This question is related to question 1.23 of "Pattern Recognition and Machine Learning" by Bishop.
The question asks "Derive the criterion for minimizing the expected loss when there is a general loss matrix and general prior probabilities for the classes".
The expected loss is given by equation 1.80:
$$\mathbb{E}[L] = \sum_k \sum_j \int_{R_j} L_{kj} p(\vec{x},C_k) d\vec{x} \tag{1.80} $$ where $R_j$ is a decision region, a region such that if $\vec{x}\in R_j$ then we classify $\vec{x}$ into class $C_j$, and $L_{jk}$ is the loss matrix, a zero-diagonal matrix expressing how bad the loss associated with a mistake $j\neq k$ is.
My query is that I have no idea what this question is asking me to do. What variable are we supposed to change to minimise this, and how can we express the answer? We don't know anything about the probabilities $p(\vec{x}, C_j)$, or the regions $R_k$, so I can't figure out what result I'm supposed to come to.
There is no answer in the solution manual for this question.
There is one similar unanswered question here but this just resorts to saying that we are minimising the above value, which seems a little too obvious.