Parallel Algorithm for Non-Monotone DR-Submodular Maximization
This work addresses a fundamental optimization problem in machine learning and AI, with incremental improvements in parallel efficiency for researchers and practitioners in submodular optimization.
The authors tackled the problem of maximizing a non-monotone DR-submodular function under a cardinality constraint by developing a new parallel algorithm that achieves a 1/e - ε approximation using O(log n log(1/ε)/ε^3) parallel rounds, nearly matching the best sequential approximation and outperforming previous parallel methods in rounds and solution quality.
In this work, we give a new parallel algorithm for the problem of maximizing a non-monotone diminishing returns submodular function subject to a cardinality constraint. For any desired accuracy $ε$, our algorithm achieves a $1/e - ε$ approximation using $O(\log{n} \log(1/ε) / ε^3)$ parallel rounds of function evaluations. The approximation guarantee nearly matches the best approximation guarantee known for the problem in the sequential setting and the number of parallel rounds is nearly-optimal for any constant $ε$. Previous algorithms achieve worse approximation guarantees using $Ω(\log^2{n})$ parallel rounds. Our experimental evaluation suggests that our algorithm obtains solutions whose objective value nearly matches the value obtained by the state of the art sequential algorithms, and it outperforms previous parallel algorithms in number of parallel rounds, iterations, and solution quality.