Risdefined X Rd and is randomvectorP .

These counts have very high global sensitivity.

Algorithmic \emph{replicability} has recently been introduced to address the need for reproducible experiments in machine learning. A \emph{replicable online learning} algorithm is one that takes the same sequence of decisions across different executions in the same environment, with high probability. We initiate the study of algorithmic replicability in \emph{constrained} MAB problems, where a learner interacts with an unknown stochastic environment for $T$ rounds, seeking not only to maximize reward but also to satisfy multiple constraints. Our main result is that replicability can be achieved in constrained MABs. Specifically, we design replicable algorithms whose regret and constraint violation match those of non-replicable ones in terms of $T$. As a key step toward these guarantees, we develop the first replicable UCB-like algorithm for \emph{unconstrained} MABs, showing that algorithms that employ the optimism in-the-face-of-uncertainty principle can be replicable, a result that we believe is of independent interest.

However, a theoretical understanding of their success in practice is still a mystery. Moreover, recent advances [34] on fast convergence in games are limited to no-regret algorithms such as online mirror descent, which satisfy stability.

We study the connection between gradient-based meta-learning and convex optimisation. We observe that gradient descent with momentum is a special case of meta-gradients, and building on recent results in optimisation, we prove convergence rates for meta-learning in the single task setting.