While most existing bandit solutions are designed under a centralized setting (i.e., data is readily available at a central server), in response to the increasing application

A recent line of work shows that, by adding uniform random perturbations, first-order (FO) methods can efficiently escape saddle points and converge to SOSP .

In the following we provide additional results and details that did not fit into our main paper. In Appendix A we provide precise definitions and a complete proof of our identifiability theorem. We then discuss the assumptions underlying this result and their generalization in Appendix B. Appendix C covers implicit latent causal models (ILCMs) and their training, while Appendix D provides details for our experiments. We describe causal structure with SCMs. Qualcomm AI Research is an initiative of Qualcomm Technologies, Inc. a probability measure We will need to reason about vectors being "equal up to permutation and elementwise reparameteri-zations".

Next, we derive generalization bounds for the primal gap in nonconvex-concave settings.

We consider distributed stochastic variational inequalities (VIs) on unbounded domains with the problem data that is heterogeneous (non-IID) and distributed across many devices.

We consider two scalings of the first step learning rate η . For small η, we establish a Gaussian equivalence property for the trained feature map, and prove that the learned kernel improves upon the initial random feature model, but cannot defeat the best linear model on the input.