Metropolis Light Transport is not unbiased

I believe MLT is a biased algorithm, as it doesn't sample rays randomly. Many papers discuss something called "start-up bias", which results from choosing the paths to be perturbed - those paths are rated as 'more important' by the algorithm.

One would think that as long as completely new paths to mutate are regularly chosen, then the algorithm will eventually converge to the same solution as normal path tracing with no mutating of paths. To take the extreme case, if every possible (within the computational accuracy of the machine) path is sampled an equal number of times, it doesn't matter if you did that using path mutation or not.

Another question, then, is whether or not the mutation process leads the renderer to implicitly favour some paths over others. For example, paths right on the edge of the light may have fewer valid paths near them and will thus be sampled less often. If this is the case, then I think MLT is ultimately biased.