In reward-poisoning attacks against reinforcement learning (RL), an attacker can perturb the environment reward r_t into r_t+δ_t at each step, with the goal of forcing the RL agent to learn a nefarious policy. We categorize such attacks by the infinity-norm constraint on δ_t: We provide a lower threshold below which reward-poisoning attack is infeasible and RL is certified to be safe; we provide a corresponding upper threshold above which the attack is feasible. Feasible attacks can be further categorized as non-adaptive where δ_t depends only on (s_t,a_t, s_t+1), or adaptive where δ_t depends further on the RL agent's learning process at time t. Non-adaptive attacks have been the focus of prior works. However, we show that under mild conditions, adaptive attacks can achieve the nefarious policy in steps polynomial in state-space size |S|, whereas non-adaptive attacks require exponential steps. We provide a constructive proof that a Fast Adaptive Attack strategy achieves the polynomial rate. Finally, we show that empirically an attacker can find effective reward-poisoning attacks using state-of-the-art deep RL techniques.