a different way. We next show that this hardness can be strengthened to an NP-hardness for an efficiently computable $f$. This allows for the implementation of any oracle for $f$ or its derivatives. Thus assuming the Exponential Time Hypothesis [@ImpagliazzoP01], our result implies the oracle model lower bounds. Additionally, it rules out efficient non-blackbox algorithms that could examine the implementation of $f$ beyond point evaluations. We leave open the question of whether other oracle lower bounds [@NemiroskiY; @Nesterov14; @Bubeck15; @Hazan16] in optimization can be strengthened to NP-hardness results.

We next look at the large $\lambda$ case. As discussed above, for large enough $\lambda$ sampling must be hard if optimization is. [*Is hardness of optimization the only obstruction to efficient sampling?*]{} We answer this question in the negative. We exhibit a family of functions for which optimization is easy, but where sampling is NP-hard for large enough $\lambda$. We draw on extensive work on the discrete analogs of these questions, where $f$ is simple (e.g. linear) but ${\mathcal{X}}$ is a discrete set.

Our upper bound on optimization for this family can be strengthened to work under weaker models of access to the function, where we only have blackbox access to the 