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New research establishes PPAD-hardness for min-max optimization

By PulseAugur Editorial · [4 sources] ·

Researchers have established new theoretical hardness results for min-max optimization problems involving quadratic polynomials. These findings demonstrate that computing approximate stationary points over a hypercube is PPAD-hard, even under specific constraints like multilinear polynomials and limited monomial appearances. This complexity also extends to two-team zero-sum polymatrix games. Separately, a study on learning polynomial surrogates over the Boolean hypercube under subgaussian noise characterizes the minimax sample complexity, showing it scales as n^(d+1) for degree-d polynomials and ns^2 for s-sparse Fourier-Walsh polynomials. AI

RANK_REASON The cluster consists of two academic papers published on arXiv detailing theoretical computer science and machine learning research.

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New research establishes PPAD-hardness for min-max optimization

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COVERAGE [4]

  1. arXiv cs.LG TIER_1 English(EN) · Martino Bernasconi, Matteo Castiglioni, Andrea Celli, Alexandros Hollender ·

    The Complexity of Min-Max Optimization for Quadratic Polynomials

    arXiv:2606.17000v1 Announce Type: cross Abstract: We prove that computing approximate stationary points of min-max optimization over the hypercube is PPAD-hard for quadratic polynomials. This holds even when the polynomials are multilinear, each variable appears in at most three …

  2. arXiv cs.LG TIER_1 English(EN) · Alexandros Hollender ·

    The Complexity of Min-Max Optimization for Quadratic Polynomials

    We prove that computing approximate stationary points of min-max optimization over the hypercube is PPAD-hard for quadratic polynomials. This holds even when the polynomials are multilinear, each variable appears in at most three monomials, and the approximation factor is inverse…

  3. arXiv stat.ML TIER_1 English(EN) · Jasper van Doornmalen, Mathieu Molina, Victor Verdugo, Jos\'e Verschae ·

    Tight $L_\infty$ Sample Complexity for Low-Degree and Sparse Boolean Polynomials

    arXiv:2606.17319v1 Announce Type: new Abstract: Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube. To ensure that optimizing the surrogate yields good solutions for the underlying…

  4. arXiv stat.ML TIER_1 English(EN) · José Verschae ·

    Tight $L_\infty$ Sample Complexity for Low-Degree and Sparse Boolean Polynomials

    Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube. To ensure that optimizing the surrogate yields good solutions for the underlying objective, we require uniform $L_\infty$-error …

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