Related papers: Monotone Contractions
We study the links between the values of stochastic games with varying stage duration $h$, the corresponding Shapley operators $\bf{T}$ and ${\bf{T}}\_h$and the solution of $\dot f\_t = ({\bf{T}} - Id )f\_t$. Considering general non…
We study the integration and approximation problems for monotone and convex bounded functions that depend on $d$ variables, where $d$ can be arbitrarily large. We consider the worst case error for algorithms that use finitely many function…
We introduce a new class of asymptotic contractions that employs two quasi-metrics defined directly in terms of the underlying mapping. The contraction condition compares these two quantities via a sequence of bounding functions that…
The UNIQUE GAMES problem is a central problem in algorithms and complexity theory. Given an instance of UNIQUE GAMES, the STRONG UNIQUE GAMES problem asks to find the largest subset of vertices, such that the UNIQUE GAMES instance induced…
We consider a monotone submodular maximization problem whose constraint is described by a logic formula on a graph. Formally, we prove the following three `algorithmic metatheorems.' (1) If the constraint is specified by a monadic…
In this paper, we study the tradeoff between the approximation guarantee and adaptivity for the problem of maximizing a monotone submodular function subject to a cardinality constraint. The adaptivity of an algorithm is the number of…
In cooperative game theory, the primary focus is the equitable allocation of payoffs or costs among agents. However, in the practical applications of cooperative games, accurately representing games is challenging. In such cases, using an…
We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…
We consider (i) the problem of finding a (possibly mixed) Nash equilibrium in congestion games, and (ii) the problem of finding an (exponential precision) fixed point of the gradient descent dynamics of a smooth function $f:[0,1]^n…
We generalize the monotone local search approach of Fomin, Gaspers, Lokshtanov and Saurabh [J. ACM 2019], by establishing a connection between parameterized approximation and exponential-time approximation algorithms for monotone subset…
We investigate adaptive sublinear algorithms for detecting monotone patterns in an array. Given fixed $2 \leq k \in \mathbb{N}$ and $\varepsilon > 0$, consider the problem of finding a length-$k$ increasing subsequence in an array $f \colon…
Given a set $P$ of $n$ planar points, two axes and a real-valued score function $f()$ on subsets of $P$, the Optimal Planar Box problem consists in finding a box (i.e. axis-aligned rectangle) $H$ maximizing $f(H\cap P)$. We consider the…
Recently, a framework for the approximation of the entire set of $\epsilon$-efficient solutions (denote by $E_\epsilon$) of a multi-objective optimization problem with stochastic search algorithms has been proposed. It was proven that such…
Shapley operators of undiscounted zero-sum two-player games are order-preserving maps that commute with the addition of a constant. We characterize the fixed point sets of Shapley operators, in finite dimension (i.e., for games with a…
In large-scale applications, such as machine learning, it is desirable to design non-convex optimization algorithms with a high degree of parallelization. In this work, we study the adaptive complexity of finding a stationary point, which…
We extend the weak-strong uniqueness principle for mean-field game (MFG) systems to a broad class of second-order stationary and time-dependent problems. Under standard monotonicity, growth, and coercivity assumptions on the Hamiltonian,…
In this paper, we address two main topics. First, we study the problem of minimizing the sum of a smooth function and the composition of a weakly convex function with a linear operator on a closed vector subspace. For this problem, we…
We design algorithms for minimizing $\max_{i\in[n]} f_i(x)$ over a $d$-dimensional Euclidean or simplex domain. When each $f_i$ is $1$-Lipschitz and $1$-smooth, our method computes an $\epsilon$-approximate solution using $\widetilde{O}(n…
We consider the problem of maximizing submodular functions in single-pass streaming and secretaries-with-shortlists models, both with random arrival order. For cardinality constrained monotone functions, Agrawal, Shadravan, and Stein gave a…
We consider the problem of how to determine a fair source coding rate allocation method for the lossless data compression problem in multiterminal networks, e.g, the wireless sensor network where there are a large number of sources to be…