{"paper":{"title":"Profit Maximization in Bilateral Trade against a Smooth Adversary","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A broker can achieve near-optimal regret in bilateral trade when valuations follow a smooth adversary.","cross_cats":["cs.LG"],"primary_cat":"cs.GT","authors_text":"Chris Schwiegelshohn, Federico Fusco, Paul D\\\"utting, Simone Di Gregorio","submitted_at":"2026-05-12T19:12:57Z","abstract_excerpt":"Bilateral trade models the task of intermediating between two strategic agents, a seller and a buyer, who wish to trade a good. We study this problem from the perspective of a profit-maximizing broker within an online learning framework, where the agents' valuations are generated by a smooth adversary.\n  We devise a learning algorithm that guarantees a $\\tilde{O}(\\sqrt{T})$ regret bound, which is tight in the time horizon $T$ up to poly-logarithmic factors. This matches the minimax rate for the stochastic i.i.d. case, and is also well separated from the adversarial setting, where sublinear-reg"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We devise a learning algorithm that guarantees a Õ(√T) regret bound, which is tight in the time horizon T up to poly-logarithmic factors. This matches the minimax rate for the stochastic i.i.d. case, and is also well separated from the adversarial setting, where sublinear-regret is unattainable.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The valuations are generated by a smooth adversary, which allows leveraging a continuity property of smooth instances combined with hierarchical net-construction of the broker's action space analyzed via algorithmic chaining.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A learning algorithm achieves tight Õ(√T) regret for profit maximization in bilateral trade against smooth adversaries, matching stochastic rates via continuity and algorithmic chaining.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A broker can achieve near-optimal regret in bilateral trade when valuations follow a smooth adversary.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1717447886a50f32bb88d8e1a97e82b5eeb6b5799de2527f0d644fab3cb58be8"},"source":{"id":"2605.12664","kind":"arxiv","version":1},"verdict":{"id":"fe2900f4-28c2-49df-b27e-733126283180","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:12:23.136127Z","strongest_claim":"We devise a learning algorithm that guarantees a Õ(√T) regret bound, which is tight in the time horizon T up to poly-logarithmic factors. This matches the minimax rate for the stochastic i.i.d. case, and is also well separated from the adversarial setting, where sublinear-regret is unattainable.","one_line_summary":"A learning algorithm achieves tight Õ(√T) regret for profit maximization in bilateral trade against smooth adversaries, matching stochastic rates via continuity and algorithmic chaining.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The valuations are generated by a smooth adversary, which allows leveraging a continuity property of smooth instances combined with hierarchical net-construction of the broker's action space analyzed via algorithmic chaining.","pith_extraction_headline":"A broker can achieve near-optimal regret in bilateral trade when valuations follow a smooth adversary."},"references":{"count":86,"sample":[{"doi":"","year":null,"title":"Counterspeculation, auctions, and competitive sealed tenders , author=. J. 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