About weight, penalty and biases
Hi everyone, I was trying to clarify the parameters of BQM and CQM, but I am confused about CQM 'weight' and 'penalty' parameters and 'quadratic' and 'linear' (referred to biases) in the BQM.
To my knowledge, 'weight' in CQM is referred to the amount I care about a constraint: if I allow it to be violated, I would give 'weight' a less value than to another constraint which I care more.
About 'penalty', said parameter can be 'linear' or 'quadratic', but I am not sure what it refers to specifically, and which is its relation with 'weight'.
Finally, the biases that can be 'linear' or 'quadratic' in the BQM refer to the coefficients that multiply the variables of the problem. Are the biases in the BQM equivalent to 'penalty' in the CQM?
Thanks in advance.
Comments
Hello,
For the CQM there are soft and hard constraints. If a weight value is provided then it is treated as a soft constraint. The violated weighted soft constraint can either be penalized by the weight value multiplied by the violation (linear) or by its square (quadratic). As you can see, these values relate to the constraints, while the linear and quadratic terms of the BQM are the weights of the variables themselves (linear) and their interactions with one another (quadratic).
The BQM documentation outlines this equation, where x values represent the variables, a values represent the linear biases, and b values represent the quadratic biases. Penalty models can be used to represent constraints on BQMs that takes a slightly different approach from CQM constraints.
Hopefully this helps to clarify things a little bit. Please let us know if you have any more questions.
The Problem-Solving Handbook is a great resource for problem formulation and various resources available. It goes into detail about how to think about problems and what the various parts represent. We would definitely recommend giving it a browse too.
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