{"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/functional-regularization-for-reinforcement-1","title":"Functional Regularization for Reinforcement Learning via Learned Fourier Features","arxiv_id":"2112.03257","date":"2021-12-06","proceeding":"NeurIPS 2021 12","authors":["Alexander C. Li","Deepak Pathak"],"abstract":"We propose a simple architecture for deep reinforcement learning by embedding inputs into a learned Fourier basis and show that it improves the sample efficiency of both state-based and image-based RL. We perform infinite-width analysis of our architecture using the Neural Tangent Kernel and theoretically show that tuning the initial variance of the Fourier basis is equivalent to functional regularization of the learned deep network. That is, these learned Fourier features allow for adjusting the degree to which networks underfit or overfit different frequencies in the training data, and hence provide a controlled mechanism to improve the stability and performance of RL optimization. Empirically, this allows us to prioritize learning low-frequency functions and speed up learning by reducing networks' susceptibility to noise in the optimization process, such as during Bellman updates. Experiments on standard state-based and image-based RL benchmarks show clear benefits of our architecture over the baselines. Website at https://alexanderli.com/learned-fourier-features","url_abs":"https://arxiv.org/abs/2112.03257v1","url_pdf":"https://arxiv.org/pdf/2112.03257v1.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":"functional-regularization-for-reinforcement-1","repo_url":"https://github.com/alexlioralexli/learned-fourier-features","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"deep-reinforcement-learning","task_name":"Deep Reinforcement Learning"},{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"},{"task_slug":"reinforcement-learning-1","task_name":"Reinforcement Learning (RL)"},{"task_slug":"reinforcement-learning-2","task_name":"reinforcement-learning"}],"methods":[{"method_slug":"speed","method_name":"SPEED"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2112.03257","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2112.03257"}},"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/alexlioralexli/learned-fourier-features","reach":null}],"summary":{"ran":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":1,"samples":[{"code_sha256_prefix":"cb4bbd790ff8fbde","entry":"FourierMLP","repo":"alexlioralexli/learned-fourier-features","repo_kind":"official","path":"state-SAC-LFF/models/mlp.py","file_url":"https://github.com/alexlioralexli/learned-fourier-features/blob/HEAD/state-SAC-LFF/models/mlp.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"cb4bbd790ff8fbde"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}