  We tackle the Multi-task Batch Reinforcement Learning problem. Given multiple
datasets collected from different tasks, we train a multi-task policy to
perform well in unseen tasks sampled from the same distribution. The task
identities of the unseen tasks are not provided. To perform well, the policy
must infer the task identity from collected transitions by modelling its
dependency on states, actions and rewards. Because the different datasets may
have state-action distributions with large divergence, the task inference
module can learn to ignore the rewards and spuriously correlate $\textit{only}$
state-action pairs to the task identity, leading to poor test time performance.
To robustify task inference, we propose a novel application of the triplet
loss. To mine hard negative examples, we relabel the transitions from the
training tasks by approximating their reward functions. When we allow further
training on the unseen tasks, using the trained policy as an initialization
leads to significantly faster convergence compared to randomly initialized
policies (up to $80\%$ improvement and across 5 different Mujoco task
distributions). We name our method $\textbf{MBML}$
($\textbf{M}\text{ulti-task}$ $\textbf{B}\text{atch}$ RL with
$\textbf{M}\text{etric}$ $\textbf{L}\text{earning}$).
