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Self-play red-teaming improves language-model safety by pitting attacker and defender roles against each other in a zero-sum game. However, real adversaries increasingly use mosaic attacks: multi-turn sequences whose individual fragments are innocuous in isolation yet assemble into a harmful payload. We develop a theor...
We study the online allocation of indivisible goods among $n$ agents, where each good must be allocated immediately and irrevocably upon arrival. Against an adaptive adversary, Neoh and Teh [2026] proved that no algorithm can guarantee a positive approximation to proportionality up to one good (PROP1) that is independe...
A learning-augmented framework based on predicting joint value-size types, proving consistency under perfect predictions, robustness to prediction error, and showing that separate predictions of value and size marginals are insufficient to recover strong fairness guarantees is developed.
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