Related papers: (weak) Calibration is Computationally Hard
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
The complexity of computing equilibrium refinements has been at the forefront of algorithmic game theory research, but it has remained open in the seminal class of potential games; we close this fundamental gap in this paper. We first show…
Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive, and sometimes even impossible to…
State minimization of combinatorial filters is a fundamental problem that arises, for example, in building cheap, resource-efficient robots. But exact minimization is known to be NP-hard. This paper conducts a more nuanced analysis of this…
The robust PCA problem, wherein, given an input data matrix that is the superposition of a low-rank matrix and a sparse matrix, we aim to separate out the low-rank and sparse components, is a well-studied problem in machine learning. One…
We study efficient algorithms for Sparse PCA in standard statistical models (spiked covariance in its Wishart form). Our goal is to achieve optimal recovery guarantees while being resilient to small perturbations. Despite a long history of…
Approximating a definite integral of product of cosines to within an accuracy of n binary digits where the integrand depends on input integers x[k] given in binary radix, is equivalent to counting the number of equal-sum partitions of the…
We study public goods games, a type of game where every player has to decide whether or not to produce a good which is public, i.e., neighboring players can also benefit from it. Specifically, we consider a setting where the good is…
Calibration means that forecasts and average realized frequencies are close. We develop the concept of forecast hedging, which consists of choosing the forecasts so as to guarantee that the expected track record can only improve. This…
NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such…
Cut games are among the most fundamental strategic games in algorithmic game theory. It is well-known that computing an exact pure Nash equilibrium in these games is PLS-hard, so research has focused on computing approximate equilibria. We…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…
We consider the non-convex non-concave objective function in two-player zero-sum continuous games. The existence of pure Nash equilibrium requires stringent conditions, posing a major challenge for this problem. To circumvent this…
We consider the problem of Robust PCA in the fully and partially observed settings. Without corruptions, this is the well-known matrix completion problem. From a statistical standpoint this problem has been recently well-studied, and…
We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a $\ell_\infty$-trust-region (i.e. cube). Our paper covers three topics. We explain the relevance…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
In this paper, we compute $\epsilon$-approximate Nash equilibria in atomic splittable polymatroid congestion games with convex Lipschitz continuous cost functions. The main approach relies on computing a pure Nash equilibrium for an…
This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to…
We present efficient approximation algorithms for finding Nash equilibria in anonymous games, that is, games in which the players utilities, though different, do not differentiate between other players. Our results pertain to such games…