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Conditional gradient methods for stochastically constrained convex minimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use increasing-size minibatches with SPIDER variance reduction instead of the single-sample variance-reduction scheme | H-1SFW, yielding H-SPIDER-FW · Stochastically constrained convex minimization | lmo calls: \mathcal{O}(\epsilon^{-6}) -> \mathcal{O}(\epsilon^{-2}) | Helped |
| Use increasing-size minibatches with SPIDER variance reduction instead of the single-sample variance-reduction scheme | H-1SFW, yielding H-SPIDER-FW · Stochastically constrained convex minimization | stochastic first-order oracle calls: \mathcal{O}(\epsilon^{-6}) -> \mathcal{O}(\epsilon^{-4}) | Helped |
| Process linear constraints stochastically using H-SPIDER-FW rather than SHCGM's deterministic constraint handling | Conditional-gradient methods for stochastic constraints · Stochastically constrained convex minimization | lmo calls: \mathcal{O}(\epsilon^{-3}) -> \mathcal{O}(\epsilon^{-2}) | Helped |
| Process constraints stochastically with H-1SFW rather than using SHCGM | Conditional-gradient methods for stochastic constraints · Stochastically constrained convex minimization | sfo calls: \mathcal{O}(\epsilon^{-3}) -> \mathcal{O}(\epsilon^{-6}) | Hurt |
| Use H-1SFW or H-SPIDER-FW instead of SHCGM | Conditional-gradient optimization on synthetic SDPs · Synthetic SDPs | objective suboptimality | Helped |
| Use H-1SFW or H-SPIDER-FW instead of SHCGM | Conditional-gradient optimization on synthetic SDPs · Synthetic SDPs | feasibility | Helped |
| Use H-1SFW or H-SPIDER-FW instead of SHCGM | K-means SDP relaxation · MNIST, k-means SDP | objective suboptimality | Helped |
| Use H-1SFW or H-SPIDER-FW instead of SHCGM | K-means SDP relaxation · MNIST, k-means SDP | feasibility | Helped |
| Use H-1SFW or H-SPIDER-FW instead of SHCGM | Uniform Sparsest Cut SDP · Network Repository graphs | objective suboptimality | Helped |
| Use H-1SFW or H-SPIDER-FW instead of SHCGM | Uniform Sparsest Cut SDP · Network Repository graphs | feasibility | Helped |
| Use the heavy-tailed Stable distribution rather than the benign synthetic-data distribution | H-1SFW and H-SPIDER-FW compared with SHCGM · Synthetic SDPs with heavy-tailed Stable entries | convergence speed | Mixed |
| Replace projection-based steps with conditional-gradient steps using an LMO | Stochastic constrained convex optimization · Stochastically constrained convex minimization | stochastic first-order oracle calls: \mathcal{O}(\epsilon^{-2}) -> \mathcal{O}(\epsilon^{-4}) | Hurt |
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