weakness which decreased my score. Some line by line comments: - lines 32 - 37: You discuss how the regret cannot be sublinear, but proceed to prove that your method achieves T^{1/2} regret. Do you mean that the prediction error over the entire horizon T cannot be sublinear? - eq after line 145: typo --- i goes from 1 to n and since M,N are W x k x n x m, the index i should go in the third position. Based on the proof, the summation over u should go from tau to t, not from 1 to T. - line 159: typo -- "M" --> Theta_hat - line 188: use Theta_hat for consistency. - line 200: typo -- there should no Pi in the polynomial. - line 212: typo --- "beta^j" --> beta_j - line 219: the vector should be indexed - lines 227 - 231: the predictions in hindsight are denoted once by y_t^* and once by hat{y}_t^* - eq after line 255: in the last two terms hat{y}_t --> y_t Comments on the Appendix: - General comment about the Appendix: the references to Theorems and equations are broken. It is not clear if a reference points to the main text or to the appendix. - line 10: Consider a noiseless LDS... - line 19: typo -- N_i ---> P_i - equation (21): same comment about the summation over u as above. - line 41: what is P? - line 46: typo --- M_omega' ---> M_ell' - eq (31): typo -- no parenthesis before N_ell - line 56: the projection formula is broken - eq (56): why did you use Holder in that fashion? By assumption the Euclidean norm of x is bounded, so Cauchy Schwartz would avoid the extra T^{1/2}. ================== In line 40 of the appendix you defined R_x to be a bound on \|x\|_2 so there is no need for the inequality you used in the rebuttal. Maybe there is a typo in line 40, \|x\|_2 maybe should be \|x\|_\infty
- lines 32 - 37: You discuss how the regret cannot be sublinear, but proceed to prove that your method achieves T^{1/2} regret. Do you mean that the prediction error over the entire horizon T cannot be sublinear?