  Cosmological acceleration is difficult to accommodate in theories of
fundamental interactions involving supergravity and superstrings. An
alternative is that the acceleration is not universal but happens in a large
localized region, which is possible in theories admitting regular black holes
with de Sitter-like interiors. We considerably strengthen this scenario by
placing it in a global anti-de Sitter background, where the formation of 'de
Sitter bubbles' will be enhanced by mechanisms analogous to the
Bizon-Rostworowski instability in general relativity. This opens an arena for
discussing the production of multiple accelerating universes from anti-de
Sitter fluctuations. We demonstrate such collapse enhancement by explicit
numerical work in the context of a simple two-dimensional dilaton-gravity model
that mimics the spherically symmetric sector of higher-dimensional gravities.
