Related papers: A forward algorithm for a class of Markov zero-sum…
This paper considers a two-person zero-sum continuous-time Markov pure jump game in Borel state and action spaces over a fixed finite horizon. The main assumption on the model is the existence of a drift function, which bounds the reward…
This paper investigates the two-person zero-sum stochastic games for piece-wise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion on a general state space. Here, the transition and cost/reward rates…
We present a fast numerical algorithm for large scale zero-sum stochastic games with perfect information, which combines policy iteration and algebraic multigrid methods. This algorithm can be applied either to a true finite state space…
Existing studies on provably efficient algorithms for Markov games (MGs) almost exclusively build on the "optimism in the face of uncertainty" (OFU) principle. This work focuses on a different approach of posterior sampling, which is…
A recent method for solving zero-sum partially observable stochastic games (zs-POSGs) embeds the original game into a new one called the occupancy Markov game. This reformulation allows applying Bellman's principle of optimality to solve…
On a filtered probability space $(\Omega,\mathcal{F},P,\mathbb{F}=(\mathcal{F}_t)_{t=0,\dotso,T})$, we consider stopper-stopper games $\overline V:=\inf_{\Rho\in\bT^{ii}}\sup_{\tau\in\T}\E[U(\Rho(\tau),\tau)]$ and $\underline…
Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…
In this paper, we consider the problem of optimization and learning for constrained and multi-objective Markov decision processes, for both discounted rewards and expected average rewards. We formulate the problems as zero-sum games where…
The paper deals with a zero-sum differential game in which the dynamical system is described by a fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ The goal of the first (second) player is to…
Multi-Agent Reinforcement Learning (MARL) -- where multiple agents learn to interact in a shared dynamic environment -- permeates across a wide range of critical applications. While there has been substantial progress on understanding the…
We consider Dynkin games for Markov processes associated with semi-Dirichlet forms. Dynkin games are the optimal stopping games introduced as the models of zero-sum games by two players. We prove that the solution to the certain variational…
For zero-sum two-player continuous-time games with integral payoff and incomplete information on one side, one shows that the optimal strategy of the informed player can be computed through an auxiliary optimization problem over some…
While the topic of mean-field games (MFGs) has a relatively long history, heretofore there has been limited work concerning algorithms for the computation of equilibrium control policies. In this paper, we develop a computable policy…
Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to…
Semi-Markov model is one of the most general models for stochastic dynamic systems. This paper deals with a two-person zero-sum game for semi-Markov processes. We focus on the expected discounted payoff criterion with state-action-dependent…
We study policy optimization algorithms for computing correlated equilibria in multi-player general-sum Markov Games. Previous results achieve $O(T^{-1/2})$ convergence rate to a correlated equilibrium and an accelerated $O(T^{-3/4})$…
We study a two player repeated zero-sum game with asymmetric information introduced by Renault in which the underlying state of the game undergoes Markov evolution (parameterized by a transition probability $\frac 12\le p\le 1$). H\"orner,…
We consider a stochastic differential equation that is controlled by means of an additive finite-variation process. A singular stochastic controller, who is a minimizer, determines this finite-variation process, while a discretionary…
We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the…
A zero-sum two-person Perfect Information Semi-Markov game (PISMG) under limiting ratio average payoff has a value and both the maximiser and the minimiser have optimal pure semi-stationary strategies. We arrive at the result by first…