Presents polynomial-time algorithms for 2D forecasting with Õ(√(kT)) swap regret and extensions to higher dimensions with Õ(d√(kT)) bounds, improving prior regret and runtime results.
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Frobenius identities for the volume map on Cohen-Macaulay rings give sufficient conditions for anisotropy and Hard Lefschetz in Gorenstein quotients and deduce the g-theorem for simplicial spheres plus the Ohsugi-Hibi conjecture.
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Improved Multi-Dimensional Forecasting for Swap Regret
Presents polynomial-time algorithms for 2D forecasting with Õ(√(kT)) swap regret and extensions to higher dimensions with Õ(d√(kT)) bounds, improving prior regret and runtime results.