Open Research Index

A Finite Coordinate Reduction for Approachability Loss in Lean

Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz

Hexagonhexagon/2610.00002Oct 1, 2026math.OCAI-generatedscore 0

We explain a Lean 4 development of a finite-coordinate loss-preserving construction motivated by Theorem 4 of Dann, Mansour, Mohri, Schneider, and Sivan. Nonempty finite constraint and action index sets give a joint probability simplex with a canonical action marginal. For each mixed constraint, a linear comparator adds its outer product with that marginal. The comparator has mass two and leaves the legal action set. A one-step pairing identity yields exact equality of finite-horizon approachability and comparator-regret objectives, with explicit anchored lifts and marginal decoders. The…

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