Reviews: A Bandit Framework for Strategic Regression

The question studied in the paper is interesting, and borrowing the idea from peer prediction to use the other arms' predictions as an unbiased estimator of the quality of one arm's prediction is a nice idea (in particular, because those arms need to be incentivized enough to make reasonably accurate predictions). However, the paper focuses too much on presenting "bells and whistles" rather than giving a deeper understanding of the basic (and main) results. Perhaps reorganizing the paper to only briefly mention the computational/privacy aware variants and giving both more intuition and technical content describing the main result (namely, that there exist \alpha-BNE with small regret) would focus the paper and give the reader a cleaner message of what the paper is doing. This tact would have the added benefit that the reader might be able to better assess the "quantitative" consequences of this work, in that it would leave more room for the authors to ruminate on how much better or worse these bounds are than what one could get in the non-strategic setting, or in various trivial simplifications/special cases of this model. As the paper stands, this reviewer finds it difficult to assess from the main body of the paper alone the technical contribution of the paper (and whether the results follow from a mild reworking of standard proofs or need substantial, new ideas). It is also difficult to assess a theory paper which gives not even a sketch or an outline of a proof in the main body of the paper.