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. 2022 Jan 31;6(4):555–564. doi: 10.1038/s41562-021-01263-w

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 2 — a, Item-level learning under full feedback (Exp. 1) simulated with symmetric Model Q1. Top, exemplary evolution of item values Q (a.u.) over trials. Bottom, simulated probability of making a correct choice for each item pairing (aggregated across all trials in the top panel). b, Simulated task performance (mean proportion correct choices on the second half of the trials) of asymmetric Model Q2 across different learning rates α⁺ (winning items) and α⁻ (losing items). For values on the diagonal (dashed white line), Q2 is equivalent to Q1. The black dot indicates parameters used for the simulation of symmetric learning in a. The red triangle indicates parameters used for the simulation of asymmetric learning in c. c, Same as a, but using Model Q2 with asymmetric learning rates. d, Same as a, but for Model Q1* in a partial-feedback scenario (Exps. 2–4). e,f, Same as b and c, but using model Q2* under partial feedback. Note that asymmetric learning leads to lower performance under full feedback (b) but improves performance under partial feedback (e). Asymmetric learning results in a compressed value structure that is asymptotically stable under partial feedback (f) but not under full feedback (c).