A Appendix A.1 Proof of Theorem 1 Theorem 1 (Algorithmic Stability Generalization in Expectation) Fix a task t 2 P

Inequality (8) as we did in Section 4.2. This prevents the network's output from becoming arbitrarily large. Gaussian distributions and would require much more computation during gradient steps. After sampling a base learner's initialization, we re-scale the network such that its parameters lie within a ball of radius A.5.1 PAC-BUS using Mini-Batches of T asks We present the P AC-BUS algorithm modified for mini-batches of tasks to improve training times. After training is complete, we aim to compute the upper bound.