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arXiv · 1609.02762

Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

Milan Korda·Didier Henrion·Colin N. Jones
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Abstract

We study the convergence rate of moment-sum-of-squares hierarchies of semidefinite programs for optimal control problems with polynomial data. It is known that these hierarchies generate polynomial under-approximations to the value function of the optimal control problem and that these under-approximations converge in the L1 norm to the value function as their degree d tends to infinity. We show that the rate of this convergence is O(1/ log log d). We treat in detail the continuous-time infinite-horizon discounted problem and describe in brief how the same rate can be obtained for the finite-horizon continuous-time problem and for the discrete-time counterparts of both problems.

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Milan Korda, Didier Henrion, Colin N. Jones. 2016-09-09. Convergence rates of moment-sum-of-squares hierarchies for optimal control problems. https://arxiv.org/abs/1609.02762

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