{"id":2559,"date":"2024-05-09T04:35:57","date_gmt":"2024-05-09T04:35:57","guid":{"rendered":"https:\/\/elo-x.eu\/?p=2559"},"modified":"2024-05-09T04:36:00","modified_gmt":"2024-05-09T04:36:00","slug":"regularization-matters-in-reinforcement-learning","status":"publish","type":"post","link":"https:\/\/elo-x.eu\/?p=2559","title":{"rendered":"Regularization Matters in (Reinforcement) Learning"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"2559\" class=\"elementor elementor-2559\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-66fe843 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"66fe843\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2006bda\" data-id=\"2006bda\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8302e86 elementor-widget elementor-widget-page-title\" data-id=\"8302e86\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"page-title.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\n\t\t<div class=\"hfe-page-title hfe-page-title-wrapper elementor-widget-heading\">\n\n\t\t\t\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">\n\t\t\t\t\t\t\t\t\n\t\t\t\tRegularization Matters in (Reinforcement) Learning  \n\t\t\t<\/h2 > \n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-23f9cd1 my-divider elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"23f9cd1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7d3efe9 elementor-widget elementor-widget-text-editor\" data-id=\"7d3efe9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"color: #352a87;\"><span style=\"font-size: 24px;\">Yuan Zhang, Neurorobotics Lab, University of Freiburg<\/span><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-31bbb35 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"31bbb35\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d843487\" data-id=\"d843487\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-391b193 elementor-widget elementor-widget-text-editor\" data-id=\"391b193\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"color: var( --e-global-color-text ); font-weight: var( --e-global-typography-text-font-weight ); font-size: 1rem;\">Reinforcement learning (RL) is recognized as lacking generalization and robustness under environmental perturbations, which excessively restricts its application for real-world robotics.&nbsp;<\/span><span style=\"color: var( --e-global-color-text ); font-weight: var( --e-global-typography-text-font-weight ); font-size: 1rem;\">To handle such problems, regularization is definitely a class of methods we could look into, as we don\u2018t want our learning to be overfitting. Here are some selective works in this direction.&nbsp;<\/span><\/p>\n<div><span style=\"color: var( --e-global-color-text ); font-weight: var( --e-global-typography-text-font-weight ); font-size: 1rem;\">&nbsp;<\/span><\/div>\n<p><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6c37975 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6c37975\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2c92c57\" data-id=\"2c92c57\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b7a88c2 my-divider elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"b7a88c2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6f16671 elementor-widget elementor-widget-heading\" data-id=\"6f16671\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Robust Reinforcement Learning in Continuous Control Tasks with Uncertainty Set Regularization<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0f49a89 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0f49a89\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-394217d\" data-id=\"394217d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4c6f680 elementor-widget elementor-widget-text-editor\" data-id=\"4c6f680\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><u>Zhang, Yuan, Jianhong Wang, and Joschka Boedecker. 2023. \u201cRobust Reinforcement Learning in Continuous Control Tasks with Uncertainty Set Regularization.\u201d In . https:\/\/openreview.net\/forum?id=keAPCON4jHC.<\/u><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8722eb8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8722eb8\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-72a2899\" data-id=\"72a2899\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-957f7c1 elementor-widget elementor-widget-text-editor\" data-id=\"957f7c1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Reinforcement learning (RL) is recognized as lacking generalization and robustness under environmental perturbations, which excessively restricts its application for real-world robotics. Prior work claimed that adding regularization to the value function is equivalent to learning a robust policy under uncertain transitions. Although the regularization-robustness transformation is appealing for its simplicity and efficiency, it is still lacking in continuous control tasks. In this paper, we propose a new regularizer named Uncertainty Set Regularizer (USR), to formulate the uncertainty set on the parametric space of a transition function. To deal with unknown uncertainty sets, we further propose a novel adversarial approach to generate them based on the value function. We evaluate USR on the Real-world Reinforcement Learning (RWRL) benchmark and the Unitree A1 Robot, demonstrating improvements in the robust performance of perturbed testing environments and sim-to-real scenarios.\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-73c1594\" data-id=\"73c1594\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-705973c elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"705973c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"525\" height=\"175\" src=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/rrl-1024x342.png\" class=\"attachment-large size-large wp-image-2570\" alt=\"\" srcset=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/rrl-1024x342.png 1024w, https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/rrl-300x100.png 300w, https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/rrl-768x257.png 768w, https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/rrl.png 1537w\" sizes=\"100vw\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8293732 elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"8293732\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"525\" height=\"182\" src=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/rrl_result.png\" class=\"attachment-large size-large wp-image-2571\" alt=\"\" srcset=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/rrl_result.png 921w, https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/rrl_result-300x104.png 300w, https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/rrl_result-768x266.png 768w\" sizes=\"100vw\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-39a0a9c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"39a0a9c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a84db57\" data-id=\"a84db57\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bbe0921 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bbe0921\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2076f04\" data-id=\"2076f04\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9bc8ee2 my-divider elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"9bc8ee2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8c42272 elementor-widget elementor-widget-heading\" data-id=\"8c42272\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">UDUC: An Uncertainty-driven Approach for Robust Control<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8b2acb0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8b2acb0\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-022ac0e\" data-id=\"022ac0e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8b4e6ee elementor-widget elementor-widget-text-editor\" data-id=\"8b4e6ee\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><u>Zhang, Yuan,Jasper Hoffman, and Joschka Boedecker. 2024. \u201cUDUC: An Uncertainty-driven Approach for Robust Control.\u201d https:\/\/arxiv.org\/abs\/2405.02598.<\/u><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f5d541a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f5d541a\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-b177eb9\" data-id=\"b177eb9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b88aabf elementor-widget__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"b88aabf\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Learning-based techniques have become popular in both model predictive control (MPC) and reinforcement learning (RL). Probabilistic ensemble (PE) models offer a promising approach for modelling system dynamics, showcasing the ability to capture uncertainty and scalability in high-dimensional control scenarios. However, PE models are susceptible to mode collapse, resulting in non-robust control when faced with environments slightly different from the training set.\u00a0<span style=\"color: var( --e-global-color-text ); font-weight: var( --e-global-typography-text-font-weight ); font-size: 1rem;\">In this paper, we introduce the uncertainty-driven robust control (UDUC) loss as an alternative objective for training PE models, drawing inspiration from contrastive learning. We analyze the robustness of UDUC loss through the lens of robust optimization and evaluate its performance on the challenging Real-world Reinforcement Learning (RWRL) benchmark, which involves significant environmental mismatches between the training and testing environments.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-f23afdf\" data-id=\"f23afdf\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9e19741 elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"9e19741\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"525\" height=\"214\" src=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/uduc-1024x417.png\" class=\"attachment-large size-large wp-image-2568\" alt=\"\" srcset=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/uduc-1024x417.png 1024w, https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/uduc-300x122.png 300w, https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/uduc-768x313.png 768w, https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/uduc-1536x626.png 1536w, https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/uduc.png 2029w\" sizes=\"100vw\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a5a8337 elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"a5a8337\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"525\" height=\"225\" src=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/uduc_result-1024x438.png\" class=\"attachment-large size-large wp-image-2569\" alt=\"\" srcset=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/uduc_result-1024x438.png 1024w, https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/uduc_result-300x128.png 300w, https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/uduc_result-768x328.png 768w, https:\/\/elo-x.eu\/wp-content\/uploads\/2024\/05\/uduc_result.png 1508w\" sizes=\"100vw\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>February 5th to 9th, 2023, Milano, Italy<\/p>\n","protected":false},"author":18,"featured_media":2047,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[],"class_list":["post-2559","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-projects"],"_links":{"self":[{"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/posts\/2559","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/users\/18"}],"replies":[{"embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2559"}],"version-history":[{"count":22,"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/posts\/2559\/revisions"}],"predecessor-version":[{"id":2587,"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/posts\/2559\/revisions\/2587"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/media\/2047"}],"wp:attachment":[{"href":"https:\/\/elo-x.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2559"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2559"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2559"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}