Near-Optimal Algorithms for Omniprediction

• URL: http://arxiv.org/abs/2501.17205v2
• Date: Thu, 30 Jan 2025 01:45:23 GMT
• Title: Near-Optimal Algorithms for Omniprediction
• Authors: Princewill Okoroafor, Robert Kleinberg, Michael P. Kim,
• Abstract summary: We give near-optimal learning algorithms for omniprediction, in both the online and offline settings. Online learning algorithm achieves near-optimal complexity across a number of measures. offline learning algorithm returns an efficient $(mathcalL_mathrmBV,mathcalH,varepsilon(m)$)
• Score: 6.874077229518565
• License:
• Abstract: Omnipredictors are simple prediction functions that encode loss-minimizing predictions with respect to a hypothesis class $\mathcal{H}$, simultaneously for every loss function within a class of losses $\mathcal{L}$. In this work, we give near-optimal learning algorithms for omniprediction, in both the online and offline settings. To begin, we give an oracle-efficient online learning algorithm that acheives $(\mathcal{L},\mathcal{H})$-omniprediction with $\tilde{O}(\sqrt{T \log |\mathcal{H}|})$ regret for any class of Lipschitz loss functions $\mathcal{L} \subseteq \mathcal{L}_\mathrm{Lip}$. Quite surprisingly, this regret bound matches the optimal regret for \emph{minimization of a single loss function} (up to a $\sqrt{\log(T)}$ factor). Given this online algorithm, we develop an online-to-offline conversion that achieves near-optimal complexity across a number of measures. In particular, for all bounded loss functions within the class of Bounded Variation losses $\mathcal{L}_\mathrm{BV}$ (which include all convex, all Lipschitz, and all proper losses) and any (possibly-infinite) $\mathcal{H}$, we obtain an offline learning algorithm that, leveraging an (offline) ERM oracle and $m$ samples from $\mathcal{D}$, returns an efficient $(\mathcal{L}_{\mathrm{BV}},\mathcal{H},\varepsilon(m))$-omnipredictor for $\varepsilon(m)$ scaling near-linearly in the Rademacher complexity of $\mathrm{Th} \circ \mathcal{H}$.

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