Large deviations in the first iterations

[grandowife]

Hi there, 

Lately, I am working on an iterative algorithm to alternately optimize two targets, i.e., U and V.

For U, it supposes to aggerates all past info, while the V only focuses on a specific sample and assumed to be orthogonal.

My objective function is generally formulated as:

1/t * sum_(i=1)^(t)   || X_i - U *( V_i )^T * X_i  ||_{F}  

My algorithm can be described as:

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for t = 1 to T

  1,  Draw a random sample X_t

  2,  Calculate the corresponding V_t based on U_t-1 by defining a sub-problem on Grassmannian manifold 

       and then solving it by the CG algorithm (ps.  this step is reached by using the Manopt toolbox and the 'maxiter' in CG is set to only 1.)

  3.  Calculate the U_t by aggerating all past info (i.e., that is t samples) in a closed-form solution

end.

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Then I evaluate the performance (basic accuracy) at the initialization step (based on the intialized U, i.e., U_0) and every iteration.

However, I found the performance varies significantly at the first iteration by only learning one sample, and begin to vibrates in a small range.

For example, 

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Iterations  |        0       |        1        |        2        |       3        |       4         |         5       |  

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Accuracy  |     76%     |      86%     |     86.5%   |     87%     |    86.3%   |    86.89%  | 

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Could anyone tell me how to solve this problem? It seems like I set a very large learning rate, however, there is no actually learning rate in CG algorithm and the closed-form solution.

Best wishes

Qiuying