相关论文: HSVI can solve zero-sum Partially Observable Stoch…

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…

We consider zero-sum stochastic games with perfect information and finitely many states and actions. The payoff is computed by a function which associates to each infinite sequence of states and actions a real number. We prove that if the…

We analyze best response dynamics for finding a Nash equilibrium of an infinite horizon zero-sum stochastic linear quadratic dynamic game (LQDG) with partial and asymmetric information. We derive explicit expressions for each player's best…

Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…

The Partially Observable Markov Decision Process has long been recognized as a rich framework for real-world planning and control problems, especially in robotics. However exact solutions in this framework are typically computationally…

We introduce two-level discounted games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted game and the lower level game is an undiscounted reachability game. Two-level games model…

Markov Decision Processes (MDPs) are stochastic optimization problems that model situations where a decision maker controls a system based on its state. Partially observed Markov decision processes (POMDPs) are generalizations of MDPs where…

We consider two-player partial-observation stochastic games on finite-state graphs where player 1 has partial observation and player 2 has perfect observation. The winning condition we study are \omega-regular conditions specified as parity…

In this paper, we study nonzero-sum separable games, which are continuous games whose payoffs take a sum-of-products form. Included in this subclass are all finite games and polynomial games. We investigate the structure of equilibria in…

Reward optimization in fully observable Markov decision processes is equivalent to a linear program over the polytope of state-action frequencies. Taking a similar perspective in the case of partially observable Markov decision processes…

Stochastic games are a classical model in game theory in which two opponents interact and the environment changes in response to the players' behavior. The central solution concepts for these games are the discounted values and the value,…

The classical, complete-information two-player games assume that the problem data (in particular the payoff matrix) is known exactly by both players. In a now famous result, Nash has shown that any such game has an equilibrium in mixed…

Planning under uncertainty is critical to robotics. The Partially Observable Markov Decision Process (POMDP) is a mathematical framework for such planning problems. It is powerful due to its careful quantification of the non-deterministic…

We present a robust framework with computational algorithms to support decision makers in sequential games. Our framework includes methods to solve games with complete information, assess the robustness of such solutions and, finally,…

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…

The Common Information (CI) approach provides a systematic way to transform a multi-agent stochastic control problem to a single-agent partially observed Markov decision problem (POMDP) called the coordinator's POMDP. However, such a POMDP…

In this paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function characterized as the unique viscosity solution to the…

Partially Observable Markov Decision Process (POMDP) is a framework applicable to many real world problems. In this work, we propose an approach to solve POMDPs with multimodal belief by relying on a policy that solves the fully observable…

We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general \cadlag measurable processes. As a by-product of…

Recent superhuman results in games have largely been achieved in a variety of zero-sum settings, such as Go and Poker, in which agents need to compete against others. However, just like humans, real-world AI systems have to coordinate and…