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arXiv · 1403.4175

Approximate Dynamic Programming based on Projection onto the (min,+) subsemimodule

Chandrashekar Lakshminarayanan·Shalabh Bhatnagar
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Abstract

We develop a new Approximate Dynamic Programming (ADP) method for infinite horizon discounted reward Markov Decision Processes (MDP) based on projection onto a subsemimodule. We approximate the value function in terms of a $(\min,+)$ linear combination of a set of basis functions whose $(\min,+)$ linear span constitutes a subsemimodule. The projection operator is closely related to the Fenchel transform. Our approximate solution obeys the $(\min,+)$ Projected Bellman Equation (MPPBE) which is different from the conventional Projected Bellman Equation (PBE). We show that the approximation error is bounded in its $L_\infty$-norm. We develop a Min-Plus Approximate Dynamic Programming (MPADP) algorithm to compute the solution to the MPPBE. We also present the proof of convergence of the MPADP algorithm and apply it to two problems, a grid-world problem in the discrete domain and mountain car in the continuous domain.

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Chandrashekar Lakshminarayanan, Shalabh Bhatnagar. 2014-03-17. Approximate Dynamic Programming based on Projection onto the (min,+) subsemimodule. https://arxiv.org/abs/1403.4175

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