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.
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arXiv:2610.26976v1 Announce Type: new Abstract: We establish sharp degree bounds for Putinar sum-of-squares (SOS) certificates in terms of the positivity margin $\delta$. For any fixed Archimedean qu...
The paper presents linear programming formulations and strongly polynomial algorithms for robust Markov decision processes (RMDPs) with rational polyhedral state-action rectangular uncertainty in rewards and transitions. By encoding a finite sequence of robust policy-iteration steps, a single LP is constructed whose optimal solutions recover the robust optimal value and all optimal stationary randomized policies. The authors provide a general complexity analysis of robust policy iteration, improving known bounds for α1 and α1∞ RMDPs and establishing new strongly polynomial bounds for general interval, weighted α1, and Wasserstein RMDPs, as well as turn‑based stochastic games with these uncertainty sets.
The paper proves that computing an approximate correlated equilibrium for a polytope game is PPAD‑complete, showing it is polynomial‑time equivalent to finding a Nash equilibrium. It introduces the notion of a fixed set—a finite set contained in the convex hull of its image under a continuous function—and demonstrates that computing such a fixed set is PPAD‑hard even at inverse polynomial precision.
arXiv:2504. 03432v4 Announce Type: replace-cross Abstract: Solving (Stampacchia) variational inequalities (SVIs) is a foundational problem at the heart of optimization.
arXiv:2609.22757v1 Announce Type: cross Abstract: A (coarse) correlated equilibrium (CE) is information-value-free (IVF) if a player can match the payoff obtained from recommendations by committing t...
arXiv:2606. 28308v1 Announce Type: cross Abstract: Many two-player zero-sum games admit not a unique Nash equilibrium but a convex set of them: a polytope of profiles that all share the minimax value V* yet prescribe different behaviour.