Corpus ID: 152282688

Solving Empirical Risk Minimization in the Current Matrix Multiplication Time

@article{Lee2019SolvingER,
  title={Solving Empirical Risk Minimization in the Current Matrix Multiplication Time},
  author={Y. Lee and Z. Song and Qiuyi Zhang},
  journal={ArXiv},
  year={2019},
  volume={abs/1905.04447}
}
  • Y. Lee, Z. Song, Qiuyi Zhang
  • Published 2019
  • Computer Science, Mathematics
  • ArXiv
  • Many convex problems in machine learning and computer science share the same form: \begin{align*} \min_{x} \sum_{i} f_i( A_i x + b_i), \end{align*} where $f_i$ are convex functions on $\mathbb{R}^{n_i}$ with constant $n_i$, $A_i \in \mathbb{R}^{n_i \times d}$, $b_i \in \mathbb{R}^{n_i}$ and $\sum_i n_i = n$. This problem generalizes linear programming and includes many problems in empirical risk minimization. In this paper, we give an algorithm that runs in time \begin{align*} O^* ( ( n^{\omega… CONTINUE READING
    21 Citations
    Algorithms and Hardness for Linear Algebra on Geometric Graphs
    • 1
    • PDF
    Total Least Squares Regression in Input Sparsity Time
    • 3
    • PDF
    A Deterministic Linear Program Solver in Current Matrix Multiplication Time
    • J. Brand
    • Mathematics, Computer Science
    • SODA
    • 2020
    • 16
    • PDF
    Coordinate Methods for Matrix Games
    • 3
    • PDF
    Minimizing Convex Functions with Integral Minimizers
    • 2
    • PDF
    Quantum algorithms for Second-Order Cone Programming and Support Vector Machines
    • 7
    • PDF
    Faster Dynamic Matrix Inverse for Faster LPs
    • 22
    • PDF
    Bipartite Matching in Nearly-linear Time on Moderately Dense Graphs
    • 7
    • PDF

    References

    SHOWING 1-10 OF 92 REFERENCES
    Non-convex Finite-Sum Optimization Via SCSG Methods
    • 144
    • PDF
    On the Local Minima of the Empirical Risk
    • 23
    • PDF
    Further Limitations of the Known Approaches for Matrix Multiplication
    • 23
    • Highly Influential
    • PDF
    Variance Reduction for Faster Non-Convex Optimization
    • 271
    • PDF
    Minimizing finite sums with the stochastic average gradient
    • 786
    • PDF