Stochastic gradient methods have been a widespread practice in machine learning.

In particular, we consider group-structured and boundedfdivergence uncertainty sets. Our approach relies on an accelerated method that queries a ball optimization oracle, i.e., a subroutine that minimizes the objective within a small ball around the query point. Our main contribution is efficient implementations of this oracle for DRO objectives.

Specifically, we extend the Catalyst approach originally designed fordeterministic objectives tothe stochastic setting.

See also, e.g., [1] fora Bayesianinferenceperspective.

Stochastic gradient methods have been a widespread practice in machine learning.

Forinstance,comparedto existing solutions, we showthat SCLTS plays the (non-optimal) baseline action at most O(logT) times (compared toO( T)). Finally, we make connections to another studied form of "safety constraints" that takes the form of anupper bound on the instantaneous reward.

Insteadof (2), consider (Q 1 ,..., Q q ) = argmin Rubin, D. Statistics, pages Rubin, D. comment.

We begin by proving the lower bound on coverage. The formal proof of this statement is standard at this point, so we simply refer to [3] for the remaining technical details. The proof for the upper bound also immediatelyfollowsfrom(S6)byapplyingLemma2in[3]. The proof is essentially an application of the main result in [2]. This will become apparent after we reduce our claim to the setting in the aforementioned paper.

In particular, using stochastic gradients in MAML update steps is crucial for RL problems since computation of exact gradients requires access to a large number of possible trajectories.