Online Inference in Distributional Temporal-Difference Learning
We study online statistical inference for functionals of the return distribution under a fixed policy. The return distribution is estimated by nonparametric distributional temporal-difference learning from a single Markov trajectory. For the Polyak--Ruppert averaged estimator, we prove that its root-$T$ error converges weakly to a centered Gaussian random element in Cramér space. We also prove that, conditionally on the observed trajectory, the root-$T$ difference between the bootstrap and original averages converges weakly to the same Gaussian limit. These results justify bootstrap inference for smooth statistical functionals, including variance, CVaR, expected shortfall, and expectiles....
| Authors | Yang Peng, Liangyu Zhang |
|---|---|
| Primary category | stat.ML |
| Published | 14 August 2026 |
| Last updated at source | 14 August 2026 |
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