freealgorithmthatlearnstasksseparatelyrequiressamplesatleast PT t=1Kt|Πt|. Forthefirstargument,weuseinduction. Onroundt,assuming

The agent receives 0 reward on all but the last statetin the t-th task. There are twoactions, one for staying on the current state and the other one for moving forward,i.e. By [50], the total number of steps needed to learnMT is at leastAT3. The lower bound can only be achieved by carefully designed exploration strategy,which accounts for theunderlyingfunctionclass. The model setting and hyper-parameters are the sameinTorch-rl.