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However, in the absence of convexity or concavity, existing approaches study convergence to an approximate saddle point or first-order stationary points, which may be arbitrarily far from global optima. In this work, we present an algorithmic framework for computing the global minimax value in convex--non-concave and non-convex--concave min-max optimization. For convex--non-concave min-max problems, we use a reformulation that transforms the problem into a non-concave--convex max-min optimization problem with suitably defined feasible sets and objective function. This reformulation can be viewed as an extension of Sion's minimax theorem to the convex--non-concave setting. We then introduce EXOTIC -- an Exact, Optimistic, Tree-based algorit","title":"EXOTIC: An Exact, Optimistic, Tree-Based Algorithm for Min-Max Optimization","url":"https://arxiv.org/abs/2508.12479","vendor":"arxiv_cs_ai"},"summary":"arXiv:2508.12479v2 Announce Type: replace-cross \nAbstract: Min-max optimization arises in many domains such as game theory, adversarial machine learning, etc. For these problems, gradient-based methods are well understood and enjoy strong guarantees. However, in the absence of convexity or concavity, existing approaches study convergence to an approximate saddle point or first-order stationary points, which may be arbitrarily far from global optima. In this work, we present an algorithmic framework for computing the global minimax value in convex--non-concave and non-convex--concave min-max optimization. For convex--non-concave min-max problems, we use a reformulation that transforms the problem into a non-concave--convex max-min optimization problem with suitably defined feasible sets and objective function. This reformulation can be viewed as an extension of Sion's minimax theorem to the convex--non-concave setting. We then introduce EXOTIC -- an Exact, Optimistic, Tree-based algorit","title":"EXOTIC: An Exact, Optimistic, Tree-Based Algorithm for Min-Max Optimization","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-26T04:43:39Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2508.12479"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:74716eef26e0e2b47f300a3d9a49a6f07ea10af5f6a7cd4c42263b7cd4fd7564c1c12795c10da0edc24fab38da54f7e2daa8460c5f8ff80475603006c5d41e04","signer":"crovia.substrate","subject":{"observed_at":"2026-05-26T04:43:39Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2508.12479"},"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":"b39a396d8eebceb3a4268524ce160b48304879bd131dcfe05725fa900e01fae9","leaf_index":151881,"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":"5b663443a01ab47efba97a66b82a338f91558916d384fd372da295badfdc5029","side":"left"},{"sibling":"21feb7b4739ca5100d8bb222d5a5d728f28c554470325eb22946f46ba013f3f5","side":"right"},{"sibling":"b097c6aa1b0cb6390caece0ebf686dfffdb501976df9d29aacd0d1c3a5766d01","side":"right"},{"sibling":"a18ebfcf09804a1a3d1460a1a525471af2c538716e18636ff7f6ac0f4bfe86eb","side":"left"},{"sibling":"49b8c9727635fdd981df583b669e175f1170b08bdba307177d6d6b058c971fb4","side":"right"},{"sibling":"c23ac699c8ca8a0fb511bf1c4d94cfad5180bb945b651ec04bb28c5f3ed8bdfc","side":"right"},{"sibling":"7bd757323466f2d5e9a78f8308b6ddad9ce121c71e69a2be470e169f21e5583b","side":"left"},{"sibling":"b8013a4d5795f8230d3abb917aff567dadf5c7a3494daf94843cddd93f67ecf8","side":"right"},{"sibling":"6c8b632bc887ad8683d2d08a66a66babfd1e8e43de4b1b760ed3f3d35d5b02e1","side":"left"},{"sibling":"879666fab72e779ab55d0564eaabd64b00534fd6bba7f18412c7f31f61ffd09f","side":"right"},{"sibling":"f40ccedd90c323817e961adc0a2e2db82b8aabe192b6c9d5a373ff988987b207","side":"right"},{"sibling":"b85ea61ae405eed84392a7b6b1eee5536f5a38d6b04070638e23ec7b71e3443a","side":"right"},{"sibling":"d415e6939aee710631f5062799379b547d2c3e3d9a68f263bbb5a693285ab2ca","side":"left"},{"sibling":"e5893793e3591ed7f5e58ca94ffcfba46bb30f69fb1c25d5ba8ef49eb99f9126","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"e3eecaf996dbe7229a7bb1d234c97aea97a252c5f7c89f8547b6d091db0f0e40","side":"right"},{"sibling":"55bcbd4da3e20d93931f7e58673f10232e81a5b1514d7396cb4b71e8f95788d0","side":"right"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","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":152106,"merkle_root":"ac5182c6f3dd09931f2a689df5f4be36df7b55e55bcf106e195671f5ed55fd8f","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260526T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-26T05:37:34Z","sig_algorithm":"ed25519","signature":"a401243fbd2c077d29a623c6ef616c78fbd5c8ce1930afa7af7165b2386e5a8cf15d5094983a1c962e71b27b911a3f3ce09c8cfab9393be2ce5ce8ee6513da06","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_942cfb010c288455739394d91e3c80e50114ca6919708d2057d0713e581ae4ba"}}