New Sequential Minimal Optimization Algorithm for Support Vector Regression with MAPE Loss
Researchers have derived a Sequential Minimal Optimization (SMO) algorithm for support vector regression using Mean Absolute Percentage Error (MAPE) loss, addressing sample-dependent dual box constraints that had not previously been handled in the SMO literature. The work proves that the MAPE modification only alters two components of the standard SMO iteration—working-set selection and analytic-update clipping—while leaving the rest of the algorithm structurally unchanged. The algorithm outperforms established solvers (OSQP, MOSEK, Clarabel) in wall-time benchmarks and succeeds on a large-scale benchmark where a patched LIBSVM implementation fails to converge.
A preprint posted to arXiv presents a new Sequential Minimal Optimization algorithm tailored for epsilon-support vector regression (SVR) with MAPE loss, a formulation theoretically suited to forecasting tasks where errors are measured in relative rather than absolute terms. The central theoretical contribution is a structural-invariance result showing that adapting SMO to MAPE loss requires changes only to working-set selection and analytic-update clipping, leaving gradient bookkeeping and curvature computation identical to classical epsilon-SVR. Building on this invariance, the authors introduce four efficiency improvements: asymmetric freeze-counters, warm-starting, block working-set updates of size four, and per-pair tolerance scaling. The paper also resolves a previously open convergence problem for the odd-symmetry kernel variant through adaptive spectral regularization. Numerical experiments across eleven synthetic configurations confirm solution agreement with reference solvers within standard tolerance, and wall-time benchmarks show the new algorithm achieves the lowest median runtime against OSQP, MOSEK, and Clarabel on every tested configuration. At production scale, the algorithm converges on the California Housing dataset while a patched LIBSVM implementation hits its iteration ceiling without satisfying optimality conditions. An open-source R package and a solver-adaptation recipe are provided to facilitate adoption.
What's missing
The paper has not yet undergone peer review, as it is a preprint. Empirical evaluation is limited to synthetic configurations and one real-world benchmark (California Housing); performance on a broader range of real forecasting datasets remains untested.
What different sources said
- arXiv stat.MLCenter
Sequential Minimal Optimization for $\varepsilon$-SVR with MAPE Loss and Sample-Dependent Box Constraints
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