Related papers: Value Function Approximation in Zero-Sum Markov Ga…

We introduce a modification of Perron's method, where semi-solutions are considered in a carefully defined asymptotic sense. With this definition, we can show, in a rather elementary way, that in a zero-sum game or a control problem (with…

We consider deterministic Markov decision processes (MDPs) and apply max-plus algebra tools to approximate the value iteration algorithm by a smaller-dimensional iteration based on a representation on dictionaries of value functions. The…

In this paper, we consider a differential stochastic zero-sum game in which two players intervene by adopting impulse controls in a finite time horizon. We provide a numerical solution as an approximation of the value function, which turns…

We study the problem of finding the Nash equilibrium in a two-player zero-sum Markov game. Due to its formulation as a minimax optimization program, a natural approach to solve the problem is to perform gradient descent/ascent with respect…

Robust Markov decision processes (RMDPs) extend standard Markov decision processes (MDPs) to account for uncertainty in the transition probabilities. RMDPs have an uncertainty set that defines a set of possible transition functions, each of…

Value decomposition has long been a fundamental technique in multi-agent dynamic programming and reinforcement learning (RL). Specifically, the value function of a global state $(s_1,s_2,\ldots,s_N)$ is often approximated as the sum of…

In reinforcement learning (RL) , one of the key components is policy evaluation, which aims to estimate the value function (i.e., expected long-term accumulated reward) of a policy. With a good policy evaluation method, the RL algorithms…

In this paper, we investigate a partially observable zero sum games where the state process is a discrete time Markov chain. We consider a general utility function in the optimization criterion. We show the existence of value for both…

We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two continuous-time Markov chains (X, Y), where X is only observed by player 1 and Y only by player 2, implying that…

In this work, we consider a cooperative multi-agent Markov decision process (MDP) involving m agents. At each decision epoch, all the m agents independently select actions in order to maximize a common long-term objective. In the policy…

We optimize finite horizon multi-agent reach-avoid Markov decision process (MDP) via \emph{local feedback policies}. The global feedback policy solution yields global optimality but its communication complexity, memory usage and computation…

Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…

Reinforcement learning in non-stationary environments is challenging due to abrupt and unpredictable changes in dynamics, often causing traditional algorithms to fail to converge. However, in many real-world cases, non-stationarity has some…

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 $O(T^{-3/4})$…

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…

We consider a general type of non-Markovian impulse control problems under adverse non-linear expectation or, more specifically, the zero-sum game problem where the adversary player decides the probability measure. We show that the upper…

Optimization under uncertainty is a fundamental problem in learning and decision-making, particularly in multi-agent systems. Previously, Feldman, Kalai, and Tennenholtz [2010] demonstrated the ability to efficiently compete in repeated…

An abundance of recent impossibility results establish that regret minimization in Markov games with adversarial opponents is both statistically and computationally intractable. Nevertheless, none of these results preclude the possibility…

One often encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for controlled Markov chains. In this paper, we provide a method to construct sub-optimal policies along with a bound…

The goal of reinforcement learning is estimating a policy that maps states to actions and maximizes the cumulative reward of a Markov Decision Process (MDP). This is oftentimes achieved by estimating first the optimal (reward) value…