{"paper":{"title":"Fast Rates for Inverse Reinforcement Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Min-Max-IRL with linear rewards achieves fast O(n^{-1}) rates for KL divergence and parameter error.","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Andreas Schlaginhaufen, Maryam Kamgarpour","submitted_at":"2026-05-14T09:07:31Z","abstract_excerpt":"We establish novel structural and statistical results for entropy-regularized min-max inverse reinforcement learning (Min-Max-IRL) with linear reward classes in finite-horizon MDPs with Borel state and action spaces. On the structural side, we show that maximum likelihood estimation (MLE) and Min-Max-IRL are equivalent at the population level, and at the empirical level under deterministic dynamics. On the statistical side, exploiting pseudo-self-concordance of the Min-Max-IRL loss, we prove that both the trajectory-level KL divergence and the squared parameter error in the Hessian norm decay "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"exploiting pseudo-self-concordance of the Min-Max-IRL loss, we prove that both the trajectory-level KL divergence and the squared parameter error in the Hessian norm decay at the fast rate O(n^{-1})","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Min-Max-IRL loss is pseudo-self-concordant (invoked to obtain the fast rates); the paper also relies on linear reward classes and finite-horizon structure.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Entropy-regularized Min-Max-IRL achieves O(n^{-1}) rates for trajectory-level KL divergence and squared parameter error in the Hessian norm under misspecification in Borel MDPs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Min-Max-IRL with linear rewards achieves fast O(n^{-1}) rates for KL divergence and parameter error.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"bfa8145161c9336b7e436930a09c57512a8cb7955123c678a607181eef9fee97"},"source":{"id":"2605.14599","kind":"arxiv","version":1},"verdict":{"id":"1f54522c-080f-4431-8dd7-6a9ef9846f93","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T05:00:25.431896Z","strongest_claim":"exploiting pseudo-self-concordance of the Min-Max-IRL loss, we prove that both the trajectory-level KL divergence and the squared parameter error in the Hessian norm decay at the fast rate O(n^{-1})","one_line_summary":"Entropy-regularized Min-Max-IRL achieves O(n^{-1}) rates for trajectory-level KL divergence and squared parameter error in the Hessian norm under misspecification in Borel MDPs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Min-Max-IRL loss is pseudo-self-concordant (invoked to obtain the fast rates); the paper also relies on linear reward classes and finite-horizon structure.","pith_extraction_headline":"Min-Max-IRL with linear rewards achieves fast O(n^{-1}) rates for KL divergence and parameter error."},"references":{"count":14,"sample":[{"doi":"","year":null,"title":"Ifβ >0, thenπ=π⋆ r if and only ifAπ t,r(s,a) = 0for all(t,s)andν-a.e.a∈A","work_id":"348aead3-28f6-4a73-aad0-6efa6d362dce","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"9 Proof.Inpart 1, the implicationπ=π⋆ r =⇒Aπ t,r = 0ν-a.s","work_id":"79ae2fb4-bca0-4204-a96d-1fde78f1ee1a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"For allα∈[0,1], e−αSH(θ0)⪯H(θα)⪯eαSH(θ0).(15)","work_id":"c5900a65-3f16-457c-a12a-d782f5f071c6","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Then ψ(−S)∥∆∥2 H(θ0) ≤DJ⋆(θ1,θ0)≤ψ(S)∥∆∥2 H(θ0)","work_id":"57d2e3a1-9581-4113-b9f8-9f247bc13db6","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Then χ(−S)∥∆∥2 H(θ0) ≤DJ⋆(θ1,θ0) +DJ⋆(θ0,θ1) =⟨∆,∇J⋆(θ1)−∇J⋆(θ0)⟩ ≤χ(S)∥∆∥2 H(θ0)","work_id":"ec733bd1-90de-4b61-b6dd-10f9ad17f874","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":14,"snapshot_sha256":"650b51d63afe485d146a8caad391eb3eccf020e412d3a0004a1b8d9b15c52489","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"92bda282e56769e5ba3a253b5ec0780111c2c53fab76e7b7417df882716967a2"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}