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Question: is this approach stable? #1

@dublinsky

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@dublinsky

Recently I rewrite this approach with C++, and I obtained a weird result.
The first backward pass result is shown below,
Qx[4]: -75.6918 -77.3853 -28.5434 Qu[4]: -0.0436368 -0.0438127 Qx[3]: -75.8709 -77.5666 -28.5759 Qu[3]: -0.0327869 -0.0329636 Qx[2]: -76.0401 -77.7375 -28.5987 Qu[2]: -0.021885 -0.0220624 Qx[1]: -76.1995 -77.898 -28.6115 Qu[1]: -0.0109373 -0.0111152 Qx[0]: -76.3489 -78.048 -28.6145 Qu[0]: 5e-05 -0.000128326 succeed one time, new cost 94.44449565662705, previous cost 143.59513469841465
then the second backward approach explode, the result is shown below,
Qx[4]: -2.11124e+32 -2.21674e+32 -2.20281e+32 Qu[4]: -1.65692e+30 -1.66778e+30 Qx[3]: -2.11882e+32 -2.22514e+32 -2.21208e+32 Qu[3]: -8.82049e+29 -8.9053e+29 Qx[2]: -2.12163e+32 -2.22839e+32 -2.21606e+32 Qu[2]: -3.42022e+29 -3.47915e+29 Qx[1]: -2.12191e+32 -2.22883e+32 -2.21695e+32 Qu[1]: -4.64779e+28 -4.96836e+28 Qx[0]: -2.12188e+32 -2.22883e+32 -2.21702e+32 Qu[0]: 3.12553e+15 -4.84196e+26 failed, the regularization has been alerted, rho = 1.6e-08
the initial condition of cost to go is proper and correct, any guess of the reasons?

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