In particular, we leverage the concept of stability in the literature of partial differential equation tostudy the asymptotic behavior ofthe learned solution asthe loss approaches zero. Withthis concept, we study animportant class of high-dimensional non-linear PDEs in optimal control, the Hamilton-JacobiBellman (HJB) Equation, and provethat for generalLp Physics-Informed Loss, a wide class of HJB equation is stable only ifp is sufficiently large.

In the adversarial streaming model, the input is a sequence of adaptive updates that defines an underlying dataset and the goal is to approximate, collect, or compute some statistic while using space sublinear in the size of the dataset.

Machine learning (ML) algorithms can solve many prediction tasks with greater accuracy than classical methods.

For all tabular experiments, we used -greedy exploration with = 0.1. Furthermore, during pretraining and training, we used a maximum episode-length of 100. For evaluation, we set = 0, and ran 10 evaluation episodes. We used a fixed step-sizeα for all tabular experiments. Therefore, there is stochasticity in the update target even in deterministic environments due to exploration of the behavior policy.