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Bilevel Optimization: Convergence Analysis and Enhanced Design
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the refined AID-BiO analysis with constant inner-loop steps and warm starts instead of the previous analysis | AID-BiO · Deterministic bilevel optimization | Gc(f, ε): \mathcal{O}(\kappa^4\epsilon^{-1}) -> \mathcal{O}(\kappa^3\epsilon^{-1}) | Helped |
| Use the refined AID-BiO analysis with constant inner-loop steps and warm starts instead of the previous analysis | AID-BiO · Deterministic bilevel optimization | Gc(g, ε): \mathcal{O}(\kappa^5\epsilon^{-5/4}) -> \mathcal{ O}(\kappa^4\epsilon^{-1}) | Helped |
| Use the refined AID-BiO analysis with constant inner-loop steps and warm starts instead of the previous analysis | AID-BiO · Deterministic bilevel optimization | JV(g, ε): \mathcal{O}\left(\kappa^4\epsilon^{-1}\right) -> \mathcal{O}\left(\kappa^{3}\epsilon^{-1}\right) | Helped |
| Use the refined AID-BiO analysis with constant inner-loop steps and warm starts instead of the previous analysis | AID-BiO · Deterministic bilevel optimization | HV(g, ε): \mathcal{\widetilde O}\left(\kappa^{4.5}\epsilon^{-1}\right) -> \mathcal{ O}\left(\kappa^{3.5}\epsilon^{-1}\right) | Helped |
| Use the stocBiO mini-batch hypergradient estimator rather than BSA | Stochastic bilevel optimization · Stochastic bilevel optimization | Gc(F, ε): \mathcal{O}(\kappa^6\epsilon^{-2}) -> \mathcal{O}(\kappa^5\epsilon^{-2}) | Helped |
| Use the stocBiO mini-batch hypergradient estimator rather than BSA | Stochastic bilevel optimization · Stochastic bilevel optimization | Gc(G, ε): \mathcal{O}(\kappa^9\epsilon^{-3}) -> \mathcal{O}(\kappa^9\epsilon^{-2}) | Helped |
| Use the stocBiO mini-batch hypergradient estimator rather than BSA | Stochastic bilevel optimization · Stochastic bilevel optimization | JV(G, ε): \mathcal{O}\left(\kappa^6\epsilon^{-2}\right) -> \mathcal{ O}\left(\kappa^5\epsilon^{-2}\right) | Helped |
| Use exponentially decaying batch sizes for the Neumann-series Hessian-vector terms instead of uniform batch sizes | stocBiO · Stochastic bilevel optimization | Samples for hypergradient estimation: \mathcal{O}\big( \epsilon^{-1}(\log\frac{1}{\epsilon})^2\big) -> \mathcal{O}\left(\epsilon^{-1}\log \frac{1}{\epsilon}\r | Helped |
| Warm-start inner-loop and hypergradient-estimation updates from the preceding outer iteration | AID-BiO · Deterministic bilevel optimization | Test accuracy | Helped |
| Use a constant rather than increasing number of inner-loop steps | AID-BiO · FC100 and miniImageNet, 5-way 5-shot | Test accuracy | Helped |
| Use AID-BiO rather than ITD-BiO | Deterministic bilevel optimization · FC100 and miniImageNet, 5-way 5-shot | Test accuracy | Helped |
| Use ITD-BiO rather than ANIL at a large inner-loop step count | Few-shot meta-learning · miniImageNet and FC100 | Training stability | Helped |
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