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We consider two indicator families which are often used for similar algorithmic purposes, but which are geometrically different. The hypervolume indicator is based on a dystopian reference point and measures dominated volume in objective space. The R2 indicator is based on a utopian point and evaluates approximation sets through weighted Tchebycheff scalarization envelopes. The purpose of the paper is to make precise which preference transformations preserve exact computation, Pareto compatibility, and monotonicity properties, and which transformations change the underlying geometry. On the hypervolume side, we revisit canonical EHVI through the Deng representation, formulate product-density weighted EHVI in desirability coordinates, discuss cone-based EHVI as ordinary EHVI after a linear cone transformation, and separat","title":"Preference-Shaped Expected Hypervolume and R2 Improvement: Exact Computation and Monotonicity","url":"https://arxiv.org/abs/2605.28746","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.28746v2 Announce Type: replace-cross \nAbstract: This paper studies preference-shaped expected improvement criteria for Bayesian multiobjective optimization. We consider two indicator families which are often used for similar algorithmic purposes, but which are geometrically different. The hypervolume indicator is based on a dystopian reference point and measures dominated volume in objective space. The R2 indicator is based on a utopian point and evaluates approximation sets through weighted Tchebycheff scalarization envelopes. 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On the hypervolume side, we revisit canonical EHVI through the Deng representation, formulate product-density weighted EHVI in desirability coordinates, discuss cone-based EHVI as ordinary EHVI after a linear cone transformation, and separat","title":"Preference-Shaped Expected Hypervolume and R2 Improvement: Exact Computation and Monotonicity","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-29T04:43:58Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.28746"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:edd839fa5f79da069fb6f1a520c0e68e15a8cf75b644357880753b029da9571dfe6ddefda6cf7baab7470b545e134015d9fc922b0ea102c6d758d628437a8807","signer":"crovia.substrate","subject":{"observed_at":"2026-05-29T04:43:58Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.28746"},"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":"11506c9f877e6759f923dc2c0193836ba3532daa9181faf4011d30f9c238af47","leaf_index":158201,"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":"73f800c24abb314f78fb2471222becfeb0ac3d7d474ae728cdfd3b07a28f6c5c","side":"left"},{"sibling":"9b4232cb4936bb98a8725293a9cb3204d14859e50ee46b2b3fb78fb04e2b36b0","side":"right"},{"sibling":"65d989969113a3175caf210b6db7e3eb3b3cad7215e90b118c17af0f9fa64592","side":"right"},{"sibling":"50dd1378c389178716dfe3ffa60d95aa32faccb0a24d38a3db1a07a3a6818fa7","side":"left"},{"sibling":"13b571990b526d576c061a7414f5f3729a072a004742894731445915838000df","side":"left"},{"sibling":"682a65c5be3c1bc5d64a09340a34e0702bf499b96139c8bf17318babc5920016","side":"left"},{"sibling":"2496d8181c3184c4ea7973d99293dedbb754d677261137e3c8c5546635804645","side":"left"},{"sibling":"463d4726f68bda2bbf724c72553fd53d88ea99a3d4a713f9b8a1b2d9fde12933","side":"left"},{"sibling":"002471ff5893cd2a2890119cbfe4a9456bfb46cf31fa6aee377650afe6ae0c92","side":"left"},{"sibling":"1dcc44e23fbb0218b13591e4b584eca3600dcf365769cb741e0ecd33b25b8c56","side":"right"},{"sibling":"fcf16a6f44025801f5b83e928acce764352ddbc06ae3043d8cde9a409933e6d8","side":"right"},{"sibling":"78982294dee68f9db9288c64d7e507c7865fda96e1b6f7ccff5c8bb152e93c49","side":"left"},{"sibling":"995b421824624a8282c7f44e64c64ee35344800f477ae1845b41be14d3fab94c","side":"right"},{"sibling":"66331bac84ca0f8983eb09fac7eaf95af234f1b82680b793eabff4ee25caac40","side":"left"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"eef0e8906a749d3470f89beeedc723f37a5737010bbb0dcc7cf91515338e5a3e","side":"right"},{"sibling":"1a07e481a9407d71aad078ce854cdeee362163c887fe10f889b0ecf0b5e749ad","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":158251,"merkle_root":"485e6b31fe60c8beba5b394808c7e4c32448b2ff65c2482c480ca0e2a2eda718","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260529T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-29T05:37:37Z","sig_algorithm":"ed25519","signature":"bbf9f005201182fce4f9d94c7a9d01a508b56daf7d9611bd73514f5f616bc059d0e5e1f2edfc95716e6fe08ef5fae38b558cbf7f2fd8f9d5dfe4c34a54c83005","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_e75b11bc3f817a737ea2335e23d43a527fe6dd5154432ef05f08eea6e93b0ff6"}}