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Guarantees for Tuning the Step Size using a Learning-to-Learn Approach
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the last-iteration loss directly instead of its log as the meta-objective (ablation) | Step-size tuning for gradient descent on a quadratic objective · Quadratic objective | meta-gradient magnitude: exponentially small for 0<η<2/L; exponentially large for η>2/L | Hurt |
| Use (1/t) log of the last-iteration loss as the meta-objective (ablation) | Step-size tuning for gradient descent · Quadratic objective | meta-gradient magnitude: O(L^3/(c_min^2 α(L-α))) | Helped |
| Compute the log-loss meta-gradient with standard backpropagation rather than the derived formula (ablation) | Step-size tuning for gradient descent · Quadratic objective | meta-training convergence: exponentially large/small in number of inner-steps t | Hurt |
| Evaluate the meta-objective on a separate validation set instead of the training set | Step-size tuning for least-squares gradient descent · n,n₁,n₂∈[d/4,3d/4], large noise | expected squared parameter error on new tasks: train-by-train: Ω(1)σ^2; train-by-validation: ||w*||-Ω(1) | Helped |
| Use training loss rather than validation loss as the meta-objective | Step-size tuning for least-squares gradient descent · Large sample size | expected squared parameter error on new tasks: (1+ε)dσ^2/n | No clear effect |
| Use train-by-validation instead of train-by-train for the MLP optimizer | MLP optimizer on MNIST · 1000 samples with 20% label noise | test accuracy | Helped |
| Increase the sample size while using train-by-train | MLP optimizer on MNIST · Whole MNIST dataset without label noise | test accuracy | No clear effect |
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