  Efficient exploration is one of the main challenges in reinforcement learning
(RL). Most existing sample-efficient algorithms assume the existence of a
single reward function during exploration. In many practical scenarios,
however, there is not a single underlying reward function to guide the
exploration, for instance, when an agent needs to learn many skills
simultaneously, or multiple conflicting objectives need to be balanced. To
address these challenges, we propose the \textit{task-agnostic RL} framework:
In the exploration phase, the agent first collects trajectories by exploring
the MDP without the guidance of a reward function. After exploration, it aims
at finding near-optimal policies for $N$ tasks, given the collected
trajectories augmented with \textit{sampled rewards} for each task. We present
an efficient task-agnostic RL algorithm, \textsc{UCBZero}, that finds
$\epsilon$-optimal policies for $N$ arbitrary tasks after at most $\tilde
O(\log(N)H^5SA/\epsilon^2)$ exploration episodes. We also provide an
$\Omega(\log (N)H^2SA/\epsilon^2)$ lower bound, showing that the $\log$
dependency on $N$ is unavoidable. Furthermore, we provide an $N$-independent
sample complexity bound of \textsc{UCBZero} in the statistically easier setting
when the ground truth reward functions are known.
