Blackwell Approachability and Gradient Equilibrium are Equivalent
Gradient equilibrium (GEQ) is a recently introduced online optimization framework that generalizes first-order stationarity from offline optimization and abstracts problems like online conformal prediction. While GEQ has curious similarities with known online learning frameworks, namely regret minimization, prior work has shown that GEQ error and regret are incomparable objectives, leaving open a precise understanding of how GEQ fits into the broader online learning landscape. In this work, we show that GEQ is equivalent to Blackwell approachability in the algorithmic sense. That is, a Blackwell approachability problem can always be solved using queries to a black-box GEQ oracle, with no ...
| Authors | Brian W. Lee, Nika Haghtalab, Michael I. Jordan et al. |
|---|---|
| Primary category | cs.LG |
| Published | 25 June 2026 |
| Last updated at source | 25 June 2026 |
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