I have an issue with the implementation of a particular problem to be optimized with a Bayesian Optimization (it could be argued that it is not the best choice for this particular case, but let's say I have no other choices).
Now, I have N decisional variables. These variables control the way a time series is quantized into discrete values. Without going into much details, I want to optimize a performance index related to the way the signal is quantized. So, there is an optimal quantization, which does not consist in equally spaced intervals, and I want to find this quantization.
Now, each decisional variable is the space between two dotted lines in the figure above (in that example, ). Ideally, this signal has a maximum value B. Therefore, each decisional variable is bounded in the interval . Moreover, they can be set to integer (no need for more precision).
For the very nature of the problem, I want the maximum possible generalization, so I would like the optimizer to take into account every possible combination of variables, with the only constraint being of course the following:
where are the variables. Still, I want every to assume any possible value in the defined interval. So for instance extreme choices where one variable is equal to B and the other ones are 0 should be feasible and possibly generated. If I try to set the number of variables to or so (I would need to work with similar numbers), the Bayesian Optimization fails at attempting to find feasible sets of parameters: it eventually generates 10000 combinations of variables, but no combinations (or at most 1-2 of them) satisfy the sum constraint. Now, is there a way to increase the number of randomly generated variables (let's say from 10000 up to 10^7 or even more), so that enough combinations are produced satisfying this constraint?
Thank you in advance!