On Optimal poliy parameters

[jpfeifer]

A couple of points:

1. The cscolve in csolve from Born & Pfeifer (2018) is not an alternative. That one was used to compute the certainty equivalent for a given optimal policy, i.e. to solve an exact equation, not to minimize an objective.
2. It is well-known that local and global optimizers differ in their performance, see e.g.

Cmaes vs csminwel

csminwel is a Newton-type local optimizer. If you are close to the global mode, it will quickly converge to this this mode. But it can also converge to a local mode, i.e. fail to find the global one because it is local. cmaes is a global optimizer. It will be slower but has a higher likelihood of finding the global mode instead of just a local one.

Local optimizers will often depend on the starting point as they converge to the next local optimum.
3. As csminwel uses derivatives, it will typically show quadratic convergence and will be fast, but that comes with the downside of being local.
4. It is also well-known that loss functions tend to become very flat for large parameter values, so that bounds should be imposed. See e.g. A question about OSR command and policy frontier
5. The jump you describe above is not visible in the screenshot, but may indicate a large problem. Without the files it is impossible to tell.