Epigraph projections for fast general convex programming
Authors: Po-Wei Wang, Matt Wytock, Zico Kolter
ICML 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section we compare our method to existing methods for general convex programming based on conic solvers. Our approach is implemented in Epsilon (Epigraph Proximal Solver), a library based on the ideas described in this paper: Epsilon accepts general convex programs specified according to the DCP ruleset, transforms them to a sum of proximal and epigraph operators as in Theorem 1, and solves them by employing the library of operator implementations described previously. Epsilon is open source and available at http://epopt.io, and all examples here are included in the distribution. We highlight the benchmark problems briefly in this section, and include a full description in Appendix A. Epsilon integrates directly with cvxpy (Diamond & Boyd, 2015) and thus we make the natural comparison between Epsilon and the existing solvers which solve the conic form. In particular, we compare Epsilon to ECOS (Domahidi et al., 2013), an interior point method, and SCS (O Donoghue et al., 2013), the splitting conic solver . In general, interior point methods achieve highly accurate solutions but have trouble scaling to larger problems and so it is unsurprising that Epsilon is able to solve problems to moderate accuracy several orders of magnitude faster than ECOS. On the other hand, SCS employs an operator splitting method that is similar in spirit to Epsilon, both being variants of ADMM. The main difference between Epsilon and SCS is in the intermediate representation to which operator splitting is applied: SCS solves |
| Researcher Affiliation | Academia | Po-Wei Wang POWEIW@CS.CMU.EDU Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA 15213 USA Matt Wytock MWYTOCK@STANFORD.EDU Electrical Engineering Department, Stanford University, Stanford, CA 94305 USA J. Zico Kolter ZKOLTER@CS.CMU.EDU School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213 USA |
| Pseudocode | Yes | Algorithm 1 Implicit dual newton method for epigraph projection ... Algorithm 2 Linear time algorithm for absolute epigraph |
| Open Source Code | Yes | Epsilon is open source and available at http://epopt.io, and all examples here are included in the distribution. |
| Open Datasets | Yes | Standard problems We begin with a few standard machine learning problems: Lasso (Tibshirani, 1996), sparse inverse covariance estimation (Banerjee et al., 2008) and image classification on MNIST (Le Cun et al., 1998). |
| Dataset Splits | No | The paper mentions problem sizes (e.g., "1500 examples, 5000 features for Lasso; 2000 examples, 1000 features for MNIST") but does not specify train/validation/test splits or methodology. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU/GPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions software tools like cvx (Grant & Boyd, 2008), cvxpy (Diamond & Boyd, 2015), ECOS (Domahidi et al., 2013), and SCS (O Donoghue et al., 2013) with citations to their respective papers, but does not provide explicit version numbers for these software dependencies. |
| Experiment Setup | No | The paper does not provide specific experimental setup details such as hyperparameter values, training configurations, or system-level settings. |