Sure. For example, if your environment is such that the process of exploitation can alter your environment in such a way that your earlier judgment of "the most valuable thing" is no longer reliable, then an iterative cycle of explore-exploit-explore can potentially get you better results.
Of course, you can treat each loop of that cycle as a separate optimization problem and use the abovementioned strategy.
Could I replace "can potentially get you better results" with "will get you better results on average"?
This is for anyone in the LessWrong community who has made at least some effort to read the sequences and follow along, but is still confused on some point, and is perhaps feeling a bit embarrassed. Here, newbies and not-so-newbies are free to ask very basic but still relevant questions with the understanding that the answers are probably somewhere in the sequences. Similarly, LessWrong tends to presume a rather high threshold for understanding science and technology. Relevant questions in those areas are welcome as well. Anyone who chooses to respond should respectfully guide the questioner to a helpful resource, and questioners should be appropriately grateful. Good faith should be presumed on both sides, unless and until it is shown to be absent. If a questioner is not sure whether a question is relevant, ask it, and also ask if it's relevant.