Variance-Optimal Control Variates for Learning with Black-box Feedback
Modern models increasingly learn through black-box oracles such as humans, optimization solvers, and external tools that provide feedback without exposing their internal mechanisms. A common remedy is to learn an (action-)value function as a control variate. In this paper, we first observe that even an exact action-value function can be arbitrarily far from variance-optimal. We show that this gap arises because the value function minimizes the noise in each action's own gradient term, while an action can still affect the rest of the gradient estimator through shared parameters. A simple unbiased correction, at no extra oracle cost, can still reduce its variance by an arbitrarily large fac...
| Authors | Zihao Zhao, Shuhan Zhang, Kai Wang |
|---|---|
| Primary category | cs.LG |
| Published | 3 October 2026 |
| Last updated at source | 3 October 2026 |
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