相关论文: Universal gaps for XOR games from estimates on ten…

This paper deals with different concepts for characterizing the size of mathematical objects. A game theoretic investigation and generalization of two size concepts, which can both be formulated in topological terms, is provided: the so…

The Bayesian framework is ideally suited for induction problems. The probability of observing $x_t$ at time $t$, given past observations $x_1...x_{t-1}$ can be computed with Bayes' rule if the true distribution $\mu$ of the sequences…

We formulate and establish a generalization of Koll\'ar's injectivity theorem for adjoint bundles twisted by suitable multiplier ideal sheaves. As applications, we generalize Koll\'ar's torsion-freeness, Koll\'ar's vanishing theorem, and a…

We study the set of continuous functions that admit no spurious local optima (i.e. local minima that are not global minima) which we term \textit{global functions}. They satisfy various powerful properties for analyzing nonconvex and…

We study the problem of testing whether two tensors in $\mathbb{R}^\ell\otimes \mathbb{R}^m\otimes \mathbb{R}^n$ are isomorphic under the natural action of orthogonal groups $\textbf{O}(\ell, \mathbb{R})\times\textbf{O}(m,…

Nonlocal games play a crucial role in quantum information theory and have numerous applications in certification and cryptographic protocols. Kalai et al. (STOC 2023) introduced a procedure to compile a nonlocal game into a single-prover…

The Convex Gaussian Min-Max Theorem (CGMT) has emerged as a prominent theoretical tool for analyzing the precise stochastic behavior of various statistical estimators in the so-called high dimensional proportional regime, where the sample…

This paper considers the noncooperative maximization of mutual information in the Gaussian interference channel in a fully distributed fashion via game theory. This problem has been studied in a number of papers during the past decade for…

This paper is concerned with two-person dynamic zero-sum games. Let games for some family have common dynamics, running costs and capabilities of players, and let these games differ in densities only. We show that the Dynamic Programming…

We study potential games on unimodular random graphs of bounded degree, where players interact through the underlying network. Using the unimodular measure, we define a well-posed global potential that captures both finite- and…

We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we…

The traditional approach to choosing moves in game-playing programs is the minimax procedure. The general belief underlying its use is that increasing search depth improves play. Recent research has shown that given certain simplifying…

Increasingly in recent years, probabilistic computation has been investigated through the lenses of categorical algebra, especially via string diagrammatic calculi. Whereas categories of discrete and Gaussian probabilistic processes have…

We consider 3XOR games with perfect commuting operator strategies. Given any 3XOR game, we show existence of a perfect commuting operator strategy for the game can be decided in polynomial time. Previously this problem was not known to be…

Wigner's theorem characterizes isometries of the set of all rank one projections on a Hilbert space. In metric geometry nonexpansive maps and noncontractive maps are well studied generalizations of isometries. We show that under certain…

We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…

We generalize the deterministic simulation theorem of Raz and McKenzie [RM99], to any gadget which satisfies certain hitting property. We prove that inner-product and gap-Hamming satisfy this property, and as a corollary we obtain…

Two pertinent questions for any support theory of a monoidal triangulated category are whether it is functorial and if the tensor product property holds. To this end, we consider the complete prime spectrum of an essentially small monoidal…

We study a general version of the adversarial online learning problem. We are given a decision set $\mathcal{X}$ in a reflexive Banach space $X$ and a sequence of reward vectors in the dual space of $X$. At each iteration, we choose an…

Let T be a C^2-expanding self-map of a compact, connected, smooth, Riemannian manifold M. We correct a minor gap in the proof of a theorem from the literature: the set of points whose forward orbits are nondense has full Hausdorff…