We propose training fitted Q-iteration with log-loss (FQI-LOG) for batch reinforcement learning (RL). We show that the number of samples needed to learn a near-optimal policy with \fqilog scales with the accumulated cost of the optimal policy, which is zero in problems where acting optimally achieves the goal and incurs no cost. In doing so, we provide a general framework for proving \textit{small-cost} bounds, i.e. bounds that scale with the optimal achievable cost, in batch RL. Moreover, we empirically verify that FQI-LOG uses fewer samples than FQI trained with squared loss on problems where the optimal policy reliably achieves the goal.