Research map / Optimization / Nonconvex and smooth optimization
Hybrid Stochastic-Deterministic Minibatch Proximal Gradient: Less-Than-Single-Pass Optimization with Nearly Optimal Generalization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HSDMPG instead of SGD | Strongly-convex ERM, quadratic loss · ERM with optimization error 1/√n | IFO complexity: \mathcal{O} (n^{0.875}\log^{1.5}(n)) versus \mathcal{O} (n) | Helped |
| Use HSDMPG instead of APCG | Strongly-convex ERM, quadratic loss · ERM with optimization error 1/√n | IFO complexity: \mathcal{O} (n^{0.875}\log^{1.5}(n)) versus \Oc{n^{1.25}\log(n)} | Helped |
| Use HSDMPG instead of SVRG, SCSG, SPDC, APSDCA, AMSVRG, Catalyst, Katyusha, or Varag | Strongly-convex ERM, quadratic loss · ERM with optimization error 1/√n | IFO complexity: \mathcal{O} (n^{0.875}\log^{1.5}(n)) versus \mathcal{O} \left(n\log\left(n\right)\right) | Helped |
| Use HSDMPG instead of SGD | Strongly-convex ERM, generic loss · ERM with optimization error 1/√n | IFO complexity: \mathcal{O} \left(n^{0.875} \log^{2.25}\left(n\right) \right) versus \mathcal{O}(n) | Helped |
| Use HSDMPG instead of the compared stochastic-gradient baselines | Strongly-convex ERM · Quadratic and non-quadratic learning tasks in the experiments | IFO complexity | Helped |
| Extend the quadratic HSDMPG procedure with sequential quadratic approximation | HSDMPG · Generic strongly-convex loss | IFO complexity: \log^{1.5}(n) for the quadratic case; \log^{2.25}(n) for generic convex loss | Mixed |
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