Research map / Optimization / Implicit bias and generalization
Agnostic Learning of a Single Neuron with Gradient Descent
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a noisy teacher assumption, so the conditional label mean equals the target neuron | Gradient Descent for single-neuron learning · Noisy teacher network versus agnostic learning | population risk guarantee: O(OPT) + ε to OPT + ε | Helped |
| Use ReLU rather than a strictly increasing Lipschitz activation | Gradient Descent for agnostic single-neuron learning · Agnostic learning with marginal spread | population risk guarantee: O(OPT) to O(OPT^{1/2}) | Hurt |
| Use ReLU rather than a strictly increasing Lipschitz activation under the noisy teacher assumption | Gradient Descent for noisy teacher networks · Noisy teacher network | population risk guarantee: OPT + ε for both | No clear effect |
| Use online stochastic gradient descent in the realizable setting | Single-neuron learning · Realizable learning | sample complexity: O(ε^{-2}) to O(ε^{-1}) | Helped |
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