It should be noted that we only made a little modification to the GraphTrans model. For NTREE, we set GA T as its basic block with a 0.2 dropout probability between layers.

For the GLOW experiment we stacked three GLOW transformations at different scales eachwitheightaffinecoupling blocks spaced byactnorms andpermutations each parameterized byaCNN with twohidden layers with 512 filters each. In a recent arXiv submission, Arjovsky et al.[2] suggested that in the presence of an observable variability intheenvironmente(e.g. While this procedure workedondistributions that were very similar tobegin with, inthe majority of cases the log-likelihood fit toB did not provide informative gradients when evaluated on the transformed dataset, as the KL-divergence between distributions with disjoint supports is infinite. The code is available in lrmf_gradient_simulation.ipynb. LRMF objective(Eq 2) decreases over time and reaches zero when two datasets are aligned.

A.1 Costforincentivization We justify the way in which LIO accounts for the cost of incentivization as follows. However, both the reward-giverand recipients require sufficient time tolearn the effect ofincentives,which means that too large anα would lead to the degenerate result ofrηi = 0. On the other extreme, α = 0means there isno penalty and may result inprofligate incentivization that serves no useful purpose. Let θi for i {1,2} denote each agent's probability of taking the cooperative action. Each plot has afixed value for the incentive givenfortheotheraction. Each agent observesallagents' positions andcanmoveamong thethree available states: lever, start, and door.