Related papers: On a simple strategy weakly forcing the strong law…

Consider a strongly monotone game where the players' utility functions include a reward function and a linear term for each dimension, with coefficients that are controlled by the manager. Gradient play converges to a unique Nash…

This paper considers discounted infinite horizon mean field games by extending the probabilistic weak formulation of the game as introduced by Carmona and Lacker (2015). Under similar assumptions as in the finite horizon game, we prove…

In this paper, we propose Posterior Sampling Reinforcement Learning for Zero-sum Stochastic Games (PSRL-ZSG), the first online learning algorithm that achieves Bayesian regret bound of $O(HS\sqrt{AT})$ in the infinite-horizon zero-sum…

We investigate the problem of equilibrium computation for "large" $n$-player games. Large games have a Lipschitz-type property that no single player's utility is greatly affected by any other individual player's actions. In this paper, we…

Let (S_n)_{n\in\N} be a Z-valued random walk with increments from the domain of attraction of some \alpha-stable law and let (\xi(i))_{i\in\Z} be a sequence of iid random variables. We want to investigate U-statistics indexed by the random…

In this work we address the problem of finding feasible policies for Constrained Markov Decision Processes under probability one constraints. We argue that stationary policies are not sufficient for solving this problem, and that a rich…

Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…

Deep Reinforcement Learning (RL) methods rely on experience replay to approximate the minibatched supervised learning setting; however, unlike supervised learning where access to lots of training data is crucial to generalization,…

Offline reinforcement learning (RL) aims at learning an optimal strategy using a pre-collected dataset without further interactions with the environment. While various algorithms have been proposed for offline RL in the previous literature,…

Ye showed recently that the simplex method with Dantzig pivoting rule, as well as Howard's policy iteration algorithm, solve discounted Markov decision processes (MDPs), with a constant discount factor, in strongly polynomial time. More…

We consider average-energy games, where the goal is to minimize the long-run average of the accumulated energy. While several results have been obtained on these games recently, decidability of average-energy games with a lower-bound…

Under reasonable algebraic assumptions and under an infinite second order moment assumption, we show that the logarithm of the norm (log-norm) of a product of random i.i.d. matrices with entries in $\mathbb{R}$ or in any other local field…

We calculated a fixed strategy that minimizes the average number of guesses (minimum strategy) for the number-guessing game MOO by exhaustive search. Although the minimum strategy for a similar game, mastermind, has been reported, this…

We study finite-memory (FM) determinacy in games on finite graphs, a central question for applications in controller synthesis, as FM strategies correspond to implementable controllers. We establish general conditions under which FM…

Motivated by the study of asymptotic behaviour of the bandit problems, we obtain several strategy-driven limit theorems including the law of large numbers, the large deviation principle, and the central limit theorem. Different from the…

The underdamped, non-linear, generalized Langevin equation is widely used to model coarse-grained dynamics of soft and biological materials. By means of a projection operator formalism, we show under which approximations this equation can…

This paper studies the equilibrium properties of the ``obvious strategy profile'' in large finite-player games. Each player in such a strategy profile simply adopts a randomized strategy as she would have used in a symmetric equilibrium of…

The focus of this work is sample-efficient deep reinforcement learning (RL) with a simulator. One useful property of simulators is that it is typically easy to reset the environment to a previously observed state. We propose an algorithmic…

We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…

Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…