  Task-free continual learning (CL) aims to learn a non-stationary data stream
without explicit task definitions and not forget previous knowledge. The widely
adopted memory replay approach could gradually become less effective for long
data streams, as the model may memorize the stored examples and overfit the
memory buffer. Second, existing methods overlook the high uncertainty in the
memory data distribution since there is a big gap between the memory data
distribution and the distribution of all the previous data examples. To address
these problems, for the first time, we propose a principled memory evolution
framework to dynamically evolve the memory data distribution by making the
memory buffer gradually harder to be memorized with distributionally robust
optimization (DRO). We then derive a family of methods to evolve the memory
buffer data in the continuous probability measure space with Wasserstein
gradient flow (WGF). The proposed DRO is w.r.t the worst-case evolved memory
data distribution, thus guarantees the model performance and learns
significantly more robust features than existing memory-replay-based methods.
Extensive experiments on existing benchmarks demonstrate the effectiveness of
the proposed methods for alleviating forgetting. As a by-product of the
proposed framework, our method is more robust to adversarial examples than
existing task-free CL methods. Code is available on GitHub
\url{https://github.com/joey-wang123/DRO-Task-free}
