Distributed storage algorithms with optimal tradeoffs

One of the primary objectives of a distributed storage system is to reliably store large amounts of source data for long durations using a large number $N$ of unreliable storage nodes, each with $c$ bits of storage capacity. Storage nodes fail randomly over time and are replaced with nodes of equal capacity initialized to zeroes, and thus bits are erased at some rate $e$. To maintain recoverability of the source data, a repairer continually reads data over a network from nodes at an average rate $r$, and generates and writes data to nodes based on the read data. The distributed storage source capacity is the maximum amount of source that can be reliably stored for long periods of time. Previous research shows that asymptotically the distributed storage source capacity is at most $\left(1-\frac{e}{2 \cdot r}\right) \cdot N \cdot c$ as $N$ and $r$ grow. In this work we introduce and analyze algorithms such that asymptotically the distributed storage source data capacity is at least the above equation. Thus, the above equation expresses a fundamental trade-off between network traffic and storage overhead to reliably store source data.

Learning from partial correction

We introduce a new model of interactive learning in which an expert examines the predictions of a learner and partially fixes them if they are wrong. Although this kind of feedback is not i.i.d., we show statistical generalization bounds on the quality of the learned model.