{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/plannable-approximations-to-mdp-homomorphisms","title":"Plannable Approximations to MDP Homomorphisms: Equivariance under Actions","arxiv_id":"2002.11963","date":"2020-02-27","proceeding":null,"authors":["Elise van der Pol","Thomas Kipf","Frans A. Oliehoek","Max Welling"],"abstract":"This work exploits action equivariance for representation learning in reinforcement learning. Equivariance under actions states that transitions in the input space are mirrored by equivalent transitions in latent space, while the map and transition functions should also commute. We introduce a contrastive loss function that enforces action equivariance on the learned representations. We prove that when our loss is zero, we have a homomorphism of a deterministic Markov Decision Process (MDP). Learning equivariant maps leads to structured latent spaces, allowing us to build a model on which we plan through value iteration. We show experimentally that for deterministic MDPs, the optimal policy in the abstract MDP can be successfully lifted to the original MDP. Moreover, the approach easily adapts to changes in the goal states. Empirically, we show that in such MDPs, we obtain better representations in fewer epochs compared to representation learning approaches using reconstructions, while generalizing better to new goals than model-free approaches.","url_abs":"https://arxiv.org/abs/2002.11963v1","url_pdf":"https://arxiv.org/pdf/2002.11963v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"plannable-approximations-to-mdp-homomorphisms","repo_url":"https://github.com/ElisevanderPol/prae","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"},{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2002.11963","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2002.11963"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/ElisevanderPol/prae","reach":null}],"summary":{"ran_violates":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"0e24171fdbb18324","entry":"squeeze_samples","repo":"ElisevanderPol/prae","repo_kind":"official","path":"prae/trainers.py","file_url":"https://github.com/ElisevanderPol/prae/blob/HEAD/prae/trainers.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"0e24171fdbb18324"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}