Related papers: On Bellman's Optimality Principle for zs-POSGs

We first study an optimal stopping problem in which a player (an agent) uses a discrete stopping time in order to stop optimally a payoff process whose risk is evaluated by a (non-linear) $g$-expectation. We then consider a non-zero-sum…

We study optimality for the safety-constrained Markov decision process which is the underlying framework for safe reinforcement learning. Specifically, we consider a constrained Markov decision process (with finite states and finite…

This paper addresses the problem of learning a Nash equilibrium in $\gamma$-discounted multiplayer general-sum Markov Games (MG). A key component of this model is the possibility for the players to either collaborate or team apart to…

In this paper, I introduce a novel benchmark in games, super-Nash performance, and a solution concept, optimin, whereby players maximize their minimal payoff under unilateral profitable deviations by other players. Optimin achieves…

The paper is concerned with a variant of the continuous-time finite state Markov game of control and stopping where both players can affect transition rates, while only one player can choose a stopping time. We use the dynamic programming…

Zero-sum stochastic games provide a rich model for competitive decision making. However, under general forms of state uncertainty as considered in the Partially Observable Stochastic Game (POSG), such decision making problems are still not…

We consider the problem of optimally utilizing $N$ resources, each in an unknown binary state. The state of each resource can be inferred from state-dependent noisy measurements. Depending on its state, utilizing a resource results in…

This paper considers the problem of designing optimal algorithms for reinforcement learning in two-player zero-sum games. We focus on self-play algorithms which learn the optimal policy by playing against itself without any direct…

We consider the problem of finding the best memoryless stochastic policy for an infinite-horizon partially observable Markov decision process (POMDP) with finite state and action spaces with respect to either the discounted or mean reward…

We propose a new objective function for finite-horizon episodic Markov decision processes that better captures Bellman's principle of optimality, and provide an expression for the gradient of the objective.

We contribute the first provable guarantees of global convergence to Nash equilibria (NE) in two-player zero-sum convex Markov games (cMGs) by using independent policy gradient methods. Convex Markov games, recently defined by Gemp et al.…

Computing approximate Nash equilibria in multi-player general-sum Markov games is a computationally intractable task. However, multi-player Markov games with certain cooperative or competitive structures might circumvent this…

The overall aim of our research is to develop techniques to reason about the equilibrium properties of multi-agent systems. We model multi-agent systems as concurrent games, in which each player is a process that is assumed to act…

This paper characterizes differentiable and subgame Markov perfect equilibria in a continuous time intertemporal decision problem with non-constant discounting. Capturing the idea of non commitment by letting the commitment period being…

We consider the problem of computing a mixed-strategy generalized Nash equilibrium (MS-GNE) for a class of games where each agent has both continuous and integer decision variables. Specifically, we propose a novel Bregman…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

This paper studies partially observable two-person zero-sum semi-Markov games under a probability criterion, in which the system state may not be completely observed. It focuses on the probability that the accumulated rewards of player 1…

This paper aims to solve the optimal strategy against a well-known adaptive algorithm, the Hedge algorithm, in a finitely repeated $2\times 2$ zero-sum game. In the literature, related theoretical results are very rare. To this end, we make…

Many security and other real-world situations are dynamic in nature and can be modelled as strictly competitive (or zero-sum) dynamic games. In these domains, agents perform actions to affect the environment and receive observations --…

In this paper, we consider discrete-time partially observed mean-field games with the risk-sensitive optimality criterion. We introduce risk-sensitivity behaviour for each agent via an exponential utility function. In the game model, each…