For vector-valued linear prediction with convex Lipschitz losses, ERM's sample complexity is Θ̃(k/ε²), and any d-dimensional stochastic convex optimization problem embeds into this setting with k=Θ(d) outputs.
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Complexity of Vector-valued Prediction: From Linear Models to Stochastic Convex Optimization
For vector-valued linear prediction with convex Lipschitz losses, ERM's sample complexity is Θ̃(k/ε²), and any d-dimensional stochastic convex optimization problem embeds into this setting with k=Θ(d) outputs.