R-max — targets the objective risk sensitivity revises → Risk-sensitive performance criteria

R-max's headline guarantee is near-optimal performance, but "optimal" there means optimal with respect to expected total reward — the same objective risk-sensitive-performance-criteria was proposed to move away from. R-max's optimism ensures it eventually converges to the expected- reward-maximizing policy in the fewest possible exploratory steps; it says nothing about the variance of outcomes along the way or the probability of a rare catastrophic episode, because those are not part of what it is proven to optimize. Risk-sensitive-performance-criteria instead replaces the expected-total-reward objective itself with worst-case guarantees, bounded probability of very bad outcomes, or variance penalties, precisely to catch what an expected-value optimality proof like R-max's cannot (concrete-problems, §"Risk-Sensitive Performance Criteria:", p. 14). The two are not competing algorithms; one is an algorithm whose proof target the other argues is the wrong target.