The results will be sensitive to the splits, so you should compare models on the same partitioning of the data. Compare these two approaches:
- Approach 1 will compare two models, but use the same CV partitioning.
- Approach 2 will compare two models, but the first model will have a different CV partitioning than second.
We'd like to select the best model. The problem with approach 2 is that the difference in performance between the two models will come from two different sources: (a) the differences between the two folds and (b) the differences between the algorithms themselves (say, random forest and logistic regression). If one model out-performs the other, we won't know if that difference in performance is entirely, partially, or not at all due to the differences in the two CV partitions. On the other hand, any difference in performance using approach 1 cannot be due to differences in how the data were partitioned, because the partitions are identical.
To fix the partioning, use cvTools to create your (repeated) CV partitions and store the results.
There's nothing wrong with the (nested) algorithm presented, and in fact, it would likely perform well with decent robustness for the bias-variance problem on different data sets. You never said, however, that the reader should assume the features you were using are the most "optimal", so if that's unknown, there are some feature selection issues that must first be addressed.
FEATURE/PARAMETER SELECTION
A lesser biased approached is to never let the classifier/model come close to anything remotely related to feature/parameter selection, since you don't want the fox (classifier, model) to be the guard of the chickens (features, parameters). Your feature (parameter) selection method is a $wrapper$ - where feature selection is bundled inside iterative learning performed by the classifier/model. On the contrary, I always use a feature $filter$ that employs a different method which is far-removed from the classifier/model, as an attempt to minimize feature (parameter) selection bias. Look up wrapping vs filtering and selection bias during feature selection (G.J. McLachlan).
There is always a major feature selection problem, for which the solution is to invoke a method of object partitioning (folds), in which the objects are partitioned in to different sets. For example, simulate a data matrix with 100 rows and 100 columns, and then simulate a binary variate (0,1) in another column -- call this the grouping variable. Next, run t-tests on each column using the binary (0,1) variable as the grouping variable. Several of the 100 t-tests will be significant by chance alone; however, as soon as you split the data matrix into two folds $\mathcal{D}_1$ and $\mathcal{D}_2$, each of which has $n=50$, the number of significant tests drops down. Until you can solve this problem with your data by determining the optimal number of folds to use during parameter selection, your results may be suspect. So you'll need to establish some sort of bootstrap-bias method for evaluating predictive accuracy on the hold-out objects as a function of varying sample sizes used in each training fold, e.g., $\pi=0.1n, 0.2n, 0,3n, 0.4n, 0.5n$ (that is, increasing sample sizes used during learning) combined with a varying number of CV folds used, e.g., 2, 5, 10, etc.
OPTIMIZATION/MINIMIZATION
You seem to really be solving an optimization or minimization problem for function approximation e.g., $y=f(x_1, x_2, \ldots, x_j)$, where e.g. regression or a predictive model with parameters is used and $y$ is continuously-scaled. Given this, and given the need to minimize bias in your predictions (selection bias, bias-variance, information leakage from testing objects into training objects, etc.) you might look into use of employing CV during use of swarm intelligence methods, such as particle swarm optimization(PSO), ant colony optimization, etc. PSO (see Kennedy & Eberhart, 1995) adds parameters for social and cultural information exchange among particles as they fly through the parameter space during learning. Once you become familiar with swarm intelligence methods, you'll see that you can overcome a lot of biases in parameter determination. Lastly, I don't know if there is a random forest (RF, see Breiman, Journ. of Machine Learning) approach for function approximation, but if there is, use of RF for function approximation would alleviate 95% of the issues you are facing.
Best Answer
What you need to do is called "nested cross validation". These questions/answers in CV deal with it:
Use of nested cross-validation
Nested cross validation for model selection
How to split the dataset for cross validation, learning curve, and final evaluation?
and others. Just search for "nested cross validation"