Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

Publications

3 Hybrid Markov Game Controller Design Algorithms for Nonlinear Systems

Authors: R. Sharma, M. Gopal

Abstract:

Markov games can be effectively used to design controllers for nonlinear systems. The paper presents two novel controller design algorithms by incorporating ideas from gametheory literature that address safety and consistency issues of the 'learned' control strategy. A more widely used approach for controller design is the H∞ optimal control, which suffers from high computational demand and at times, may be infeasible. We generate an optimal control policy for the agent (controller) via a simple Linear Program enabling the controller to learn about the unknown environment. The controller is facing an unknown environment and in our formulation this environment corresponds to the behavior rules of the noise modeled as the opponent. Proposed approaches aim to achieve 'safe-consistent' and 'safe-universally consistent' controller behavior by hybridizing 'min-max', 'fictitious play' and 'cautious fictitious play' approaches drawn from game theory. We empirically evaluate the approaches on a simulated Inverted Pendulum swing-up task and compare its performance against standard Q learning.

Keywords: Fictitious Play, Cautious Fictitious Play, InvertedPendulum, Controller, Markov Games, Mobile Robot.

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2 Trajectory-Based Modified Policy Iteration

Authors: R. Sharma, M. Gopal

Abstract:

This paper presents a new problem solving approach that is able to generate optimal policy solution for finite-state stochastic sequential decision-making problems with high data efficiency. The proposed algorithm iteratively builds and improves an approximate Markov Decision Process (MDP) model along with cost-to-go value approximates by generating finite length trajectories through the state-space. The approach creates a synergy between an approximate evolving model and approximate cost-to-go values to produce a sequence of improving policies finally converging to the optimal policy through an intelligent and structured search of the policy space. The approach modifies the policy update step of the policy iteration so as to result in a speedy and stable convergence to the optimal policy. We apply the algorithm to a non-holonomic mobile robot control problem and compare its performance with other Reinforcement Learning (RL) approaches, e.g., a) Q-learning, b) Watkins Q(λ), c) SARSA(λ).

Keywords: Markov Decision Process (MDP), Mobile robot, Policy iteration, Simulation.

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1 Markov Game Controller Design Algorithms

Authors: Rajneesh Sharma, M. Gopal

Abstract:

Markov games are a generalization of Markov decision process to a multi-agent setting. Two-player zero-sum Markov game framework offers an effective platform for designing robust controllers. This paper presents two novel controller design algorithms that use ideas from game-theory literature to produce reliable controllers that are able to maintain performance in presence of noise and parameter variations. A more widely used approach for controller design is the H∞ optimal control, which suffers from high computational demand and at times, may be infeasible. Our approach generates an optimal control policy for the agent (controller) via a simple Linear Program enabling the controller to learn about the unknown environment. The controller is facing an unknown environment, and in our formulation this environment corresponds to the behavior rules of the noise modeled as the opponent. Proposed controller architectures attempt to improve controller reliability by a gradual mixing of algorithmic approaches drawn from the game theory literature and the Minimax-Q Markov game solution approach, in a reinforcement-learning framework. We test the proposed algorithms on a simulated Inverted Pendulum Swing-up task and compare its performance against standard Q learning.

Keywords: Reinforcement learning, Markov Decision Process, Matrix Games, Markov Games, Smooth Fictitious play, Controller, Inverted Pendulum.

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