Journal ArticleDOI
Guaranteed performance regions in Markovian systems with competing decision makers
Nahum Shimkin,Adam Shwartz +1 more
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TLDR
A decision maker is facing a dynamic system which is being controlled by himself/herself as well as by other decision makers, and whether this decision maker can guarantee a performance vector which approaches this desired set is considered for the worst-case scenario.Abstract:
A decision maker is facing a dynamic system which is being controlled by himself/herself as well as by other decision makers. He/she considers a vector of performance measures. Acceptable performance is defined through a set in the space of performance vectors. Whether this decision maker can guarantee a (time-averaged) performance vector which approaches this desired set is considered for the worst-case scenario, in which other decision makers may, for selfish reasons, try to exclude his/her vector from the desired set. For a controlled Markov model of the system, a sufficient condition for approachability is given, and appropriate control strategies are constructed. Under certain recurrence conditions, a complete characterization of approachability is then provided for convex sets. The mathematical formulation leads to a theory of approachability for stochastic games with vector payoffs. A simple queuing example illustrates this approach. >read more
Citations
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Book ChapterDOI
Convex Analytic Methods in Markov Decision Processes
TL;DR: The convex analytic approach to classical Markov decision processes wherein they are cast as a static convex programming problem in the space of measures is described.
Journal Article
A Geometric Approach to Multi-Criterion Reinforcement Learning
Shie Mannor,Nahum Shimkin +1 more
TL;DR: This work captures the problem of reinforcement learning in a controlled Markov environment with multiple objective functions of the long-term average reward type using a stochastic game model, where the learning agent is facing an adversary whose policy is arbitrary and unknown, and where the reward function is vector-valued.
Journal ArticleDOI
Individual Equilibrium and Learning in Processor Sharing Systems
Eitan Altman Inria,Nahum Shimkin +1 more
TL;DR: This work shows that any Nash equilibrium point consists of threshold decision rules and establishes the existence and uniqueness of a symmetric equilibrium point, and considers a reasonable dynamic learning scheme, which converges to the symmetric Nash equilibrium Point.
Journal ArticleDOI
On sequential strategies for loss functions with memory
TL;DR: It is shown that key properties, that hold for finite-state strategies in the context of memoryless loss functions, do not carry over to the case of loss functions with memory, and an infinite family of randomized finite- state strategies is seen to be the most appropriate reference class for this case.
Book ChapterDOI
Constrained Markov Games: Nash Equilibria
Eitan Altman,Adam Shwartz +1 more
TL;DR: The theory of constrained Markov games is developed based on the theory of sensitivity analysis of mathematical programs developed by Dantzig, Folkman, and Shapiro and characterized all stationary Nash equilibria as fixed points of some coupled Linear Programs.
References
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Journal ArticleDOI
Stochastic Games
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Journal ArticleDOI
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TL;DR: The description for this book, Contributions to the Theory of Games (AM-40), Volume IV, will be forthcoming.