Interesting! Yeah, I'm not terribly familiar with CH. Generally speaking, the trouble with the stochastic setting (perhaps you're already aware of this) is that it doesn't satisfy a very tempting (!) notion of sub-problem optimality that holds trivially in the deterministic setting. We used to have a simple counterexample in the paper but I think we might have had to remove it due to space constraints (here [1] is a copy). So I'd have to really think about what you're saying; it's not obvious to me that it should work in the stochastic setting, but perhaps it does. But thanks for the pointers either way, that's useful to know!
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Interesting! Yeah, I'm not terribly familiar with CH. Generally speaking, the trouble with the stochastic setting (perhaps you're already aware of this) is that it doesn't satisfy a very tempting (!) notion of sub-problem optimality that holds trivially in the deterministic setting. We used to have a simple counterexample in the paper but I think we might have had to remove it due to space constraints (here [1] is a copy). So I'd have to really think about what you're saying; it's not obvious to me that it should work in the stochastic setting, but perhaps it does. But thanks for the pointers either way, that's useful to know!
[1] https://drive.google.com/uc?id=0B0wBMIQFZpbwSERxUWRXUE94d1E