Autoregressive Learning in Joint KL: Sharp Oracle Bounds and Lower Bounds
We study the fundamental and timely problem of learning long sequences in autoregressive modeling and next-token prediction under model misspecification, measured by the joint Kullback--Leibler (KL) divergence. Our goal is to characterize how the sequence horizon \(H\) affects both approximation and estimation errors in this joint-distribution, sequence-level regime. By establishing matching upper and lower bounds, we provide, to our knowledge, the first complete characterization of long-horizon error behavior under the natural joint KL objective, with improved rates and optimality justification relative to existing work. On the approximation side, we show that joint KL admits a horizon-f...
| Authors | Yunbei Xu, Yuzhe Yuan, Ruohan Zhan |
|---|---|
| Primary category | cs.LG |
| Published | 12 May 2026 |
| Last updated at source | 12 May 2026 |
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