Optimization algorithms on Riemannian manifolds used in this paper to optimize the acquisition function inageometry-awaremanner,havebeen developed bytaking advantage oftheEuclidean tangent spaceTxMlinked to each pointxon the manifoldM.

Foreacharma, letr(a) and cj(a) be, resp., the meanrewardandmeanresource-j consumption,i.e.,(r(a);c1(a),..., cd(a)):=Eo Da[o].We sometimeswriter =( r(a): a 2 [K])andcj =( cj(a): a 2 [K])asvectorsoverarms. Second, weuseatighterversionof Eq. (3.6) (see AppendixD.3):

In other words, a person's subsequent trajectory has likely been traveled by others. Based on this hypothesis, we propose to forecast a person's future trajectory by learning from the implicit scene regularities. We call the regularities, inherently derived from the past dynamics of the people and the environment in the scene, scene history.

Werecallthisresult from [4] (see Theorem 7 thereinformoredetails).

The general concept is to represent the training loss as a function of both the agent parameters and the hyperparameters. The agent optimizes the parameters to minimize this loss function, w.r.t the current hyperparameters.