Research map / Optimization / Nonconvex and smooth optimization
Characterization of Excess Risk for Locally Strongly Convex Population Risk
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use local strong convexity around population minima to analyze proper iterative algorithms | Convex problems · Convex problems | expected excess risk upper bound: \mathcal{O}(1/\sqrt{n}) -> \tilde{\mathcal{O}}(1/n) | Helped |
| Use local strong convexity and strict saddle conditions for proper algorithms | Non-convex problems · Non-convex problems (d / n ≤ O(1)) | expected excess risk upper bound: \mathcal{O}(\sqrt{d/n}) -> \tilde{\mathcal{O}}(1/\sqrt{n}) | Helped |
| Require that empirical risk has no spurious local minima with high probability | Proper algorithm approximating SOSP · Non-convex problems (d / n ≤ O(1)) | expected excess risk upper bound: \tilde{\mathcal{O}}(1/\sqrt{n}) -> \tilde{\mathcal{O}}(1/n) | Helped |
| Use a general convex-problem bound without the local strong convexity assumption | Convex problems · Convex problems | expected excess risk upper bound: \tilde{\mathcal{O}}(1/n) vs. \mathcal{O}(1/\sqrt{n}) | Hurt |
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