منابع مشابه
Lipschitz Games
The Lipschitz constant of a finite normal–form game is the maximal change in some player's payoff when a single opponent changes his strategy. We prove that games with small Lipschitz constant admit pure ǫ-equilibria, and pinpoint the maximal Lipschitz constant that is sufficient to imply existence of pure ǫ-equilibrium as a function of the number of players in the game and the number of strate...
متن کاملLipschitz Bandits without the Lipschitz Constant
We consider the setting of stochastic bandit problems with a continuum of arms indexed by [0, 1]. We first point out that the strategies considered so far in the literature only provided theoretical guarantees of the form: given some tuning parameters, the regret is small with respect to a class of environments that depends on these parameters. This is however not the right perspective, as it i...
متن کاملSimplicial Lipschitz optimization without the Lipschitz constant
In this paper we propose a new simplicial partition-based deterministic algorithm for global optimization of Lipschitz-continuous functions without requiring any knowledge of the Lipschitz constant. Our algorithm is motivated by the well-known Direct algorithm which evaluates the objective function on a set of points that tries to cover the most promising subregions of the feasible region. Almo...
متن کاملG : Bandits , Experts and Games 10 / 10 / 16 Lecture 6 : Lipschitz Bandits
Motivation: similarity between arms. In various bandit problems, we may have information on similarity between arms, in the sense that ‘similar’ arms have similar expected rewards. For example, arms can correspond to “items” (e.g., documents) with feature vectors, and similarity can be expressed as some notion of distance between feature vectors. Another example would be the dynamic pricing pro...
متن کاملLipschitz Percolation
We prove the existence of a (random) Lipschitz function F : Z → Z such that, for every x ∈ Z, the site (x, F (x)) is open in a site percolation process on Z. The Lipschitz constant may be taken to be 1 when the parameter p of the percolation model is sufficiently close to 1.
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ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 2013
ISSN: 0364-765X,1526-5471
DOI: 10.1287/moor.1120.0557