The authors wish to note the following: "We wish to acknowledge that during the writing of our manuscript we had access to an unpublished preprint from the Princeton group of H. Yang and coauthors, which similarly dealt with the theory of feedback control of Janus particles based on optically heated self-thermophoretic motion of Janus particles (photon nudging).* Through the state-of-the-art realization of 3D control, they analyzed the statistics and traveling time for a hot microswimmer in light of the optimal strategy for run-and-tumble motion of Escherichia coli. They developed a rigorous theory for evaluating on-time (self-propulsion period) and off-time (rotational diffusion period) distributions by making use of the first-passage time distribution (FPTD), which agreed with exponential tails known in biology. The optimum acceptance angle for self-propulsion was determined as 90 degrees for photon nudging, similar to the prediction for the optimal chemotactic strategy for E. coli (27). The same paper (27) hinted to us to use the probability distribution function with absorbing boundary conditions in solving the heat (diffusion) equation. The solution can be found in Selmke's paper* and our paper, as well as Zauderer's book (25). However, the normalization factor, which is necessary to compare the theory and the simulation, cannot be found to the best of our knowledge except for in our paper. FPTD is used to formulate the exact solution of the average displacement during active Brownian motion (ABM) in our paper, while in Selmke's paper,* it is used either to obtain exponential tails in on-time/offtime distribution or to obtain an asymptotic form to conclude the optimal acceptance angle to be 90 degrees. Our results revealed that the optimal angle varies from 0 to 90 degrees depending on signal to noise ratio for the deterministic feedback. Therefore, the usages and conclusions are very different."Accordingly, we wish to add the following text on page 1 in the right column: 'Researchers have been inspired by chemotactic behaviors of microorganisms and implemented such functions to self-propelled particles (11, 12, 34) for targeting their motion. Run-and-tumble is a well-known strategy for tactic behavior of E. coli, and it has been thoroughly compared with ABM of self-propelled particles from the view point of statistical mechanics (35)(36)(37)(38). The concept of run-and-tumble has been applied to Janus particles (13). The optimization of the run-andtumble algorithm for controlling microswimmers has been carried out rigorously using a first-passage time approach (Selmke et al., unpublished*).' "We apologize for the oversight in removing the reference to Selmke et al., which had been included in an earlier version of the paper. The reference was deleted because PNAS does not allow citations to unpublished work." Published under the PNAS license.www.pnas.org/cgi