Related papers: A New Approach to Drifting Games, Based on Asympto…
Zero-sum Dynkin games under Poisson constraints, where players can only stop at the event times of a Poisson process, have been studied widely in the recent literature. The constraint can be modelled in two ways: either both players share…
We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…
We consider quantitative notions of parity automaton and parity game aimed at modelling resource-aware behaviour, and study (memory-full) strategies for exhibiting accepting runs that require a minimum amount of initial resources,…
Two-player zero-sum games are a well-established model for synthesising controllers that optimise some performance criterion. In such games one player represents the controller, while the other describes the (adversarial) environment, and…
We address the synthesis of control policies for unknown discrete-time stochastic dynamical systems to satisfy temporal logic objectives. We present a data-driven, abstraction-based control framework that integrates online learning with…
This paper considers a stochastic approximation algorithm, with decreasing step size and martingale difference noise. Under very mild assumptions, we prove the non convergence of this process toward a certain class of repulsive sets for the…
We consider a general problem of finding a strategy that minimizes the exponential moment of a given cost function, with an emphasis on its relation to the more common criterion of minimization the expectation of the first moment of the…
We consider an $N$-player game where the states of the players evolve with time as Stochastic Differential Equations (SDEs) with interaction only in the drift terms. Each player controls the drift of the SDE satisfied by her state process,…
In this paper, we present exploitability descent, a new algorithm to compute approximate equilibria in two-player zero-sum extensive-form games with imperfect information, by direct policy optimization against worst-case opponents. We prove…
In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold, and the probability of success in sequences of optimal stopping problems. This method, based on the resolution of a first-order…
Combinatorial Game Theory has also been called `additive game theory', whenever the analysis involves sums of independent game components. Such {\em disjunctive sums} invoke comparison between games, which allows abstract values to be…
In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…
From the standpoint of game theory, dominoes is a game that has not received much attention (specially the variety known as draw). It is usually thought that this game is already solved, given general results in game theory. However, the…
We consider the simple random walk on the $N$-dimensional integer lattice from the perspective of evaluating asymptotically the duration of play in the multidimensional gambler\apost s ruin problem. We show that, under suitable rescalings,…
We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…
Stochastic optimal control and games have a wide range of applications, from finance and economics to social sciences, robotics, and energy management. Many real-world applications involve complex models that have driven the development of…
Inverse game theory is utilized to infer the cost functions of all players based on game outcomes. However, existing inverse game theory methods do not consider the learner as an active participant in the game, which could significantly…
The success of adversarial formulations in machine learning has brought renewed motivation for smooth games. In this work, we focus on the class of stochastic Hamiltonian methods and provide the first convergence guarantees for certain…