a counterbalanced order, dictated by a Latin square design. In both exploiting blocks, the computer would generate a response matrix inverse to the participant’s response selections every 3 trials (after20). For example, if the participants played Rock on the first 3 trials, the computer would play Paper on the next 3 trials and so on. In both exploitable blocks, the computer expressed the same bias for one of the items (66.67%), with the specific item bias also counterbalanced across participants. Additional manipulations involving display information in Experiments 5–10 were collapsed for the purposes of this analysis. All studies were approved by the Research Ethics Board 2 at the University of Alberta (PRO00087988). Participants provided informed consent from the undergraduate community at the University of Alberta as part of the Psychology Research Participation scheme, and received performance-independent course credit.

Following response selection, RPS selections were displayed for opponent (on the left; blue glove) and / or participant (on the right; white glove) for 1000 ms. This display was removed for 500 ms and then the outcome of the trial was presented for 1000 ms in the form of ‘WIN’ (+1; green font), ‘LOSS’ (−1; red font), or ‘DRAW’ (0; yellow font) as appropriate. The outcome was removed and the player’s score was updated across a 500 ms period, after which the next trial began with a response selection prompt.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability

The authors declare that the data supporting the findings of this study are available within the supplementary information files.

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Acknowledgements

The authors would like to thank Rimsa Dahal, Kelsey MacLellan, Noah Mitchell and Danielle Vavrek for assistance with data collection. The studies were funded by an NSERC Discovery Grant (RGPIN-2019-04954), an Alberta Gambling Research Grant, and start-up monies provided by the University of Alberta (RES0042096).

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B.J.D. designed the studies. A.A. analysed the data. B.J.D. and A.A. wrote the manuscript.

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Correspondence to Benjamin James Dyson.

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Dyson, B.J., Asad, A. A micro-genesis account of longer-form reinforcement learning in structured and unstructured environments. npj Sci. Learn. 6, 19 (2021). https://doi.org/10.1038/s41539-021-00098-4

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