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We frame AIF as policy optimization and show that, for closed-loop control policies, EFE minimization can be formulated as a convex Markov decision process (MDP). In this formulation, the pragmatic terms are linear in the predictive state marginals and therefore equivalent to reward maximization in a latent MDP, while the epistemic value introduces a nonlinear component that distinguishes EFE minimization from standard reinforcement learning. This perspective further reveals the epistemic drive of active inference as a policy-dependent (performative) reward. We analyze finite-horizon, discounted, and average-reward formulations of EFE and derive a mirror descent (MD) algorithm that locally linearizes the objective around the current state marginals, yieldi","title":"Active Inference as a Convex Markov Decision Process","url":"https://arxiv.org/abs/2607.20152","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.20152v1 Announce Type: cross \nAbstract: Active Inference (AIF) frames adaptive behavior as the minimization of expected free energy (EFE), combining epistemic and pragmatic objectives within a single variational principle. We frame AIF as policy optimization and show that, for closed-loop control policies, EFE minimization can be formulated as a convex Markov decision process (MDP). In this formulation, the pragmatic terms are linear in the predictive state marginals and therefore equivalent to reward maximization in a latent MDP, while the epistemic value introduces a nonlinear component that distinguishes EFE minimization from standard reinforcement learning. This perspective further reveals the epistemic drive of active inference as a policy-dependent (performative) reward. We analyze finite-horizon, discounted, and average-reward formulations of EFE and derive a mirror descent (MD) algorithm that locally linearizes the objective around the current state marginals, yieldi","title":"Active Inference as a Convex Markov Decision Process","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-23T04:43:18Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.20152"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:08a39eba2adce1e0f2a7505e4ae7ff2db463c723b1b04a3f3f8b4474d86f2c6ce83300ded01a26dfa62a3b2a8bd8a8be10256f14b6139434c1551082f405c604","signer":"crovia.substrate","subject":{"observed_at":"2026-07-23T04:43:18Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.20152"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"1dfff2d31163106b73c6e2609fb943c591ab62348597a41b5062dfe9295044e1","leaf_index":343724,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"f39e006be73ee492418a081ff2a25c7fb70bf130f7ca2734dac5a34dc81ad31d","side":"right"},{"sibling":"be914074f91b8465957eadaf052f958b047ec5e10f22080980b570d5ecb5a9ca","side":"right"},{"sibling":"c5881939735ccae4a24655bee541f70dc4652f0b636d151bf102941857fc57cf","side":"left"},{"sibling":"2b39f3bc49cf620baeef26ef7b5bb034dc5874ed3959cb0dcb56c336d02d0443","side":"left"},{"sibling":"72f453080d08508dcf5f5ff9c6b8d987847b0d04d27122cb022d3c34cceb86b0","side":"right"},{"sibling":"d554ecd3aa257e29b6c50bece8bb2c0eb94fdebe011a3aedfb86c1bca550c7bc","side":"left"},{"sibling":"ee80ef54fb43556fbc0cdc6b587800c87489c2cca696f33b35a13d71508c0f19","side":"right"},{"sibling":"fbe8bc0f33cd1a297ce2f845b101ed1107ebb67f2c2577c28ed032c1046d3b97","side":"left"},{"sibling":"6ecdcc1e2fb6ab44777fffbb7c8297d723018c63aac9d90c7a1bbebe728d84cf","side":"right"},{"sibling":"93d7d8e0e882d05b2a15bb707a824979a0427907eb47e687c712906674a0d345","side":"left"},{"sibling":"92219a3ef58cd145d94f071b0b9396cec3707812b02a8c7c63f2d0e22340552b","side":"left"},{"sibling":"4eb402d67bd4bf583b0434363061166fe259c34cc6c42adb32dcfbff0a9f5767","side":"left"},{"sibling":"2dd9cb2521044ee7c6b74f2315e0a0253b8df0d04a7b810bbbbe7da5a9788769","side":"left"},{"sibling":"21d66dd41003813f710b7617944f1bfba3258658a5d3370c21cad8f9e945bc99","side":"left"},{"sibling":"941f71d7ce3990a507b8f485de3f872a51d0e9a8c59405d76c2ae6f4a6af494a","side":"right"},{"sibling":"6281b6f7a93c44e3c4895bc65cfcb6f2be24dd725f4f46540ec022a6e215f4e8","side":"right"},{"sibling":"77025bcb374a7ad74f520643e20a8ae1205a7ee78507b0beb93117760f1c29d3","side":"left"},{"sibling":"6baede22892163664bb2e4d92cf75e6b290761533a6c39491c3afd89bb3a0252","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":343944,"merkle_root":"afab58f71597d393a7a61b857dac2eacb72fd1c04cd1432c2622d7b19309dffd","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260723T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-23T05:38:39Z","sig_algorithm":"ed25519","signature":"1a58fdc6367d0c86f83d2385be748e0800a64bcf9987c92fadca53deda009cd390d2070302c2b6e44841febfd864637c323ba12c7a1e9ae58fdf2a0cf546ac01","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_d7841f305ebe9c52dfd9f8ebd86bf8bf37e2e7d32dac498a384271f18b7da35c"}}