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.
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.
arXiv:2610. 04049v2 Announce Type: replace-cross Abstract: We study the maximization of a nonnegative $k$-submodular function, not assumed monotone, in which each of $n$ elements receives one of $k\ge2$ labels or stays unselected and the selected elements must satisfy a constraint.
arXiv:2610. 00545v1 Announce Type: new Abstract: We study adversarial online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed sets.
arXiv:2608. 02588v1 Announce Type: cross Abstract: In [AS21], Axiotis and Sviridenko conjectured that the linear dependence on the restricted condition number in sparse convex optimization cannot be improved by a polynomial-time algorithm.
arXiv:2610.20416v1 Announce Type: new Abstract: For the fundamental problem of prediction from expert advice, Freund asked whether one could compete with a comparator that switches $k$ times among on...
arXiv:2601. 21243v3 Announce Type: replace-cross Abstract: We consider max-min and min-max problems with objective functions that are possibly non-smooth, submodular with respect to the minimiser and concave with respect to the maximiser.
arXiv:2602. 20376v3 Announce Type: replace-cross Abstract: We study the problem of maximizing a complex-valued quadratic form over the $K^{\text{th}}$ roots of unity.