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На этой неделе на семинаре выступит Алексей Бойко, аспирант Сколтеха с рассказом о том, как можно использовать Tensor Train разложение для решения уравнения Беллмана.
Четверг, ШАД
Аудитория: Стенфорд
19:00
Approximate Dynamic Programming with Tensor Train Decomposition
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Reinforcement Learning has emerged as a way of solving Bellman Equation by means of fitting generic function approximators by statistical sampling approach.
It got a lot of attention, partially due to its ability to cope with Curse of Dimensionality of Bellman Equation.
However, recently some other mathematical approaches have appeared do deal with high-dimensional data. One of the most prominent of those is Tensor Train.
Tensor Train may be seen as SVD-alike adaptive lossy compression algorithm, which allows to perform main mathematical operation on data without uncompressing it. It may provide up to logarithmic win in memory and time complexity (N -> logN), and have beaten a bunch of area-specific state of the art methods of solving high-dimensional partial differential equations in physics and quantum chemistry .
A paper on RSS (A*-conference in Robotics) have shown, that Bellman Equation arising in continious stochastic control problems may be also subject to the magic TT conpression, allowing to perform stadard Value and Policy Iteration algorithms on CPU on a up to 12-dimensional problem with the vector state up to the size of 10^24 elements, in a time of a few hours. Inference is also may be done without GPUs on a robot device, such as RPi 3+ or Intel NUC.
Ссылки:
https://www.researchgate.net/publication/281275027_Efficient_High-Dimensional_Stochastic_Optimal_Motion_Control_using_Tensor-Train_Decompositionhttps://www.researchgate.net/publication/220412263_Tensor-Train_Decomposition