We give a Gordon-Greenwald-Marks (GGM) style black-box reduction from online learning to online multicalibration. Concretely, we show that to achieve high-dimensional multicalibration with respect to a class of functions H, it suffices to combine any no-regret learner over H with an expected variational inequality (EVI) solver. We also prove a converse statement showing that efficient multicalibration implies efficient EVI solving, highlighting how EVIs in multicalibration mirror the role of fixed points in the GGM result for $Φ$-regret. This first set of results resolves the main open question in Garg, Jung, Reingold, and Roth (SODA '24), showing that oracle-efficient online multicalibration with $\sqrt{T}$-type guarantees is possible in full generality. Furthermore, our GGM-style reduction unifies the analyses of existing online multicalibration algorithms, enables new algorithms for challenging environments with delayed observations or censored outcomes, and yields the first efficient black-box reduction between online learning and multiclass omniprediction. Our second main result is a fine-grained reduction from high-dimensional online multicalibration to (contextual) $Φ$-regret minimization. Together with our first result, this establishes a new route from external regret to Phi-regret that bypasses sophisticated fixed-point or semi-separation machinery, dramatically simplifies a result of Daskalakis, Farina, Fishelson, Pipis, and Schneider (STOC '25) while improving rates, and yields new algorithms that are robust to richer deviation classes, such as those belonging to any reproducing kernel Hilbert space.

翻译：我们给出了Gordon-Greenwald-Marks (GGM)风格的从在线学习到在线多重校准的黑盒归约。具体而言，我们证明对于函数类$H$实现高维多校正，只需将任意无遗憾学习器与期望变分不等式(EVI)求解器相结合即可。我们还证明了逆命题，即高效多校正蕴含高效EVI求解，揭示了多校正中的EVI如何映射出GGM结果中$\Phi$-遗憾的固定点角色。这组结果解决了Garg、Jung、Reingold和Roth (SODA '24)的主要开放问题，表明具有$\sqrt{T}$型保证的预言机高效在线多校正在完全一般性下是可行的。此外，我们的GGM风格归约统一了现有在线多校正算法的分析，为延迟观测或删失结果等挑战性环境催生了新算法，并首次给出了在线学习与多类全知预测之间的高效黑盒归约。我们的第二个主要结果是从高维在线多校正到（上下文）$\Phi$-遗憾最小化的精细归约。与第一个结果结合，这建立了从外部遗憾到Phi-遗憾的新路径，绕过了复杂的固定点或半分离机制，大幅简化了Daskalakis、Farina、Fishelson、Pipis和Schneider (STOC '25)的结果，同时改进了收敛速率，并产生了对更丰富偏差类（如属于任意再生核希尔伯特空间的偏差类）具有鲁棒性的新算法。