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University of Cambridge > Talks.cam > CUED Control Group Seminars > Q-learning and Pontryagin's Minimum Principle

## Q-learning and Pontryagin's Minimum PrincipleAdd to your list(s) Download to your calendar using vCal - Professor Sean Meyn (Director, Decision & Control Lab, CSL ECE UIUC)
- Wednesday 13 January 2010, 14:00-15:00
- Cambridge University Engineering Department, Lecture Theatre 6.
If you have a question about this talk, please contact Dr Ioannis Lestas.
Q-learning is a technique used to compute an optimal policy for a controlled Markov chain based on observations of the system controlled using a non-optimal policy. It has proven to be effective for models with finite state and action space. This paper establishes connections between Q-learning and nonlinear control of continuous-time models with general state space and general action space. The main contributions are summarized as follows. - The starting point is the observation that the “Q-function” appearing in Q-learning algorithms is an extension of the Hamiltonian that appears in the Minimum Principle. Based on this observation we introduce the steepest descent Q-learning (SDQ-learning) algorithm to obtain the optimal approximation of the Hamiltonian within a prescribed finite-dimensional function class.
- A transformation of the optimality equations is performed based on the adjoint of a resolvent operator. This is used to construct a consistent algorithm based on stochastic approximation that requires only causal filtering of the time-series data.
- Several examples are presented to illustrate the application of these techniques, including application to distributed control of multi-agent systems.
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