Carla Michini Congestion games allow to model competitive resource sharing in various distributed systems. Pure Nash equilibria, that are stable outcomes of a game, could be far from being socially optimal. Our goal is to identify combinatorial structures that limit the inefficiency of equilibria. This question has been mainly investigated for congestion games defined over networks. Instead, … Read more
Recently, mixed-integer programming (MIP) techniques have been applied to learn optimal decision trees. Empirical research has shown that optimal trees typically have better out-of-sample performance than heuristic approaches such as CART. However, the underlying MIP formulations often suffer from weak linear programming (LP) relaxations. Many existing MIP approaches employ big-M constraints to ensure observations are … Read more
We study the inefficiency of pure Nash equilibria in symmetric unweighted network congestion games. We first explore the impact of symmetry on the worst-case PoA of network congestion games. For polynomial delay functions with highest degree p, we construct a family of symmetric congestion games over arbitrary networks which achieves the same worst-case PoA of … Read more
Decision trees are a widely used tool for interpretable machine learning. Multivariate decision trees employ hyperplanes at the branch nodes to route datapoints throughout the tree and yield more compact models than univariate trees. Recently, mixed-integer programming (MIP) has been applied to formulate the optimal decision tree problem. To strengthen MIP formulations, it is crucial … Read more
Recently, mixed-integer programming (MIP) techniques have been applied to learn optimal decision trees. Empirical research has shown that optimal trees typically have better out-of-sample performance than heuristic approaches such as CART. However, the underlying MIP formulations often suffer from slow runtimes, due to weak linear programming (LP) relaxations. In this paper, we first propose a … Read more
We study the inefficiency of pure Nash equilibria in symmetric unweighted network congestion games defined over series-parallel networks. We introduce a quantity y(D) to upper bound the Price of Anarchy (PoA) for delay functions in class D. When D is the class of polynomial functions with highest degree p, our upper bound is 2^{p+1} − … Read more
We study the inefficiency of pure Nash equilibria in symmetric network congestion games defined over series-parallel networks with affine edge delays. For arbitrary networks, Correa (2019) proved a tight upper bound of 5/2 on the PoA. On the other hand, for extension-parallel networks, a subclass of series-parallel networks, Fotakis (2010) proved that the PoA is … Read more
We consider the problem of optimizing a linear function over a lattice polytope P contained in [0,k]^n and defined via m linear inequalities. We design a simplex algorithm that, given an initial vertex, reaches an optimal vertex by tracing a path along the edges of P of length at most O(n^6 k log k). The … Read more
We study the problem of optimizing an arbitrary weight function w’z over the metric polytope of a graph G=(V,E), a well-known relaxation of the cut polytope. We define the signed graph (G, E^-), where E^- consists of the edges of G having negative weight. We characterize the sign patterns of the weight vector w such … Read more
In this paper we show that the diameter of a d-dimensional lattice polytope in [0,k]^n is at most (k – 1/2) d. This result implies that the diameter of a d-dimensional half-integral polytope is at most 3/2 d. We also show that for half-integral polytopes the latter bound is tight for any d. Citation University … Read more